The Element Free Galerkin Method With Couple Stress Theory And Its Application In The Crack Propagation

The influence of the micro scale is not involved in the theories of elasticity and plasticity in the classical continuum mechanics and the constitutive relationships under the micro-scale. In fact, there are many cracks in the rock mass. And in the vicinity of the crack tip, there is high strain gradient which will influent the stress fields around the crack tip and the fracture behavior under the micro-scale.When the crack propagation is analyzing, the finite element method requires remeshing to represent arbitrary and complex paths because the meshes will be distorted. And there are many difficulties in solving the problems of couple stress theory, it requires special elements such as hybrid element and incompatible element. The element free Galerkin method which base on the approximation of the nodes can separate from the meshes totally or partly, so it has the accurate calculations. It requires only nodes, not elements. The pre-processing and the post-processing aresimple, the displacement will satisfy C~1 -continuity. So it is particularly promising inthe analysis of the elasticity and plasticity problems, large deformation, and fracture and so on.In the element-free Galerkin methods, the trial and test functions are constructed by moving least-squares interpolants. The governing equations are obtained by a Galerkin variational principle of energy functional. Penalty functions are introduced to enforce the essential boundary condition. The method has the advantages of the high accurate calculation and easy post-processing.Firstly, the paper introduces the element free Galerkin method, elasticity couple stress theory and the element free Galerkin method with couple stress theory. Following, it calculates the stress and the displacement value of the simple supported beam and the stress intensity factor around the hole. And it calculates the scale effect of the stress intensity factor around the hole. The stress intensity is reduced because of the influence of the couple stress. It gets bigger following the increase of a/l, and reaches to the classical theory answer. So the element free Galerkin method has more advantages than finite element method in solving couple stress problems. And it confirms that the program is correct.The element free Galerkin method is used to simulate the crack propagation of the rock mass under the pressure according to the modified maximum circumferential tensile stress criterions. And the results agree with the simulate results by the RFPA2D software. So, the method has the accurate calculation in solving the crack propagation, and is valued to be developed and applied.The paper studies the application of the element free Galerkin method with the couple stress theory on the crack propagation, and analyzes the scale effect of the initial crack-extending-angle in the rock mass under pressure. It is obtained that the less the ratio of the crack half-length to the characteristic length of the materials is, the less the initial crack-extending-angle of the crack is. Following, this paper simulates the path of the crack propagation with couple stress, and the path is smoother than without the couple stress.The work of this paper develops the application of the element free Galerkin method on the projects of the rock mass, and lays the foundation on the crack propagation for the element free Galerkin method with the couple stress theory.