A gradient micromorphic modeling for plasticity softening

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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.

Details

Original languageEnglish
Article number103925
JournalMechanics Research Communications
Volume124
Publication statusPublished - Sept 2022
Peer-reviewedYes

External IDs

Scopus 85132761581

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