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Research paper thumbnail of Determination of material parameters of isotropic and anisotropic hyper-elastic materials using boundary measured data

Journal of Theoretical and Applied Mechanics, 2015

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Research paper thumbnail of Identification of Material Parameters of a Hyper-Elastic Body With Unknown Boundary Conditions

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Research paper thumbnail of A strong-form meshfree method for stress analysis of hyperelastic materials

Engineering Analysis with Boundary Elements

Abstract A strong-form based meshfree method for stress analysis of hyperelastic materials under ... more Abstract A strong-form based meshfree method for stress analysis of hyperelastic materials under large deformations is presented in this research. The non-linear elastic response of hyperelastic materials is modeled by the compressible Mooney–Rivlin strain energy function. Simple implementation and truly meshfree nature are some of the advantages of strong-form meshfree methods. In the presented meshfree formulation, second derivatives of the strain energy function with respect to the components of the deformation gradient tensor appear. These second derivatives are obtained analytically. Various plane stress and plane strain problems with different boundary conditions are considered. The effects of the value of the shape parameter, the number of the nodes in the support domain, and the total number of nodes on the performance of the method are investigated. Various techniques for applying boundary conditions such as the direct collocation method and the use of fictitious nodes are examined, and an alternative method is presented to apply boundary conditions in the proposed meshfree method.

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Research paper thumbnail of A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials

International Journal of Mechanical Sciences

Abstract A comparative study is presented to solve the inverse problem in elasticity for the shea... more Abstract A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neo-Hookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neo-Hookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neo-Hookean material model. In addition, it was observed that the inverse problem solution was inclusion size-sensitive. Consequently, an 1-D model was introduced to broaden our understanding of this issue. This 1-D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology.

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Research paper thumbnail of Identification of hyper-viscoelastic material parameters of a soft member connected to another unidentified member by applying a dynamic load

International Journal of Solids and Structures

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Research paper thumbnail of Inflation, extension and torsion analysis of compressible functionally graded hyperelastic tubes

Acta Mechanica

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Research paper thumbnail of Determination of material parameters of isotropic and anisotropic hyper-elastic materials using boundary measured data

Journal of Theoretical and Applied Mechanics, 2015

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Research paper thumbnail of Identification of Material Parameters of a Hyper-Elastic Body With Unknown Boundary Conditions

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Research paper thumbnail of A strong-form meshfree method for stress analysis of hyperelastic materials

Engineering Analysis with Boundary Elements

Abstract A strong-form based meshfree method for stress analysis of hyperelastic materials under ... more Abstract A strong-form based meshfree method for stress analysis of hyperelastic materials under large deformations is presented in this research. The non-linear elastic response of hyperelastic materials is modeled by the compressible Mooney–Rivlin strain energy function. Simple implementation and truly meshfree nature are some of the advantages of strong-form meshfree methods. In the presented meshfree formulation, second derivatives of the strain energy function with respect to the components of the deformation gradient tensor appear. These second derivatives are obtained analytically. Various plane stress and plane strain problems with different boundary conditions are considered. The effects of the value of the shape parameter, the number of the nodes in the support domain, and the total number of nodes on the performance of the method are investigated. Various techniques for applying boundary conditions such as the direct collocation method and the use of fictitious nodes are examined, and an alternative method is presented to apply boundary conditions in the proposed meshfree method.

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Research paper thumbnail of A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials

International Journal of Mechanical Sciences

Abstract A comparative study is presented to solve the inverse problem in elasticity for the shea... more Abstract A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neo-Hookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neo-Hookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neo-Hookean material model. In addition, it was observed that the inverse problem solution was inclusion size-sensitive. Consequently, an 1-D model was introduced to broaden our understanding of this issue. This 1-D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology.

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Research paper thumbnail of Identification of hyper-viscoelastic material parameters of a soft member connected to another unidentified member by applying a dynamic load

International Journal of Solids and Structures

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Research paper thumbnail of Inflation, extension and torsion analysis of compressible functionally graded hyperelastic tubes

Acta Mechanica

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