Static And Dynamic Fracture Simulation Of Concrete Structures Based On Scaled Boundary Finite Element Method

The new cracks formed from notches, which appeared inevitably in engineering structures, can lead to catastrophic failure under the external loads (seismic force etc.) and seriously influence the degree of safety. Description of static or dynamic characteristics of crack structures and crack propagation laws are the hot issues of academic and engineering circles. Computational fracture mechanics is an efficient way for analyzing these problems. As a novel numerical method developed in recently, Scaled Boundary Finite Element Method (SBFEM) is the semi-analytical approach combining the advantages of FEM and BEM, at the same time it has its own characters. Firstly, only boundaries of the investigated domain are discretized resulting in a reduction of the spatial dimension by one as the BEM, but the fundamental solution is unnecessary. Secondly, the displacement and stress fields can be evaluated analytically in the radial direction, and accurate Stress Intensity Factors (SIFs) can be calculated straightforwardly without further introducing singular elements. In modeling unbounded domain, the radiation condition at infinity is satisfied exactly. So SBFEM is superior to solve unbounded domain and stress singularity engineering problems.A new simulating crack growth method based on super-element remeshing technique is established using advantages and characters of SBFEM and extended in dynamic fracture analysis in the dynamic dam-foundation interaction system under earthquake action. This paper broadens application of SBFEM. The innovative achievements are included:(1) The relationship between J integral and SIFs for the mixed mode crack with arbitrary inclination are desired by Rice’s integral formula using analytical expression of the displacement and stress fields in Griffith crack model. The relationship is validated using FEM and SBFEM. The maximum energy release rate is also solved using this relationship for mixed mode crack with arbitrary inclination in elastic material. Moreover, the J integral values obtained by SBFEM are more accurate and convenient than by its definition. Factors that affect the accuracy of J integral values (such as size of the discretized elements) are examined.(2) A super-element remeshing technique based on SBFEM is proposed. In the process of crack propagation simulation, each super-element passed through by the previous crack increment step is divided into two new super-elements, which may be polygons with flexibly desired shape and dimensions only the visible requirement is satisfied. Mesh size is refined merely at the crack-tip super-element is needed to ensure required accuracy of SIFs. The sophisticated crack trajectory is predicted by the Linear Elastic Fracture Mechanics (LEFM) criteria.(3) A super-element remeshing technique is developed to model both I mode and I/II mode fracture of concrete beams using cohesive crack model based on the linear asymptotic superposition assumption. The cohesive tractions to model energy dissipation in the fracture process zone (FPZ) are treated as analytical side-face forces which results in a particular solution to be sought for the governing differential equations. The induced displacement field and stress field can be solved analytically without incorporating the Cohesive Interface finite Elements (CIEs) in the crack path. As a result, nonlinear fracture of concrete structures can be handled as a linear elastic one.(4) The mesh mapping technique for super-element remeshing technique is proposed to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Mesh mapping algorithm can communicate dynamic parameters (such as displacements etc.) from previous step to the present step of crack propagation. Numerical examples indicate that the results are good agreement with those obtained from other numerical analyses reported in the literature, and the proposed method is accurately and effectively to simulate the dynamic crack propagation problem.(5) Dynamic fracture is analyzed in the dynamic gravity dam-foundation interaction system under earthquake action. The study on the applications of the non-smooth equations method in dynamic frictional contact problems with contraction joints of two crack surfaces has been carried out in order to prevent penetration of crack surfaces under seismic loads. SBFEM utilizes main advantages in modeling unbounded media (only the boundary is discretized and the infinity boundary condition is satisfied exactly) to analyze the dynamic interaction of gravity dam-foundation system under earthquake action in time domain. The effects of different initial crack lengths for stress distribution and crack propagation lengths are discussed.Numerical modeling cracking state and crack propagation process can provide necessary technical basis for the evaluation of the loading capacity and safety of the structures.