Micropolar hypoplasticity modeling of localized deformation in mixtures of face mask chips and sand

Abstract

This paper presents a novel micropolar-based hypoplastic model to reproduce the stress–strain relationship of face mask chips-sand mixtures (MSMs) and their localized deformation. Based on a critical state hypoplastic model, a non-polar hypoplastic model for MSMs is first developed with modifications and new features: (1) the cohesion induced by face mask chips is considered by introducing an additional stress tensor into the Cauchy stress tensor; (2) the initial stiffness variation in MSMs is described with a modified tangential modulus; and (3) the effective skeleton void ratio concept is introduced to capture the initial and critical void ratio variations in MSMs. The model is then extended to its micropolar terms by incorporating the micropolar theory, which includes an internal length parameter and a couple stress induced by particle rotation, with the advantage of overcoming the mesh dependency problem in the conventional finite element method (FEM) based simulations. Moreover, the new micropolar hypoplastic formulations are implemented into a FEM code. The onset and evolution of shear bands in MSMs are investigated by simulating a series of biaxial tests on both pure sand and MSMs. Numerical results are also compared to experimental observations, demonstrating that the developed micropolar hypoplastic model can adeptly capture the shear band propagation in MSMs and their mechanical responses.