Towards a robust framework for dynamic fracture simulation
Speaker: Savvas Triantafyllou (Department of Civil Engineering)
Title: Towards a robust framework for dynamic fracture simulation
Abstract: The Lagrangian formulation of finite elements (FEM) is the most commonly used method to address problems in solid mechanics. Lagrangian formulation is particularly advantageous to applications with elaborate constitutive models and history-dependent variables involving, e.g., plastic deformation, strain hardening and damage evolution. The accuracy of Lagrangian methods however greatly depends on the properties of the underlying finite element mesh. Avoiding numerical errors pertaining to mesh distortion is not a trivial task. Failure to bound such mesh-dependent errors may result in considerable loss of accuracy especially if large displacements and/or large deformations are taken into account. This is of particular importance for applications pertaining to high-speed impact loading and associated brittle fracture events. The Eulerian description of kinematics offers significant advantages this case, however treatment of history dependent constitutive models is challenging. Material point method (MPM) has been introduced as an extension of particle-in-cell methods to efficiently treat history-dependent variables. MPM combines the advantages of Eulerian and Lagrangian descriptions, resulting in a powerful tool for large scale problems involving material and geometric nonlinearities also within a large strain setting. In this presentation, the Material Point method is revisited and originally upgraded to account for brittle fracture related phenomena. A variational framework is adopted based on Griffith’s postulate for brittle fracture. The crack is approximated by means of a phase field and the resulting coupled governing equations are resolved utilizing a material point method approach.