Anisotropic hyperelastic material behavior

Hyperelastic materials are described in terms of a “strain energy potential,” which defines the strain energy stored in the material per unit of reference volume (volume in the initial configuration) as a function of the deformation at that point in the material. Two distinct formulations, strain-based and invariant-based, are used for the representation of the strain energy potential of anisotropic hyperelastic materials.

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Anisotropic Hyperelastic Behavior

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The constitutive behavior of hyperelastic materials is discussed in Hyperelastic material behavior in the context of isotropic response. However, many materials of industrial and technological interest exhibit anisotropic elastic behavior due to the presence of preferred directions in their microstructure. Examples of such materials include common engineering materials (such as fiber-reinforced composites, reinforced rubber, and wood) as well as soft biological tissues (such as those found in arterial walls and heart tissues). Under large deformations these materials exhibit highly anisotropic and nonlinear elastic behavior due to rearrangements in their microstructure, such as reorientation of the fiber directions with deformation. The simulation of these nonlinear effects requires constitutive models formulated within the framework of anisotropic hyperelasticity.