Modelling of shear localization in solids by means of energy relaxation

Tuyet B Trinh,Klaus Hackl

doi:10.1186/s40540-014-0009-0

Tuyet B Trinh, Klaus Hackl

Open Access

https://doi.org/10.1186/s40540-014-0009-0

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Abstract

An approach to the problem of shear localization is proposed. It is based on energy minimization principles associated with micro-structure developments. Shear bands are treated as laminates of first order. The micro-shear band is assumed to have a zero thickness, leading to an unbounded strain field and the special form of the energy within this micro-band. The energy is approximated by the mixture of potential of two low-strain and high-strain domains and it is non-convex. The problem of the non-convex energy arising due to the formation of shear bands is solved by energy relaxation in order to ensure that the corresponding problem is well-posed. An application of the proposed formulation to isotropic material is presented. The capability of the proposed concept is demonstrated through numerical simulation of a tension test.

Highlights

Strain localization phenomena are observed in various materials as narrow zones of intense shearing, known as shear bands
The paper focuses on a theoretical framework for the treatment of shear localization in solid materials
The theory is based on minimization principles associated with microstructure developments under the assumptions of a micro-shear band of a zero thickness and the presence of a mixture potential inside the shear band

Summary

Introduction

Strain localization phenomena are observed in various materials as narrow zones of intense shearing, known as shear bands. The formation of shear bands is accompanied by a softening response, characterized by a decrease in strength of the material with accumulated inelastic strain, often leading to complete failure [1,2]. Research on formation of shear bands has received much attention. In simulation of strain localization, mesh dependence is the direct consequence of the ill-posedness of the corresponding boundary value problem [3]. The disadvantage of the corresponding numerical models is, that the element size is required be at least an order of magnitude smaller than the width of shear zones in order to obtain results independent of the mesh size [11]

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