m‐AGC tangent visco‐plastic operator with hardening/softening, and application to the visco‐plastic relaxation analysis of stable and unstable problems using fracture‐based geomechanical interfaces.

A previous perfect visco‐plastic constitutive formulation of the Perzyna type incorporating the concepts of prescribed stress increments and m‐AGC tangent operator (m‐Assumed algorithmic generalized compliance tangent operator) is extended to the case of Hardening/Softening (H/S). This extension is possible thanks to the closed‐form solution developed for the evolution of the loading function during a visco‐plastic time step. The formulation is then applied to constitutive modeling of zero‐thickness interfaces on the basis of a well‐established fracture‐based elasto‐plastic formulation, which in this manner is extended to visco‐plasticity. The resulting model is implemented in the finite element (FE) and small‐strain context by using both a standard Newton Raphson scheme for physical visco‐plasticity in which visco‐plastic time corresponds to physical time, and a Visco‐Plastic Relaxation (VPR) scheme, in which time corresponds to a fictitious time governing the transition from the elastic to the inviscid elasto‐plastic response. The numerical implementation is verified satisfactorily for common loading cases at interfaces such as pure tension (mode I) opening and shear‐compression (mixed‐mode) cracking/sliding, showing that the visco‐plastic results match the predictions of the fracture mechanics inviscid model in the long term. In addition, it is also shown that the VPR strategy developed is capable of providing temporary stability while the equilibrium path is recovered during instability events such as a snap‐back in the load‐displacement curve. This feature opens the door to a number of potential advanced applications of the formulation developed in the geomechanical context. [ABSTRACT FROM AUTHOR]