Phase Field Fracture For Heterogeneous Materials

Most materials in nature and engineering applications are heterogeneous,such as composite materials and concrete,these two kinds of materials are widely used in aerospace engineering and civil engineering.Casualties and economic losses are often resulted from destruction of structures made by these materials.The intrinsic reason why structure fails is that microcracks initiates,propagates and merges into macrocrack at material level.Therefore,efforts devoted to study fracture behavior of heterogeneous materials are very significant not only for theoretical research but also for engineering applications.Numerical modelling techniques based on finite element method like phase field damage model can simulate crack pattern with arbitrary topology,such as bending,merging and branching.This makes phase field damage model embraced a bright future on modeling fracture behavior of materials.Based on phase field damage model,this work studied fracture behavior of heterogeneous materials.The main contents are given as follows:First,fracture behavior of heterogeneous materials with periodicity is investigated in this work by incorporated phase field damage model and homogenization method.The reference configuration made by heterogeneous materials with periodicity is transformed into equivalent structure consist of homogeneous materials via homogenization method.In this way,effect of mesoscopic information of materials on fracture behavior of macro structures can be analyzed systematically.Based on phase field damage model,this work solved fracture problem of reference configuration directly and equivalent structure indirectly and compared the obtained results.In contrast,the computational cost is greatly reduced with proper accuracy after the heterogeneous materials is homogenized.Second,the multiple phase field elasto-plastic model is established for composite materials in this work.Independent phase field variables of each constituent of composite materials are defined to describe their fracture behavior.Coupling of elastic deformation,plastic deformation and crack propagation is introduced via a novel elasto-plastic coupling energy degradation function.The multiple phase field elasto-plastic model not only can reduce to classic phase field damage model but also can incorporate specific constitutive relation of different materials.These advantages make the proposed model to be a generalized model.Third,the interface deboning phase field damage model considering interfacial effect is established in this research.Based on the enlightenment of phase field damage model,transforming discrete crack into smeared crack,this work describes discrete interface with smeared interface.Singularity of material properties between different materials is eliminated by smeared interface.Imbalance of dissipated energy at interface is avoided by regularization of crack energy release rate of interface.Optimal design scheme of materials is proposed by current study.Finally,three dimensional fracture behavior of fiber reinforced concrete is qualitatively investigated.Parameterized finite element model is explicitly constructed by Python-Abaqus.Influence of intrinsic heterogeneity of steel fiber reinforced concrete introduced by fibers on crack initiation and propagation are discussed in detail.Numerical simulation realized local damage,local branching and curvature of crack which is consist with experiment.Advantages of phase field damage model for three dimensional fracture behavior are revealed in this work.