Elastoplastic analysis of solid structures using penalty-based couple stress finite element method within framework of Cosserat continuum

Abstract

To obviate the complexities of the straight forward couple stress finite element method, the penalty-based couple stress finite element method (named PcouFEM) within the framework of the Cosserat continuum is utilized to obtain the approximate solution by relaxing the C¹ continuity. To examine the performance of the PcouFEM, three well-known numerical examples are investigated. For the analysis on stress concentration around the circular hole of the planestrain specimen, it was found that as long as the penalty factor G_c is not less than 5 times the shear modulus of the classical continuum G (i. e., G_c⩾5G), the stress concentration factors calculated by the PcouFEM with the reduced integration scheme agree well with the analytical solutions. For the strain localization analysis in the uniaxial compression test, it was observed that by applying the PcouFEM, the pathologically mesh-dependent problem associated with the conventional FEM can be alleviated or even removed, and based on numerical simulations, it is recommended to define 5G⩽G_c⩽10G from the perspective of numerical accuracy. For the soil slope subjected to an eccentric load through the rigid strip footing, it was found that the mesh-dependent problem of the shear band simulation can be largely alleviated by applying the PcouFEM.

Keywords

couple stress theory / Cosserat theory / penalty factor / stress concentration / strain localization

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