• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.10
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• pp.1057-1068
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• 2014

This paper proposes elastic-plastic constitutive relations for a composite material with two phases-inclusion and matrix phases-using a homogenization scheme. A thermodynamic framework is employed to develop non-local plasticity constitutive relations, which are specifically represented in terms of the second-order gradient terms of the internal state variables. A combined two back-stress evolution equation is also established and the degradation of the state and internal variables is expressed by continuum damage mechanics in terms of the damage factor. Then, deformation localization is analyzed; the analysis results show that the proposed model yields a wide range of shear band formation behaviors depending on the evolution of the specific internal state variables. The analysis results also show good agreement with the results of simplified Rice instability analyses.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.528-535
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• 2011

In the present, the formation of shear band under a simple shear deformation is investigated using a rate-independent elastic-plastic constitutive relations. Moreover, the strain gradient terms are incorporated to obtain a non-local plastic constitutive relation, which in turn represented using combined two-back stress hardening model. Then, the continuum damage model is also included to the proposed model. The post-localization behavior are studied by introducing a small imperfection in a work piece. The strain gradient affects the shear localization significantly such that the intensity of shear band decreases as the strain gradient coefficient increases when the J2 flow theory is employed.