Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker-Prager/Cap type constitutive model formulation

The formulation of large strain anisotropic hyper-elastoplasticity of geomaterials is examined. Attention is given to the role of structure tensors (also called fabric tensors), especially in context of the Eshelby-Mandel stress and large inelastic volume changes attributable to porosity. Both (hyper-)elastic and inelastic orthotropic symmetry, reducing to the particular case of transverse isotropy, are considered. Specific material assumptions and constitutive choices are identified for the development of a novel Anisotropic Drucker-Prager/Cap (ADPC) model formulated within the intermediate configuration consistent with multiplicative split of the deformation gradient. The model is calibrated to existing experimental measurements, including high pressure large strain triaxial compression of lithographic (Solnhofen) limestone and triaxial compression measurements on Tournemire shale assessing elastoplastic anisotropy. Manifest implications of constitutive theory are investigated, including consequences of recognizing (or not) the Eshelby-Mandel stress as energy conjugate to the plastic velocity gradient and including (or not) contribution from the skew-symmetric parts of the Mandel stress to the plastic anisotropy. Numerical simple shear experiments and large deformation simulated indentation experiments are provided in order to investigate model predictions and demonstrate the overall robustness in finite element modeling.