Theory and FE-analysis for structures with large deformation under magnetic loading

Abstract

We introduce and discuss a reduced micropolar continuum theory to simulate structures with large deformations under magnetic loading. Three numerical examples show the motivation of this model and its use in practical applications. The question of how to choose the micropolar material parameters is addressed. We use that a finite strain micropolar model would reduce to classical elasticity in the absence of curvature effects and body couples and for certain parameter ranges. This gives us information about a proper choice of material parameters. Thus, we introduce in fact a nearly classical model, but with the feature to cover large deformations and non-classical types of loading. As in shell theories, our continuum theory treats angular momentum as an explicit complementary principle. Thus, net couples—the typical loading of magnetized bodies in a magnetic field—can be modelled. Note that, in this case, the possibility for nonsymmetric Cauchy stresses is required for equilibrium, unlike classical shell theories. Micropolar theories are not commonly used, by comparison to the Boltzmann continuum. One reason may be that micropolar theories often require greater modelling effort without significant advantage. However, the simplicity of introducing physical effects like magnetic loading compensates those efforts.