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Three-dimensional modeling of strain localization in Cosserat continuum theory

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In this paper, a higher order continuum model is presented based on the Cosserat continuum theory in 3D numerical simulation of shear band localization. As the classical continuum models suffer from the pathological mesh-dependence in strain softening models, the governing equations are regularized by adding the rotational degrees-of-freedom to conventional degrees-offreedom. The fundamental relations in three-dimensional Cosserat continuum are presented and the internal length parameters are introduced in the elasto-plastic constitutive matrix to control the shear bandwidth. Finally, the efficiency of proposed model and computational algorithm is demonstrated by a 3D strip in tensile. A comparison is performed between the classical and Cosserat theories and the effect of internal length parameter is demonstrated. Clearly, a finite shear bandwidth is achieved and the load-displacement curves are uniformly converged upon different mesh sizes.

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