Modelling Anisotropic, Hyperelastic Materials in ABAQUS

ABAQUS offers the possibility to model non-linear isotropic materials as well as linear anisotropic materials. However, it is not possible to use these two capabilities at the same time in order to model anisotropic hyperelastic materials. Gurvich proposed to model such materials by means of the linear superposition of two fictitious materials: a linear anisotropic, and a hyperelastic isotropic material. Therefore, the modelling of a hyperelastic anisotropic material is converted into a material characterization problem, i.e., fitting the parameters in the strain potentials of the two fictitious materials to experimental stress strain curves. In this work, we propose an alternative solution, based on the same principle. Assuming that the anisotropic elastic tensor is known from experiments, we first obtain its directional average, which is isotropic. Then, we choose a form for the hyperelastic potential among the ones provided by ABAQUS, make it fit the linear elastic stress strain relationship generated by the isotropic tensor, and subtract the (quadratic) potential generated by the isotropic elastic tensor. This results in a hyperelastic potential with zero stiffness at zero strain. By summing this “zero-zero” potential to the (quadratic) potential generated by the anisotropic elastic tensor, we “correct” it without the need to calculate several parameters for two fictitious materials. As an example, we show the simulation of an unconfined compression test of articular cartilage.