Multi-slip and non-local evolution equations in finite elasto-plastic materials with dislocations
Keywords:
dislocations, non-Schmid flow rule, crystalline materials, non-local evolution equations, finite elasto-plasticityAbstract
The paper deals with elasto-plastic models which describe the behaviour at large strain of materials with crystalline structure, which contain continuously distributed dislocations. The non-local evolution equations for dislocation densities are derived to be compatible with the the principle of free energy imbalance, when a nonSchmid flow rule describes the evolution of the plastic distortion within the crystalographic systems. We analyze the constitutive restrictions that follow from the principle of the free energy imbalance for the case when the free energy density is dependent on the scalar dislocation densities and their gradients, and for a more general case when the influence of the tensorial measure of dislocations is considered too.
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