Continuum Damage Mechanics Analysis using Extended Finite Element Method.
Year: Sept. 2008- Feb. 2011.
Finite element method (FEM), one of the most practical numerical methods in mechanical engineering problems, has some limitations to model crack growth within the fracture mechanic analysis. In spite of all achievements, the continuum basis of FEM has remained as a source of relative disadvantage for discontinuous fracture mechanics. High dependency of crack to finite element mesh, re-meshing requirement and need to singular element in particular cases are some defects of FEM in modeling crack growth. In recent years, the Extended Finite Element Method, XFEM, based on mesh-based partition of unity method has emerged as an efficient numerical method to model discontinuities specially crack as a strong discontinuity in fracture mechanic analysis. In the XFEM, extrinsic enrichment of displacement field is applied to extend the standard displacement based approximation space which leads to improve the accuracy of discontinuous problems. The idea is to embedding discontinuous functions in FE approximation through the partition of unity concept. Therefore, the crack path is independent of finite element mesh and as a result, no re-meshing or utilizing singular elements is needed.
It is now well known that the applicability of the J-based single parameter fracture mechanics is restricted to high constraint crack geometries and materials of low ductility. For highly ductile materials, the fracture process zone is large and the crack tip fields are no longer adequately characterized by the J-integral alone. Micro-mechanically based damage models, which simulate the physical process of void nucleation, growth and coalescence using continuum mechanics equations, are among the most promising methods to investigate fracture behavior in ductile materials. The advantage of a micromechanical damage model, compared with conventional fracture mechanics, is that, in general, the model parameters are only material dependent, and not geometry dependent. The damage model allows damage assessments at every point of a structure for any geometry or loading, as long as the damage mechanisms and stress/strain fields are known. The development of micro-structural damage in engineering materials can be effectively modeled using continuum damage mechanics (CDM).
In this work, XFEM is used to model crack growth in fracture mechanic problems. After the comprehensive research on crack growth problems using XFEM, Lemaitre elastic-plastic damage model, one of most efficient continuum damage models, replaces with justify.
Keywords: Ductile crack growth; Extended Finite Element Method; Continuum Damage Mechanics.