13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- X Y -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 X Y -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) Uniform mesh (Mesh I) (b) Non-uniform mesh (Mesh II) Figure 3 Two finite element discretizations of the square plate X Y -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 DXcont 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 X Y -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 dispxcontact 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 (a) ux(Model I) (b) ux(Model II) X Y -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Dycont -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 X Y -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 dispycontact -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 (c) uy (Model I) (d) uy (Model II) Figure 4 Distribution of displacement in the square plate for frictional coefficient 0.1(Unit: m) 5.2. Frictional contact of two parts of a 3D beam In this example, a beam is divided into two identical parts by a contact surface shown in Figure 5. In order of comparison and validation, two finite element models denoted by Model I and Model II are constructed. In Model I the contact surfaces are embedded in the elements, while in Model II the contact surfaces coincide with the element boundaries. The finite element discretizations for the two models are given in Figure 6. The presented method in the framework of XFEM is used for solving Model I and the standard FEM with B-differential equation method for Model II. The material is elastic with the properties: Young’s Modulus 1e10Pa, Poisson’s ratio 0.3, frictional coefficient 0.1. At the left end of beams, part of the surface, i.e. the shadow area as shown in Figure 6, is fixed. So there are no constraints at the intersection line between contact surfaces and the boundary surfaces
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