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A unification of finite deformation J2 Von-Mises plasticity and quantitative dislocation mechanics

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Rajat Arora       Amit Acharya

We present a framework which unifies classical phenomenological J2 and crystal plasticity theories with quantitative dislocation mechanics. The theory allows the computation of stress fields of arbitrary dislocation distributions and, coupled with minimally modified classical (J2 and crystal plasticity) models for the plastic strain rate of statistical dislocations, results in a versatile model of finite deformation mesoscale plasticity. We demonstrate some capabilities of the framework by solving two outstanding challenge problems in mesoscale plasticity: 1) recover the experimentally observed power-law scaling of stress-strain behavior in constrained simple shear of thin metallic films inferred from micropillar experiments which all strain gradient plasticity models overestimate and fail to predict; 2) predict the finite deformation stress and energy density fields of a sequence of dislocation distributions representing a progressively dense dislocation wall in a finite body, as might arise in the process of polygonization when viewed macroscopically, with one consequence being the demonstration of the inapplicability of current mathematical results based on $\Gamma$-convergence for this physically relevant situation. Our calculations in this case expose a possible 'phase transition'-like behavior for further theoretical study. We also provide a quantitative solution to the fundamental question of the volume change induced by dislocations in a finite deformation theory, as well as show the massive non-uniqueness in the solution for the (inverse) deformation map of a body inherent in a model of finite strain dislocation mechanics, when approached as a problem in classical finite elasticity.

Paper can be found at link Finite_Deformation_Dislocation_Mechanics.




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