Smooth finite strain plasticity with non-local pressure support

The aim of this work is to introduce an alternative framework to solve problems of finite strain elastoplasticity including anisotropy and kinematic hardening coupled with any isotropic hyperelastic law. After deriving the constitutive equations and inequalities without any of the customary simplifications, we arrive at a new general elasto-plastic system. We integrate the elasto-plastic algebraico-differential system and replace the loading–unloading condition by a Chen–Mangasarian smooth function to obtain a non-linear system solved by a trust region method. Despite being non-standard, this approach is advantageous, since quadratic convergence is always obtained by the non-linear solver and very large steps can be used with negligible effect in the results. Discretized equilibrium is, in contrast with traditional approaches, smooth and well behaved. In addition, since no return mapping algorithm is used, there is no need to use a predictor. The work follows our previous studies of element technology and highly non-linear visco-elasticity. From a general framework, with exact linearization, systematic particularization is made to prototype constitutive models shown as examples. Our element with non-local pressure support is used. Examples illustrating the generality of the method are presented with excellent results

A new semi-implicit formulation for multiple-surface ow rules in multiplicative plasticity

We propose new integration scheme

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Mixed Strategy Constraints in Continuous Games

Equilibrium problems representing interaction in physical environments typically require continuous strategies which satisfy opponent-dependent constraints, such as those modeling collision avoidance. However, as with finite games, mixed strategies are often desired, both from an equilibrium existence perspective as well as a competitive perspective. To that end, this work investigates a chance-constraint-based approach to coupled constraints in generalized Nash equilibrium problems which are solved over pure strategies and mixing weights simultaneously. We motivate these constraints in a discrete setting, placing them on tensor games ($n$-player bimatrix games) as a justifiable approach to handling the probabilistic nature of mixing. Then, we describe a numerical solution method for these chance constrained tensor games with simultaneous pure strategy optimization. Finally, using a modified pursuit-evasion game as a motivating examples, we demonstrate the actual behavior of this solution method in terms of its fidelity, parameter sensitivity, and efficiency