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The accuracy of finite element solutions is closely tied to the mesh quality.In particular, geometrically nonlinear problems involving large and stronglylocalized deformations often result in prohibitively large element distortions.In this work, we propose a novel mesh regularization approach allowing torestore a non-distorted high-quality mesh in an adaptive manner without theneed for expensive re-meshing procedures. The core idea of this approach liesin the definition of a finite element distortion potential consideringcontributions from different distortion modes such as skewness and aspect ratioof the elements. The regularized mesh is found by minimization of thispotential. Moreover, based on the concept of spatial localization functions,the method allows to specify tailored requirements on mesh resolution andquality for regions with strongly localized mechanical deformation and meshdistortion. In addition, while existing mesh regularization schemes often keepthe boundary nodes of the discretization fixed, we propose a mesh-slidingalgorithm based on variationally consistent mortar methods allowing for anunrestricted tangential motion of nodes along the problem boundary. Especiallyfor problems involving significant surface deformation (e.g., frictionalcontact), this approach allows for an improved mesh relaxation as compared toschemes with fixed boundary nodes. To transfer data such as tensor-valuedhistory variables of the material model from the old (distorted) to the new(regularized) mesh, a structure-preserving invariant interpolation scheme forsecond-order tensors is employed, which has been proposed in our previous workand is designed to preserve important mechanical properties of tensor-valueddata such as objectivity and positive definiteness... {continued see pdf}

A novel mesh regularization approach based on finite element distortion  potentials: Application to material expansion processes with extreme volume  change