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Finite element simulation of strain localization in inelastic solids by energy relaxation

The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. The performance of the proposed concept is demonstrated through numerical simulation of tension test under plane strain conditions. Numerical results show that mesh sensitivity can be completely removed. | Vietnam Journal of Mechanics, VAST, Vol. 33, No. 4 (2011), pp. 203 – 213 FINITE ELEMENT SIMULATION OF STRAIN LOCALIZATION IN INELASTIC SOLIDS BY ENERGY RELAXATION B. T. Trinh, K. Hackl Ruhr-Universit¨ at Bochum, Universit¨ atsstr. 150 D-44801 Bochum, Germany Abstract. A new approach for the treatment of strain localization in inelastic material is proposed. It is based on energy minimization principles associated with micro-structure developments. Shear bands are treated as micro-shearing of rank-one laminates. It is assumed that the thickness of the shear band represented by its volume fraction tends to zero, and the energy inside the shear band is a function of the norm of the strain field. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. The performance of the proposed concept is demonstrated through numerical simulation of tension test under plane strain conditions. Numerical results show that mesh sensitivity can be completely removed. Keywords: Energy relaxation, shear band, strain localization. 1. INTRODUCTION Regions of high strain localization by intense shearing are referred to 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]. Predictions of the onset and evolution of shear bands play an important role in determining the safety of structures, improving mechanical properties of material and designing material microstructure. In recent years a new methodology based on energy relaxation has been developed to simulate the development of material microstructures [3]-[9]. The advantage of this theory, when applied to the problem at hand, is the natural formation of shear bands based on the energy minimization principles associated with micro-structure developments. In this paper a theoretical framework for the .