Material point method for crack propagation in anisotropic media: a phase field approach

A novel phase field formulation implemented within a material point method setting is developed to address brittle fracture simulation in anisotropic media. The case of strong anisotropy in the crack surface energy is treated by considering an appropriate variational, i.e., phase field approach. Material point method is utilized to efficiently treat the resulting coupled governing equations. The brittle fracture governing equations are defined at a set of Lagrangian material points and subsequently interpolated at the nodes of a fixed Eulerian mesh where solution is performed. As a result, the quality of the solution does not depend on the quality of the underlying finite element mesh and is relieved from mesh-distortion errors. The efficiency and validity of the proposed method is assessed through a set of benchmark problems

Χρήση μοριακής δυναμικής στη διερεύνηση μηχανικής συμπεριφοράς υλικών

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Δομοστατικός Σχεδιασμός και Ανάλυση των Κατασκευών

Phase-Field Material Point Method for dynamic brittle fracture with isotropic and anisotropic surface energy

A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly defined crack density functional. The particular case of impact driven fracture is treated by employing a discrete field approach within the material point method setting. In this, the equations of motion and phase field governing equations are solved independently for each discrete field using a predictor–corrector algorithm. Contact at the interface is resolved through frictional contact conditions. The proposed method is verified using analytical predictions. The influence of surface energy anisotropy and loading conditions on the resulting crack paths is assessed through a set of benchmark problems. Comparisons are made with the standard Phase Field Finite Element Method and experimental observations

Linear elastic fracture mechanics via the Material Point Method: a phase field approach

Fracture is one of the main failure mechanisms of materials and structural components. During the past thirty years, various methods have been introduced to simulate crack initiation and growth. These include the introduction of Element Deletion Method and re-meshing strategies within the standard Finite Element Method (FEM), cohesion based Finite Element strategies and the extended Finite Element Method. Very recently, a new method for crack propagation, namely the phase field method has been introduced; phase field models have been proven very robust in accurately predicting complex crack behavior while at the same time avoiding standard re-meshing or enriching techniques. To this point, phase field modelling has extensively been applied within a Finite Element framework while very little research and applications have been demonstrated with particle methods. However, treating the crack propagation problem using a grid based method is a challenging and computationally taxing task. The reliability and robustness of the Finite Element Method and in general mesh-based methods depends on the quality of the mesh itself. In this work, the phase field method is re-formulated and treated using an attractive Particle-In-Cell (PIC) scheme, namely the Material Point Method (MPM). In this approach, the coupled continuum/phase field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, i.e. non-deforming, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying Finite Element mesh and relieved from corresponding mesh distortion errors. This framework is then generalized for the case of anisotropic brittle fracture by introducing an anisotropic crack density functional. The anisotropic crack density functional gives rise to a family of phase field models, both second and fourth order, able to address brittle fracture simulation in anisotropic media. The proposed method is further extended into dynamic brittle fracture using both isotropic and anisotropic phase field models. Frictional contact problems involving phase field fracture are also examined and their post-fracture contact response is investigated. On the proposed model, the local contact features are naturally handled using the Eulerian mesh and the damage evolution emerges without the need to numerically track discontinuities in the displacement field e.g. with jump and tip enrichment functions as well as complex crack paths can be obtained without any additional ad hoc rules. These advantages make the derived model a robust computational tool when arbitrary crack paths occur at impact-fracture problems. Following, the proposed model is used to efficiently simulate crack paths induced from rocking response. The accuracy of the method is examined and verified based on existing analytical rocking response models; the method is then further extended into rocking system dynamics involving phase field fracture. Merits and drawbacks of the proposed formulation are examined using a set of benchmark tests. The influence of impact velocity, phase field and material point parameters on induced crack path is also examined. Validation based on experimental observations is also performed

Linear elastic fracture mechanics via the Material Point Method: a phase field approach

Fracture is one of the main failure mechanisms of materials and structural components. During the past thirty years, various methods have been introduced to simulate crack initiation and growth. These include the introduction of Element Deletion Method and re-meshing strategies within the standard Finite Element Method (FEM), cohesion based Finite Element strategies and the extended Finite Element Method. Very recently, a new method for crack propagation, namely the phase field method has been introduced; phase field models have been proven very robust in accurately predicting complex crack behavior while at the same time avoiding standard re-meshing or enriching techniques. To this point, phase field modelling has extensively been applied within a Finite Element framework while very little research and applications have been demonstrated with particle methods. However, treating the crack propagation problem using a grid based method is a challenging and computationally taxing task. The reliability and robustness of the Finite Element Method and in general mesh-based methods depends on the quality of the mesh itself. In this work, the phase field method is re-formulated and treated using an attractive Particle-In-Cell (PIC) scheme, namely the Material Point Method (MPM). In this approach, the coupled continuum/phase field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, i.e. non-deforming, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying Finite Element mesh and relieved from corresponding mesh distortion errors. This framework is then generalized for the case of anisotropic brittle fracture by introducing an anisotropic crack density functional. The anisotropic crack density functional gives rise to a family of phase field models, both second and fourth order, able to address brittle fracture simulation in anisotropic media. The proposed method is further extended into dynamic brittle fracture using both isotropic and anisotropic phase field models. Frictional contact problems involving phase field fracture are also examined and their post-fracture contact response is investigated. On the proposed model, the local contact features are naturally handled using the Eulerian mesh and the damage evolution emerges without the need to numerically track discontinuities in the displacement field e.g. with jump and tip enrichment functions as well as complex crack paths can be obtained without any additional ad hoc rules. These advantages make the derived model a robust computational tool when arbitrary crack paths occur at impact-fracture problems. Following, the proposed model is used to efficiently simulate crack paths induced from rocking response. The accuracy of the method is examined and verified based on existing analytical rocking response models; the method is then further extended into rocking system dynamics involving phase field fracture. Merits and drawbacks of the proposed formulation are examined using a set of benchmark tests. The influence of impact velocity, phase field and material point parameters on induced crack path is also examined. Validation based on experimental observations is also performed