Incompatible-mode geometrically non-linear finite element for micropolar elasticity

Abstract

In this work a new three-dimensional geometrically non-linear hexahedral micropolar finite element enhanced with incompatible modes is presented. The analytical model is expressed in terms of Biot-like stress and couple-stress tensors and corresponding Biot-like strain and curvature tensors, with a linear, elastic and isotropic constitutive law. The numerical model is derived based on the principle of virtual work, and the residual derivation together with the linearisation and static condensation procedure is given in detail. The newly developed finite element is tested against the analytical solution of the geometrically non-linear micropolar pure bending problem and the element accuracy and robustness is compared against hexahedral Lagrangian finite elements of first and second order on several numerical examples. It is shown that the newly presented element is fast convergent, more robust and more accurate than the available Lagrangian elements. Moreover, the operator split and static condensation provide for a significantly lower computational cost than standard elements.