Isogeometric and stochastic collocation methods for nonlinear probabilistic multiscale problems in solid mechanics

• Applicants: Professorin Dr. Laura De Lorenzis; Professor Dr. Hermann Georg Matthies
• Subject Area: Mechanics
• Term: from 2014 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 255747201

In this project, we intend to use the newly developed concept of isogeometric collocation (IGA-C) in combination with stochastic collocation (SC) to achieve stable and computationally efficient higher-order modeling of irreversible multiscale behaviour in solid mechanics. The basic assumption is that the microstructure of a heterogeneous solid is uncertain and hence should be modeled probabilistically. In order to describe the effects of the microscale uncertainty not only on the mean macroscopic fields, but also on their variability, a probabilistic treatment of the scale transition is also needed. As the computational cost of such stochastic computations may be orders of magnitude larger than that of simple deterministic analyses, an unprecedented computational efficiency is sought in the combination of IGA-C for the mechanical/deterministic modeling, and of an SC scheme with novel ansatz functions for the stochastic discretization. The numerical framework to be developed encompasses local and non-local elasticity and plasticity with finite strains, as well as contact, damage and fracture models.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1748: Reliable Simulation Techniques in Solid Mechanics - Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis