Project Details
Projekt
Nonlinear Fracture Dynamics: Modeling, Analysis, Approximation, and Applications
Applicants
Professorin Dr. Marita Thomas; Professorin Dr.-Ing. Kerstin Weinberg; Professor Dr. Christian Wieners
Subject Area
Mathematics
Mechanics
Mechanics
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 441212523
The correct modeling and efficient approximation of rapid deformations in nonlinear elastic and inelastic materials is a challenging task relevant for many engineering applications. Here we aim to develop efficient and reliable methods for the spatio-temporal approximation of dynamic models in solid mechanics at large strains. Our key interest lies in the investigation of criteria for the initiation and propagation of dynamic fracture in a variational setting in space and time: On the one hand, material discontinuities may arise as a property of the (weak) notion of solutions in finite strain elastodynamics with non-convex energy functionals. On the other hand, it has proved beneficial both from the analytical and computational point of view to regularize sharp material discontinuities using internal variables in terms of damage or phase-field fracture models. It is our goal to establish relations between such different concepts and to systematically investigate in these models the interplay of dynamic wave propagation and purely dissipative effects such as phase-field fracture and viscous damping both from the analytical and from the numerical point of view. In this context it is of importance to identify relations and quantify differences between models for finite strain elasticity and models for small strain elasticity. As a long term goal we aim to extend our methods to general finite strain models which also capture the evolution of plasticity and temperature. In the first funding period, we developed an efficient approximation scheme for dynamic phase-field fracture with first-order discontinuous Galerkin elements in the small strain regime, we presented a well-posedness analysis for dynamic phase-field fracture, we studied different fracture criteria and models for the phase-field evolution also for large deformations, and we analyzed fracture in simple geometries by means of GENERIC. For the second funding period, our main objectives are 1) the development of efficient and reliable methods for the approximation in space and time of finite strain models with and without phase field, 2) the investigation of propagation criteria for wave induced fracture and their corresponding formulation as phase-field model, and 3) a detailed study of the interplay of dynamic wave propagation and purely dissipative effects such as viscous damping and phase-field fracture.
DFG Programme
Priority Programmes
