A gradient micromorphic modeling for plasticity softening. (September 2022) - Yin, Bo; Zhao, Dong; Kaliske, Michael
Abstract: Localization of internal quantities, which induce material softening, potentially leads to an ill-posed global partial differential equation. Along with further developments of singularity issues in the simulations, an unwanted divergent numerical solution may occur. The work at hand attempts to formulate a ductile softening model by considering a size reduction of the plastic yield surface. An internal variable to reduce the size of the plastic yield surface is constituted by a gradient micromorphic approach. In detail, a degradation function induced by an internal softening quantity is employed to multiply the thermodynamic force of plastic hardening in the yield function. In this regard, a gradually shrinking plastic yield surface is constituted to model the overall softening response. The evolution of the internal softening variable is governed by a Kuhn–Tucker condition together with its non-local extension. The present constitutive model of the coupled softening problem is derived based on a thermodynamically consistent algorithm from a well-defined Helmholtz free energy potential, which is implemented into the context of a conventional Finite Element Method . A representative and meaningful numerical example is studied to demonstrate the capability of the present model. Highlights: Plasticity softening by reducing the size of the yield surface. A gradient extension based on a micromorphic formulation. Thermodynamically consistent derivation of the coupled problem. The remedy of pathological issues and stable numerical solution.