Titlebook: Non-standard Discretisation Methods in Solid Mechanics; Jörg Schröder,Peter Wriggers Book 2022 The Editor(s) (if applicable) and The Autho

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Novel Finite Elements - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Appc and anisotropic materials with a complex nonlinear material behavior. New ideas are pursued in a strict variational framework, based either on a mixed or virtual FE approach. A novel extension of the classical Hellinger-Reissner formulation to non-linear applications is developed. Herein, the cons

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Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations,mage, is introduced. The approach is based on a split of the Lagrange multiplier, which enforces compatibility between the mixed variables. Through this, a decoupled set of variational equations is obtained. Stability both for the continuous formulation and various discrete subspaces is shown in the

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Stress Equilibration for Hyperelastic Models,ith a stable finite element pair, an .-conforming approximation to the first Piola-Kirchhoff stress tensor is computed. This is done in the usual way in a vertex-patch-wise manner involving local problems of small dimension. The corresponding reconstructed Cauchy stress is not symmetric but its skew

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Hybrid Mixed Finite Element Formulations Based on a Least-Squares Approach, via Lagrange multipliers. Therefore, a stress-displacement least-squares formulation . is considered, which is defined by the squared .-norm applied to the first-order system of differential equations, given by the balance of momentum and the constitutive equation as well as an additional (mathemat

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