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Analysis of dynamic propagation of cracks based on Particle Discretization Scheme Finite Element Method (PDS-FEM)

Kenji Oguni (Keio University)

Eringen Medal Symposium in honor of G. Ravichandran

Tue 4:20 - 5:40

Salomon 001

In the field of solid continuum mechanics, dynamic propagation of cracks has been one of the most important and challenging research topics for decades. Although many significant findings have been made by experimentalists, these experimental results have not been completely explained by numerical analysis. Major difficulties in the analysis of dynamic propagation of cracks are i) treatment of discontinuities in displacement field, ii) re-distribution of residual nodal force and iii) determination of crack velocity. A numerical analysis method for analysis of dynamic crack propagation without rate dependent material parameters is proposed in this presentation. This method is based on PDS-FEM (Particle Discretization Scheme Finite Element Method). PDS-FEM has been developed by the authors for easy treatment of discontinuities in displacement field. PDS is a discretization scheme using characteristic functions defined on a set of conjugate geometries; Voronoi and Delaunay tessellations. Displacement field is discretized by a set of non-overlapping shape functions with embedded discontinuities. As a result, there is no need for changing discretization of displacement field for fracture. Once the displacement field is discretized by PDS, the displacement field can be regarded as rigid body motion of each Voronoi cells. Thus, Hamiltonian framework for dynamics of particles can be applied for the problem of deformation and fracture of solid continuum. Re-distribution of residual nodal force is automatically taken care of by Hamiltonian dynamics. The remaining problem is determination of crack velocity. To determine the crack velocity, energy balance between surface energy required for creating new crack surface and change in Hamiltoninan before and after fracture is considered. At this moment, preliminary results such as i) acceleration and decceleration of fracture surface growth and ii) branching of crack has been obtained.