Soils and rocks typically exhibit strongly nonlinear, inelastic load-deformation behavior. Their complex mechanical responses persist across the scales, from nanometer up to kilometer scale, and are generally linked to other multiphysical processes such as fluid flow, heat conduction, and chemical/biological transport. Capturing these complex multiphysical responses requires sound theoretical framework and robust computational algorithms.

In this work, I will present a computational framework that captures the microfracture processes triggering shear band bifurcation in porous crystalline rocks. The framework consists of computational homogenization on a representative elementary volume (REV) that upscales the pore-scale microfracture processes to the continuum scale. The assumed enhanced strain (AES) finite element approach is used to capture the discontinuous displacement field generated by the microfractures. Homogenization at the continuum scale results in incrementally nonlinear material response, which gives rise to an overall constitutive tangent tensor that varies not only with the stress state but also with loading direction.

I will motivate the talk with experimental data obtained from nanoindentation tests on Woodford shale conducted at Stanford University. Results of these indentation tests reveal strong anisotropy in the constitutive mechanical response, which is postulated to arise mainly from preferential orientation of clay particles comprising the shale sample. Indeed, this preferential orientation has been seen from FIB/SEM and TXM images of the same rock samples, which also quantify the heterogeneity of the rock at the nanometer scale. The work motivates the development of a mechanistic model for microfracturing of heterogeneous rock samples at nanometer and larger scales.