Modern Domain-based Discretization Methods for Damage and Fracture

Standard domain-based discretization methods that have been developed for continuous media are not well suited for treating propagating (or evolving) discontinuities. Indeed, they are approximation methods for the solution of partial differential equations, which are valid on a domain. Discontinuities divide this domain into two or more parts. Conventionally, special interface elements methods are placed a priori between the continuum finite elements to capture discontinuities at locations where they are expected to emerge. More recently, discretization methods have been proposed, which are more flexible than standard finite element methods, while having the potential to capture propagating discontinuities in a robust, efficient and accurate manner. Examples are meshfree methods, finite element methods that exploit the partition-of-unity property of finite element shape functions, and discontinuous Galerkin methods. In this contribution, we shall present an overview of these novel discretization techniques for capturing propagating discontinuities, including a comparison of their similarities and differences.