4640 - NUMERICAL MODELING OF SHEAR LOCALIZATION IN ELASTOPLASTIC MATERIALS

ABSTRUCT The work addresses the problem of describing shear localization at mesoscale level of deformation. In the planar problem the shear localization lines are represented as cuts. The stress vector is continuous at the banks of the cuts. The discontinuities of the tangential displacements are allowed by imposing boundary conditions at the cuts that allow gliding along the lines. In particular, the condition of the constancy of the shearing stress along the line is used. It is assumed that plasticity is localized at the shear lines, while outside the lines the material can be considered to be linearly elastic. The developed numerical algorithm realizes the method of finite elements on the problem-oriented meshes with double nodes, and allows studying the initiation and propagation of an arbitrary number of curvilinear cuts with arbitrary orientations. The lower boundary for the inter-cut distances is determined solely by the size of the finite elements. Thus both the number of the shear lines and the distances between the lines in the system can be arbitrary. The algorithm was applied for numerical analysis of the deformation mode in the vicinity of a circular hole. Shear localization at the system of cuts in the shape of the logarithmic spiral leads to overall plastic properties of the bulk material. It is demonstrated that for sufficiently close positioning of shear localization lines the obtained solutions are close to the classical solutions in the framework of continuous models. The suggested approach can be used to advantage to describe the intermediate state of material, between the classical elasticity with no shear lines, and continual plasticity when the shear lines are infinitely close to each other.