Meshfree Failure Simulations With Phase Field Models

Damage and failure of materials and structures are frequently encountered in engineering practice.The numerical simulation of damage and failure involve many issues such as damage initiation,evolution,strain softening and large deformation analysis,etc,and thus it is still an important topic nowadays.The phase field modeling approach implicitly traces the damage evolution and crack path through an independent field variable,which is governed by the phase field equation.As a result,the phase field modeling method is ideal for large scale problems.On the other hand,meshfree methods construct arbitrary order smoothing shape functions directly using the unstructured nodes and do not rely on the topologically connected elements.Consequently,meshfree methods are particularly adequate for the analysis of higher order differential equations,for example,the fourth-order phase field equation,as well as the large deformation analysis.Thus it will be desirable to develop a meshfree phase field modeling methodology for damage and failure simulation.This thesis takes the advantages of the meshfree methods and phase field modeling and proposes a meshfree damage and failure analysis method with phase field modeling.Firstly,the second order and fourth order phase models for failure analysis are discussed for elastic problems,the coupling between equilibrium and phase field equations,weak formulation,linearization and meshfree discretization are outlined in detail.The stabilized conforming nodal integration with strain smoothing is employed to accelerate the meshfree computational efficiency.Subsequently,the proposed formulation is extend to three dimensional large deformation slope failure analysis.The Lagrangian meshfree shape functions are utilized and the momentum and phase field equations are coupled within the updated Lagrangian formulation,where the soil is characterized by the rate-form elasto-plasticity model.Numerical examples evince that the proposed meshfree phase field modeling method is capable of capturing the complex large deformation slope failure patterns.