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Application of MPM to forming problem

A cutting problem is presented; the plane stress of the formed material is considered. Geometry of the problem is shown in Fig. 1 (dimensions are given in millimeters). Applying the constitutive model of the elastic-perfectly plastic body with the Huber-von Mises yield condition, calculations have been made with the following data: Young modulus = 7.3*10⁴ MPa, Poisson ratio = 0.2, yield stress = 50 MPa, mass density = 2700 kg/m³, normal traction = 100 kN/m² (acting on the left edge of the rectangle), the coefficient of friction between the cut material and the cutting tool is equal to 0.1.

Figure 1. Cutting problem

The computational mesh used in the calculations (Fig. 2) consists of 1468 triangular elements and 798 nodes. 6000 material points are defined.

Figure 2. Computational mesh

Four phases of the cutting process are demonstrated in Fig. 3, drawing the material points in layers which are vertical in the initial configuration of the body.

Figure 3. Cutting process: deformation

The above computations have been made by the use of the computer program FENAP.

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