G. Legrain - Academia.edu (original) (raw)

Papers by G. Legrain

Journal of Physics: Conference Series, 2012

The homogenization theory is a powerful approach to determine the effective thermal conductivity ... more The homogenization theory is a powerful approach to determine the effective thermal conductivity tensor of heterogeneous materials such as composites, including thermoset matrix and fibres. Once the effective properties are calculated, they can be used to solve a heat conduction problem on the composite structure at the macroscopic scale. This approach leads to good approximations of both the heat flux and temperature in the interior zone of the structure, however edge effects occur in the vicinity of the domain boundaries. In this paper, following the approach proposed in [10] for elasticity, it is shown how these edge effects can be corrected. Thus an additional asymptotic expansion is introduced, which plays the role of a boundary layer term. This expansion tends to zero far from the boundary, and is assumed to decrease exponentially. Moreover, the length of the boundary layer region can be determined from the solution of an eigenvalue problem. Numerical examples are considered for a standard multilayered material. The homogenized solutions computed with a finite element software, and corrected with the boundary layer terms, are compared to a heterogeneous finite element solution at the microscopic scale. The influences of the thermal contrast and scale factor are illustrated for different kind of boundary conditions.

Computational Mechanics, 2013

In material science, images are increasingly used as input data for computational models. In most... more In material science, images are increasingly used as input data for computational models. In most of the published papers, voxel-based finite element models are employed using a mesh that is automatically built by converting each voxel into a finite element. We have recently proposed (Legrain et al. , 2011) another computational approach for incorporating images in models, based on the extended finite element method (X-FEM) and levelsets. Its main advantages are that the mesh does not need to conform to the geometry and that a smooth representation of physical surfaces is obtained. The aim of this paper is to compare the two approaches in the framework of computational homogenization in elasticity, starting from material microstructural images. Attention will be paid to geometrical approximations, macroscopic properties and local quantities (e.g. stress oscillations, local error etc.). It is shown that the X-FEM/levelset approach is more efficient than voxel-based FEM.

International Journal of Heat and Mass Transfer, 2013

The homogenization theory is a powerful approach to determine the effective thermal conductivity ... more The homogenization theory is a powerful approach to determine the effective thermal conductivity tensor of heterogeneous materials such as composites, including thermoset matrix and fibers. Once the effective properties are calculated, they can be used to solve a heat conduction problem on the composite structure at the macroscopic scale. This approach leads to good approximations of both the heat flux and temperature fields in the interior zone of the structure; however edge effects occur in the vicinity of the domain boundaries. In this paper, following an approach proposed for elasticity problems, it is shown how these edge effects can be accounted for. An additional asymptotic expansion term is introduced, which plays the role of a "heat conduction boundary layer" (HCBL) term. This expansion decreases exponentially and tends to zero far from the boundary. Moreover, the HCBL length can be determined from the solution of an eigenvalues problem. Numerical examples are considered for a standard multilayered material and for a unidirectional carbon-epoxy composite. The homogenized solutions computed with a finite element software, and corrected with the HCBL terms are compared to a heterogeneous finite element solution at the microscopic scale. The influences of the thermal contrast and the scale factor are illustrated for different kind of boundary conditions.

International Journal for Numerical Methods in Engineering, 2011

... A geometrical conforming mesh is constructed from the image microstructure, and the fracture&... more ... A geometrical conforming mesh is constructed from the image microstructure, and the fracture's path are ... 1 presents schematically the path from an acquired image to the input for an X-FEManalysis. ... 1/16) is presented in Figure 9(b), along with the shearing micro-stresses (Von ...

International Journal for Numerical Methods in Engineering, 2005

Fracture of rubber-like materials is still an open problem. Indeed, it deals with modeling issues... more Fracture of rubber-like materials is still an open problem. Indeed, it deals with modeling issues (crack growth law, bulk behaviour) and computational issues (robust crack growth in 2D and 3D, incompressibility). The present study focuses on the application of the eXtended Finite Element Method (X-FEM) to large strain fracture mechanics for plane stress problems. Two important issues are investigated: the choice of the formulation used to solve the problem and the determination of suitable enrichment functions. It is demonstrated that the results obtained with the method are in good agreement with previously published works.

Computer Methods in Applied Mechanics and Engineering, 2012

Archives of Computational Methods in Engineering, 2010

Computational homogenization is nowadays one of the most active research topics in computational ... more Computational homogenization is nowadays one of the most active research topics in computational mechanics. Different strategies have been proposed, the main challenge being the computing cost induced by complex microstructures exhibiting nonlinear behaviors. Two quite tricky scenarios lie in (i) the necessity of applying the homogenization procedure for many microstructures (e.g. material microstructure evolving at the macroscopic level or stochastic

Heterogeneous materials involve different length scales in their mechanical properties. Obviously... more Heterogeneous materials involve different length scales in their mechanical properties. Obviously a mechanical description taking into account all the microscopic details is impossible from a computational point of view except for parts of very small dimensions. The main aim of material homogenization is defining macroscopic homogeneous properties able to represent at the macroscopic scale the real material and allowing for ignoring the microscopic scale in the numerical representation.

Finite Elements in Analysis and Design, 2013

An efficient approach is proposed in order to predict the mechanical response of complex industri... more An efficient approach is proposed in order to predict the mechanical response of complex industrial parts. As these structures are usually composed of massive and thin parts, different models have to be mixed together (plate, shells, solid). The transition between these different kinematic assumptions can be problematic and non-linear models cannot be employed depending on the plate model that is considered. Moreover, Finite Element analysis in the case of large and complex assemblies implies tedious meshing steps. The idealization and simplification of these structures into a mix of 2D and 3D Finite Elements usually takes therefore significantly more time than the analysis itself. The objective of the present contribution is to explore a calculation process that enables a simple automation of the meshing steps. Even though potentially computationally more expensive, the meshing automation may lead to drastic time reduction for the CAD to mesh process and a much tighter link between CAD and calculated assembly. Finally, easier and faster design explorations would be allowed. This strategy relies on the use of a non-conforming quadratic approximation that is defined on a sufficiently fine mesh. The eXtended Finite Element Method is used in order to alleviate meshing issues. The mesh and Level-Set function are built from the CAD input, by means of an automated approach. The strategy is verified against analytical solutions and real aerospace substructures.

Journal of Physics: Conference Series, 2012

The homogenization theory is a powerful approach to determine the effective thermal conductivity ... more The homogenization theory is a powerful approach to determine the effective thermal conductivity tensor of heterogeneous materials such as composites, including thermoset matrix and fibres. Once the effective properties are calculated, they can be used to solve a heat conduction problem on the composite structure at the macroscopic scale. This approach leads to good approximations of both the heat flux and temperature in the interior zone of the structure, however edge effects occur in the vicinity of the domain boundaries. In this paper, following the approach proposed in [10] for elasticity, it is shown how these edge effects can be corrected. Thus an additional asymptotic expansion is introduced, which plays the role of a boundary layer term. This expansion tends to zero far from the boundary, and is assumed to decrease exponentially. Moreover, the length of the boundary layer region can be determined from the solution of an eigenvalue problem. Numerical examples are considered for a standard multilayered material. The homogenized solutions computed with a finite element software, and corrected with the boundary layer terms, are compared to a heterogeneous finite element solution at the microscopic scale. The influences of the thermal contrast and scale factor are illustrated for different kind of boundary conditions.

Computational Mechanics, 2013

In material science, images are increasingly used as input data for computational models. In most... more In material science, images are increasingly used as input data for computational models. In most of the published papers, voxel-based finite element models are employed using a mesh that is automatically built by converting each voxel into a finite element. We have recently proposed (Legrain et al. , 2011) another computational approach for incorporating images in models, based on the extended finite element method (X-FEM) and levelsets. Its main advantages are that the mesh does not need to conform to the geometry and that a smooth representation of physical surfaces is obtained. The aim of this paper is to compare the two approaches in the framework of computational homogenization in elasticity, starting from material microstructural images. Attention will be paid to geometrical approximations, macroscopic properties and local quantities (e.g. stress oscillations, local error etc.). It is shown that the X-FEM/levelset approach is more efficient than voxel-based FEM.

International Journal of Heat and Mass Transfer, 2013

The homogenization theory is a powerful approach to determine the effective thermal conductivity ... more The homogenization theory is a powerful approach to determine the effective thermal conductivity tensor of heterogeneous materials such as composites, including thermoset matrix and fibers. Once the effective properties are calculated, they can be used to solve a heat conduction problem on the composite structure at the macroscopic scale. This approach leads to good approximations of both the heat flux and temperature fields in the interior zone of the structure; however edge effects occur in the vicinity of the domain boundaries. In this paper, following an approach proposed for elasticity problems, it is shown how these edge effects can be accounted for. An additional asymptotic expansion term is introduced, which plays the role of a "heat conduction boundary layer" (HCBL) term. This expansion decreases exponentially and tends to zero far from the boundary. Moreover, the HCBL length can be determined from the solution of an eigenvalues problem. Numerical examples are considered for a standard multilayered material and for a unidirectional carbon-epoxy composite. The homogenized solutions computed with a finite element software, and corrected with the HCBL terms are compared to a heterogeneous finite element solution at the microscopic scale. The influences of the thermal contrast and the scale factor are illustrated for different kind of boundary conditions.

International Journal for Numerical Methods in Engineering, 2011

... A geometrical conforming mesh is constructed from the image microstructure, and the fracture&... more ... A geometrical conforming mesh is constructed from the image microstructure, and the fracture's path are ... 1 presents schematically the path from an acquired image to the input for an X-FEManalysis. ... 1/16) is presented in Figure 9(b), along with the shearing micro-stresses (Von ...

International Journal for Numerical Methods in Engineering, 2005

Fracture of rubber-like materials is still an open problem. Indeed, it deals with modeling issues... more Fracture of rubber-like materials is still an open problem. Indeed, it deals with modeling issues (crack growth law, bulk behaviour) and computational issues (robust crack growth in 2D and 3D, incompressibility). The present study focuses on the application of the eXtended Finite Element Method (X-FEM) to large strain fracture mechanics for plane stress problems. Two important issues are investigated: the choice of the formulation used to solve the problem and the determination of suitable enrichment functions. It is demonstrated that the results obtained with the method are in good agreement with previously published works.

Computer Methods in Applied Mechanics and Engineering, 2012

Archives of Computational Methods in Engineering, 2010

Computational homogenization is nowadays one of the most active research topics in computational ... more Computational homogenization is nowadays one of the most active research topics in computational mechanics. Different strategies have been proposed, the main challenge being the computing cost induced by complex microstructures exhibiting nonlinear behaviors. Two quite tricky scenarios lie in (i) the necessity of applying the homogenization procedure for many microstructures (e.g. material microstructure evolving at the macroscopic level or stochastic

Heterogeneous materials involve different length scales in their mechanical properties. Obviously... more Heterogeneous materials involve different length scales in their mechanical properties. Obviously a mechanical description taking into account all the microscopic details is impossible from a computational point of view except for parts of very small dimensions. The main aim of material homogenization is defining macroscopic homogeneous properties able to represent at the macroscopic scale the real material and allowing for ignoring the microscopic scale in the numerical representation.

Finite Elements in Analysis and Design, 2013

An efficient approach is proposed in order to predict the mechanical response of complex industri... more An efficient approach is proposed in order to predict the mechanical response of complex industrial parts. As these structures are usually composed of massive and thin parts, different models have to be mixed together (plate, shells, solid). The transition between these different kinematic assumptions can be problematic and non-linear models cannot be employed depending on the plate model that is considered. Moreover, Finite Element analysis in the case of large and complex assemblies implies tedious meshing steps. The idealization and simplification of these structures into a mix of 2D and 3D Finite Elements usually takes therefore significantly more time than the analysis itself. The objective of the present contribution is to explore a calculation process that enables a simple automation of the meshing steps. Even though potentially computationally more expensive, the meshing automation may lead to drastic time reduction for the CAD to mesh process and a much tighter link between CAD and calculated assembly. Finally, easier and faster design explorations would be allowed. This strategy relies on the use of a non-conforming quadratic approximation that is defined on a sufficiently fine mesh. The eXtended Finite Element Method is used in order to alleviate meshing issues. The mesh and Level-Set function are built from the CAD input, by means of an automated approach. The strategy is verified against analytical solutions and real aerospace substructures.