Alberto Díaz Díaz | Centro de Investigación en Materiales Avanzados, S.C. (original) (raw)
Papers by Alberto Díaz Díaz
En este trabajo se proponen ecuaciones diferenciales generales dependientes de dos dimensiones, u... more En este trabajo se proponen ecuaciones diferenciales generales dependientes de dos dimensiones, una espacial y una temporal. Estas ecuaciones son propuestas de tal manera que se puedan modelar diferentes fenómenos físicos. Se da solución a la parte espacial de las ecuaciones generales mediante el método del elemento finto y a la temporal por medio de series de Taylor, lo que resulta en sistemas lineales con matrices de coeficientes dispersas. Estos sistemas son programados en un lenguaje C++, para tratar con el álgebra de matrices dispersas se utiliza la librería CSparse creada por Timothy A. Davis [1]. Se proponen algunos sistemas de ecuaciones sencillos de resolver analíticamente para comparar resultados con la solución obtenida con lo programado. Una vez comprobada la funcionalidad, se adapta el código para problemas de transferencia de calor y vigas de Euler en el plano. Por último, se proponen problemas de los fenómenos físicos anteriormente mencionados. Los resultados obtenido...
Mathematical Problems in Engineering, 2020
This paper presents the development of a model of homogeneous, moderately thick shells for elasto... more This paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. The model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. The stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. The generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. The generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler–Lagrange equation whic...
Mathematical Problems in Engineering, 2018
This paper presents the theoretical development of a new model of shells called SAM-H (Stress App... more This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner’s variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson’s effect of out-of-plane normal stresses on in-p...
Advances in Materials Science and Engineering, 2018
The aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by mean... more The aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by means of uniaxial tensile and compressive tests and to reveal new key aspects that must be taken into account in any predictive model. Uniaxial monotonic and creep-recovery tests were carried out at a variety of temperatures, stress levels, and load rates to get a complete description of the material response. Prior to mechanical testing, the material was subjected to a thermal rejuvenation in order to eliminate any previous aging and to obtain reliable and useful results. In every test, a complete determination of the strain state was assured by measuring axial and transverse strains with strain gauges. During the tests, significant asymmetry effects and viscous phenomena already reported by other authors were confirmed. The newest finding is that a nonlinear master transverse strain/axial strain curve matches perfectly with the experimental curves. This master curve is temperature- and rat...
Mechanics of Materials, 2002
The mechanical problem discussed in this paper focuses on the stress state estimation in a compos... more The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of Multilayered Materials (M4). The first one can be considered as a stacking sequence of Reissner-Mindlin plates (5 kinematic fields per layer), while the second is a membranar superposition (2 fields per layer plus a global one). These simplified models are able to provide finite values of interfacial stresses, even on the free edges of a structure. The current paper consists of validating the M4 by a finite element analysis through describing the stress fields in both a (0,90) s laminate in tension (free-edge problem) and a transversally microcracked (0,90) s laminate. A comparison of the various energy contributions helps yield a mechanical perspective: it appears possible to define an interply energy as well as a layer energy, these energies expressing the FE 3D reality.
Composite Structures, 2011
This article is aimed at proposing a new development of a layer-wise 2D finite-element method for... more This article is aimed at proposing a new development of a layer-wise 2D finite-element method for multilayers considering the laminated plate as a superposition of Reissner plates coupled by interfacial stresses. Here, despite the 2D description of the laminates, the interfaces show a particular behavior, elastic or elastoplastic (Von-Mises criterion). The finite element formulation is derived and an eight-node multiparticle element is detailed. The application example of a double lap joint with an elastoplastic adhesive is then considered. The adhesive layer is modeled as an interface. The loading scheme is a load-unload-load one. Interface shear and normal stresses are compared to 3D finite element results. A good agreement between both techniques is observed, particularly for the prediction of the history of the slip between the two adherends and the plastic strains in the adhesive.
Mathematical Problems in Engineering, 2020
This paper presents a model called SAM-FG (stress approach model of functionally graded shells) f... more This paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. The model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. The model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. This stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger–Reissner functional and Reissner’s variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except...
Composites Science and Technology, 2006
To approach the three-dimensional stress state in multi-layered composites, a laminate theory whi... more To approach the three-dimensional stress state in multi-layered composites, a laminate theory which considers a kinematic field per layer (particle) is used. Thus, interlaminar stresses are naturally introduced to carry out the equilibrium conditions of the plies. These stresses have a physical meaning and represent the exact out-of-plane 3D stresses calculated at the interface between two layers. These simplified models
1 Enhanced layerwise model for laminates with imperfect interfaces – Part 2:
International Journal of Solids and Structures
The aim of this paper is to analyze delaminated multilayered plates under classical loads using a... more The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only d...
Composite Structures, 2012
The aim of this paper is the enhancement and validation of a layerwise model applied to the analy... more The aim of this paper is the enhancement and validation of a layerwise model applied to the analysis of laminates with thin layers of an elastic-plastic adhesive. The thin adhesive layers are modeled as imperfect interfaces across which displacement discontinuities exist. In a previous paper, the constitutive equations of the imperfect interfaces were empirically established without following the layerwise logic. The model equations are revisited and a solid theoretical justification of the new enhanced equations is obtained by making use of the Hellinger-Reissner functional. A theoretical validation of the model is performed by comparing its predictions to those of a solid finite element resolution in the case of a T-peel joint. The results of the enhanced version of the model are very accurate whereas those of the previous version are erratic for the considered joint. As compared to the solid finite element method, an important saving in computational cost is achieved.
SAM-FG, 2020
This paper presents a model called SAM-FG (stress approach model of functionally graded shells) f... more This paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. e model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. e model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. is stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger-Reissner functional and Reissner's variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. e first one deals with a hollow sphere made of an isotropic functionally graded material. e second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. e stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.
This paper presents the theoretical development of a new model of shells called SAM-H (Stress App... more This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner's variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson's effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.
is paper presents the development of a model of homogeneous, moderately thick shells for elastody... more is paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. e model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. e stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. e generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. e generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler-Lagrange equation which includes pertinently Hellinger-Reissner functional. In the constitutive equations, Poisson's effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. e results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.
e aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by means ... more e aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by means of uniaxial tensile and compressive tests and to reveal new key aspects that must be taken into account in any predictive model. Uniaxial monotonic and creep-recovery tests were carried out at a variety of temperatures, stress levels, and load rates to get a complete description of the material response. Prior to mechanical testing, the material was subjected to a thermal rejuvenation in order to eliminate any previous aging and to obtain reliable and useful results. In every test, a complete determination of the strain state was assured by measuring axial and transverse strains with strain gauges. During the tests, significant asymmetry effects and viscous phenomena already reported by other authors were confirmed. e newest finding is that a nonlinear master transverse strain/axial strain curve matches perfectly with the experimental curves.
is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for... more is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. e model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. e model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. is stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger-Reissner functional and Reissner's variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. e first one deals with a hollow sphere made of an isotropic functionally graded material. e second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. e stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.
is paper presents the development of a model of homogeneous, moderately thick shells for elastody... more is paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. e model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. e stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. e generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. e generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler-Lagrange equation which includes pertinently Hellinger-Reissner functional. In the constitutive equations, Poisson's effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. e results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.
This paper presents the theoretical development of a new model of shells called SAM-H (Stress App... more This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner's variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson's effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.
is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for... more is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. e model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. e model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. is stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger-Reissner functional and Reissner's variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. e first one deals with a hollow sphere made of an isotropic functionally graded material. e second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. e stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.
En este trabajo se proponen ecuaciones diferenciales generales dependientes de dos dimensiones, u... more En este trabajo se proponen ecuaciones diferenciales generales dependientes de dos dimensiones, una espacial y una temporal. Estas ecuaciones son propuestas de tal manera que se puedan modelar diferentes fenómenos físicos. Se da solución a la parte espacial de las ecuaciones generales mediante el método del elemento finto y a la temporal por medio de series de Taylor, lo que resulta en sistemas lineales con matrices de coeficientes dispersas. Estos sistemas son programados en un lenguaje C++, para tratar con el álgebra de matrices dispersas se utiliza la librería CSparse creada por Timothy A. Davis [1]. Se proponen algunos sistemas de ecuaciones sencillos de resolver analíticamente para comparar resultados con la solución obtenida con lo programado. Una vez comprobada la funcionalidad, se adapta el código para problemas de transferencia de calor y vigas de Euler en el plano. Por último, se proponen problemas de los fenómenos físicos anteriormente mencionados. Los resultados obtenido...
Mathematical Problems in Engineering, 2020
This paper presents the development of a model of homogeneous, moderately thick shells for elasto... more This paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. The model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. The stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. The generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. The generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler–Lagrange equation whic...
Mathematical Problems in Engineering, 2018
This paper presents the theoretical development of a new model of shells called SAM-H (Stress App... more This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner’s variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson’s effect of out-of-plane normal stresses on in-p...
Advances in Materials Science and Engineering, 2018
The aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by mean... more The aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by means of uniaxial tensile and compressive tests and to reveal new key aspects that must be taken into account in any predictive model. Uniaxial monotonic and creep-recovery tests were carried out at a variety of temperatures, stress levels, and load rates to get a complete description of the material response. Prior to mechanical testing, the material was subjected to a thermal rejuvenation in order to eliminate any previous aging and to obtain reliable and useful results. In every test, a complete determination of the strain state was assured by measuring axial and transverse strains with strain gauges. During the tests, significant asymmetry effects and viscous phenomena already reported by other authors were confirmed. The newest finding is that a nonlinear master transverse strain/axial strain curve matches perfectly with the experimental curves. This master curve is temperature- and rat...
Mechanics of Materials, 2002
The mechanical problem discussed in this paper focuses on the stress state estimation in a compos... more The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of Multilayered Materials (M4). The first one can be considered as a stacking sequence of Reissner-Mindlin plates (5 kinematic fields per layer), while the second is a membranar superposition (2 fields per layer plus a global one). These simplified models are able to provide finite values of interfacial stresses, even on the free edges of a structure. The current paper consists of validating the M4 by a finite element analysis through describing the stress fields in both a (0,90) s laminate in tension (free-edge problem) and a transversally microcracked (0,90) s laminate. A comparison of the various energy contributions helps yield a mechanical perspective: it appears possible to define an interply energy as well as a layer energy, these energies expressing the FE 3D reality.
Composite Structures, 2011
This article is aimed at proposing a new development of a layer-wise 2D finite-element method for... more This article is aimed at proposing a new development of a layer-wise 2D finite-element method for multilayers considering the laminated plate as a superposition of Reissner plates coupled by interfacial stresses. Here, despite the 2D description of the laminates, the interfaces show a particular behavior, elastic or elastoplastic (Von-Mises criterion). The finite element formulation is derived and an eight-node multiparticle element is detailed. The application example of a double lap joint with an elastoplastic adhesive is then considered. The adhesive layer is modeled as an interface. The loading scheme is a load-unload-load one. Interface shear and normal stresses are compared to 3D finite element results. A good agreement between both techniques is observed, particularly for the prediction of the history of the slip between the two adherends and the plastic strains in the adhesive.
Mathematical Problems in Engineering, 2020
This paper presents a model called SAM-FG (stress approach model of functionally graded shells) f... more This paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. The model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. The model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. This stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger–Reissner functional and Reissner’s variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except...
Composites Science and Technology, 2006
To approach the three-dimensional stress state in multi-layered composites, a laminate theory whi... more To approach the three-dimensional stress state in multi-layered composites, a laminate theory which considers a kinematic field per layer (particle) is used. Thus, interlaminar stresses are naturally introduced to carry out the equilibrium conditions of the plies. These stresses have a physical meaning and represent the exact out-of-plane 3D stresses calculated at the interface between two layers. These simplified models
1 Enhanced layerwise model for laminates with imperfect interfaces – Part 2:
International Journal of Solids and Structures
The aim of this paper is to analyze delaminated multilayered plates under classical loads using a... more The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only d...
Composite Structures, 2012
The aim of this paper is the enhancement and validation of a layerwise model applied to the analy... more The aim of this paper is the enhancement and validation of a layerwise model applied to the analysis of laminates with thin layers of an elastic-plastic adhesive. The thin adhesive layers are modeled as imperfect interfaces across which displacement discontinuities exist. In a previous paper, the constitutive equations of the imperfect interfaces were empirically established without following the layerwise logic. The model equations are revisited and a solid theoretical justification of the new enhanced equations is obtained by making use of the Hellinger-Reissner functional. A theoretical validation of the model is performed by comparing its predictions to those of a solid finite element resolution in the case of a T-peel joint. The results of the enhanced version of the model are very accurate whereas those of the previous version are erratic for the considered joint. As compared to the solid finite element method, an important saving in computational cost is achieved.
SAM-FG, 2020
This paper presents a model called SAM-FG (stress approach model of functionally graded shells) f... more This paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. e model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. e model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. is stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger-Reissner functional and Reissner's variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. e first one deals with a hollow sphere made of an isotropic functionally graded material. e second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. e stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.
This paper presents the theoretical development of a new model of shells called SAM-H (Stress App... more This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner's variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson's effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.
is paper presents the development of a model of homogeneous, moderately thick shells for elastody... more is paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. e model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. e stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. e generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. e generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler-Lagrange equation which includes pertinently Hellinger-Reissner functional. In the constitutive equations, Poisson's effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. e results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.
e aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by means ... more e aim of this paper was to analyze in detail the mechanical behavior of a polycarbonate by means of uniaxial tensile and compressive tests and to reveal new key aspects that must be taken into account in any predictive model. Uniaxial monotonic and creep-recovery tests were carried out at a variety of temperatures, stress levels, and load rates to get a complete description of the material response. Prior to mechanical testing, the material was subjected to a thermal rejuvenation in order to eliminate any previous aging and to obtain reliable and useful results. In every test, a complete determination of the strain state was assured by measuring axial and transverse strains with strain gauges. During the tests, significant asymmetry effects and viscous phenomena already reported by other authors were confirmed. e newest finding is that a nonlinear master transverse strain/axial strain curve matches perfectly with the experimental curves.
is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for... more is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. e model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. e model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. is stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger-Reissner functional and Reissner's variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. e first one deals with a hollow sphere made of an isotropic functionally graded material. e second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. e stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.
is paper presents the development of a model of homogeneous, moderately thick shells for elastody... more is paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. e model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. e stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. e generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. e generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler-Lagrange equation which includes pertinently Hellinger-Reissner functional. In the constitutive equations, Poisson's effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. e results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.
This paper presents the theoretical development of a new model of shells called SAM-H (Stress App... more This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner's variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson's effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.
is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for... more is paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. e model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. e model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. is stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger-Reissner functional and Reissner's variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. e first one deals with a hollow sphere made of an isotropic functionally graded material. e second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. e stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.