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Abstract: This paper concerns the modeling of biological soft tissues in the framework of anisotropic hyperelasticity. A closed form solution is proposed in the special case where uniaxial unconstrained tension loading is applied to a strip modeled by Holzapfel–Gasser–Ogden''s (HGO) strain energy. The classical Cardano''s formula is used to calculate the solution. This solution is investigated for different values of which represents the angle between the collagen fibers and the circumferential direction. This study allows for the understanding of the reason why a one-to-one correspondence does not exist between the principal stretch and the fourth invariant of the right Cauchy–Green deformation tensor. It is demonstrated that the relationship becomes non-bijective when is greater than a critical angle of . The HGO model is implemented into an in-house finite element program and numerical results are in good agreement with theoretical ones. [Copyright &y& Elsevier]

Abstract: The present paper is devoted to the modeling of finite deformations of hyperelastic bodies described by Ogden''s model. For the finite element implementation, the explicit expressions of the tangent operator and the stress tensor are derived. If the eigenvalues of the right Cauchy–Green strain tensor are distinct, a simple and compact tensor formula, well adapted for numerical implementation, is proposed. A limiting technique is used to take into account the special case of coalescent eigenvalues in which non-differentiability occurs. Three test examples, including homogeneous and non-homogeneous deformations, are proposed to illustrate the developed formulation. [Copyright &y& Elsevier]

Abstract: The present paper is devoted to the modeling of finite deformations of a hyperelastic body described by Ogden''s model under contact/impact conditions. Frictional contact problems are solved by means of the bi-potential method. The first order algorithm is applied to integrate the equation of motion. The total Lagrangian formulation is adopted to describe the geometrically non-linear behavior. For the finite element implementation, the explicit expression of the tangent operator is derived including the case of repeated eigenvalues. A numerical example is given to illustrate efficiency and accuracy of the method. [Copyright &y& Elsevier]

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies by using the Hybrid Integral Approach (HIA) model introduced by the Authors. This model combines the affine behavior of chains included in the molecular 8-chains density, the interleaving constraint part and an original phenomenological integral density which allows to balance the mismatch between model and experimental data. A total Lagrangian formulation is adopted to describe the geometrical and material non-linearities and a finite element implementation is performed in the FER software. Four test examples, including homogeneous and non-homogeneous deformations, as well as complex computation involving dynamic contact and impact are proposed to show the applicability of the developed approach and the efficiency of the model. [ABSTRACT FROM AUTHOR]