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

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.

DFG Programme Priority Programmes

International Connection Austria, Netherlands, Switzerland

• A novel smooth discretization approach for elasto-plastic contact of bulky and thin structures (Applicants Popp, Alexander ;  Wall, Wolfgang A. )
• Adaptive isogeometric modeling of discontinuities in complex-shaped heterogeneous solids (Applicants Kästner, Markus ;  Peterseim, Daniel )
• Advanced Finite Element Modelling of 3D Crack Propagation by a Phase Field Approach (Applicant Müller, Ralf )
• Approximation and reconstruction of stresses in the deformed configuration for hyperelastic material models (Applicants Bertrand, Fleurianne ;  Schröder, Jörg ;  Starke, Gerhard )
• Beyond isogeometric and stochastic collocation: maximizing efficiency in stochastic non-linear computational solid mechanics (Applicants De Lorenzis, Laura ;  Matthies, Hermann Georg )
• Coordination Funds (Applicant Schröder, Jörg )
• First-order system least squares finite elements for finite elasto-plasticity (Applicants Schröder, Jörg ;  Schwarz, Alexander ;  Starke, Gerhard )
• Foundation and Application of Generalized Mixed FEM Towards Nonlinear Problems in Solid Mechanics (Applicant Carstensen, Carsten )
• High-order immersed-boundary methods in solid mechanics for structures generated by additive processes (Applicants Düster, Alexander ;  Rank, Ernst ;  Schröder, Andreas )
• Hybrid discretizations in solid mechanics for non-linear and non-smooth problems (Applicants Reese, Stefanie ;  Wieners, Christian ;  Wohlmuth, Barbara )
• Isogeometric and stochastic collocation methods for nonlinear probabilistic multiscale problems in solid mechanics (Applicants De Lorenzis, Laura ;  Matthies, Hermann Georg )
• Large-scale simulation of pneumatic and hydraulic fracture with a phase-field approach (Applicants Hesch, Christian ;  Weinberg, Kerstin )
• Novel finite elements - Mixed, Hybrid and Virtual Element formulations at finite strains for 3D applications (Applicants Schröder, Jörg ;  Wriggers, Peter )
• Reliability of efficient approximation schemes for material discontinuities described by functions of bounded variation (Applicants Bartels, Sören ;  Thomas, Marita )
• Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations (Applicants Balzani, Daniel ;  Schedensack, Mira )
• Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models (Applicants Walloth, Mirjam ;  Wick, Thomas ;  Wollner, Winnifried )

Spokesperson Professor Dr.-Ing. Jörg Schröder