SPP 1748: Reliable Simulation Techniques in Solid Mechanics - Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis

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The main objective of this Priority Programme is the development of modern non-conventional discretisation methods, based on e.g. mixed (Galerkin or least-squares) finite element or discontinuous Galerkin formulations, including the mathematical analysis for geometrically as well as physically non-linear problems in the fields of e.g. incompressibility, anisotropies and discontinuities (cracks, contact). It is the aim to pool the expertise of mechanics and mathematics in Germany and to create new and strengthen existing networks. In the framework of this cooperation the experiences should be exchanged in between the different working groups to create synergies, save time and costs and raise the efficiency. Furthermore, it is intended to lead this research union to international excellence in the field of non-conventional discretisation techniques.In detail the Priority Programme will drive research towards the following directions concerning non-conventional finite element formulations:· deep mathematical understanding of the structural requirements of reliable non-conforming finite element method (FEM) approaches for finite deformations,· mathematically sound variational formulations,· robust and stiffening-free discretisations at finite deformations for (quasi-)incompressible, isotropic and anisotropic material behaviour as well as for domains with oscillating coefficients,· accurate approximation of all process variables in the latter mentioned extremal cases,· insensitive behaviour concerning significant mesh deformation, · convergence of adaptive mesh refinement,and discontinuities:· creation of a variational basis as well as suitable discretisation techniques for discontinuities: convergence, stability and approximation properties,· resolution of discontinuities based on isogeometric formulations,· novel crack growth and crack branching models,· contact formulations based on non-conventional discretisation techniques exceeding Mortar-methods.