Model of Anisotropic Elastoplasticity in Finite Deformations Allowing for the Evolution of the Symmetry Group

A constitutive model for finite deformation anisotropic elastoplasticity, developed within the framework of the multiplicative decomposition of the deformation gradient and of the theory of the structural tensors is discussed. The main goal of the paper is to analyze the extension of fi- nite deformation plasticity to the case that material directions can evolve due to mechanical ac- tions. This is obtained by considering the structural tensors as internal variables and introducing thermodynamic forces conjugated to them. The internal energy is assumed to depend on the elas- tic strain tensor and on the structural tensors, so that, employing Clausius–Duhem dissipation inequality, evolution equations for plastic deformation and for irreversible changes in the struc- tural tensors are obtained that can consist of rotation of the material direction or also of the modification of the norm of the material directors. Examples show that the model can be used for studying the response of fiber materials like soft tissues, amorphous polymers, etc