Computational mechanics of generalized continua (COMECH)
The objective of this sub–project is to establish solid theoretical and computational foundations for the development of regularization methods to solve essentially ill–posed problems encountered in damage and fracture mechanics. Sophisticated finite element technologies have been developed recently to address crack propagation problems. They include level set methods, X–FEM methods to follow discontinuities, remeshing techniques at the crack front, insertion of cracks in finite element meshes at some stages of the simulations… These tools are undoubtedly necessary but they must be combined with clear formulations of the balance and constitutive equations. This is usually not the case since linear higher order constitutive equations are often tacitly assumed in the partial differential equations to be solved. More general frameworks will be proposed and mathematically assessed to ensure the regularization capabilities of the models, for instance by means of careful analyses like. A rationale in the formulation of regularization methods from the mathematical and physical sides is one crucial objective of this sub–project.
Interesting open problems are the extension of existing regularized approaches to brittle fracture to the domain of large deformations and material undergoing plastic deformations, eventually including multiphysical couplings. In this domain the work will span from the mathematical analysis of simplified model-problems to the numerical implementation in finite element codes for the solution of engineering applications.