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Dynamic Modelling of Ductile Damage with Extended Finite Element Method

Broumand, Pooyan | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47039 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In this thesis, based on the combination of Extended Finite Element Method (X-FEM) and appropriate material constitutive models, an efficient method is proposed to model ductile fracture under quasi-static, cyclic and dynamic conditions. X-FEM is a novel method in which with the use of appropriate enrichment functions, discontinuity geometry is separated from the computational mesh and hence the need for a remeshing step is alleviated. The non-linear material behavior in the crack tip process zone can best be modeled with methods based on continuum damage mechanics. These methods model the ductile fracture mechanisms, phenomenologically. In this thesis, in order to model the ductile fracture in static condition, a corrected version of X-FEM is extended to large deformation regime in an updated Lagrangian framework. Large strains are modeled by using a hypo-elastic model based on step-wise Green-Lagrange strain and Second-Piola Kirchhof stress. The constitutive equations are based on a non-local version of Lemaitre’s damage-plasticity model with isotropic hardening. The non-local damage is calculated by solving a Helmholtz type equation in combination with the governing equilibrium equations in an operator-split manner. Crack growth and crack direction criteria are proposed based on a weighted damage value in the crack tip region and an efficient method is presented for the crack propagation which enhances consistency and equilibrium during crack growth steps. In order to model the ductile fracture under cyclic and dynamic regimes, the dynamic extended finite element solution of the equation of motion is extended into the large deformation regime in an updated Lagrangian framework. Large strains are modeled by consideration of a hyper-elastic behavior and a method based on logarithmic Hencky strain and polar decomposition of the deformation gradient. Time domain is discretized based on explicit central difference method, which is enhanced through the use of mass lumping, reduced integration with hourglass control and numerical damping. Crack growth and crack direction criteria and required modifications of the X-FEM crack propagation problems in dynamic and cyclic regimes are discussed. In order to model the material behavior under cyclic loadings, Lemaitre’s damage-plasticity model with combined isotropic-kinematic hardening and consideration of crack closure effect is used. Under dynamic condition, the plastic work heat generation is considered and the process is assumed adiabatic. The material nonlinearity and the flow stress dependency on strain rate, hardening and temperature are modeled macroscopically with a Johnson-Cook based visco-plastic-damage model. The localization phenomenon due to damage and thermal softening is suppressed by using the visco-plastic regularization in combination with the non-local visco-plastic model in which damage is calculated based on the solution of a Helmholtz type equation for visco-palstic strain and temperature. Crack face closure is modeled by implementation of a penalty contact formulation in X-FEM. Finally, the robustness and accuracy of the proposed methods are verified in several numerical examples. The results are in good agreement with the experiments and similar numerical methods
  9. Keywords:
  10. Dynamic Modeling ; Ductile Fracture Criteria ; Extended Finite Element Method ; Large Deformation ; Damage Plasticity Model

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