On a tangential-conforming finite element formulation for the relaxed micromorphic model in 2D

摘要

The relaxed micromorphic model is a generalized continuum model that reduces the complexity of the general micromorphic theory [1] and shows many advantages such as the bounded stiffness for small sizes [2-4]. It keeps the full kinematics of the micromorphic theory but employs the matrix Curl operator of a second-order micro-distortion field for the curvature measurement. The solution of the micro-distortion exists in H(curl) while the displacement is still in H1. In this work, we introduce an H~1 × H(curl) finite element formulation of the relaxed micromorphic model. The presented mixed formulation satisfies the tangential continuity of the micro-distortion field on the element boundaries. We compare the convergence behavior of the mixed formulation with the classical H~1 × H~1 finite element formulation using numerical examples. Finally, we show the model's main characteristics and the scale-dependency of the model's components where the relaxed micromorphic model gives the different Cauchy elastic limit cases with determined elasticity tensors.