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An exact solution for a model of plasticity for powder materials in an un-steady plane strain process

Tuesday 6th January 2009 - 11:45 to 12:00
INI Seminar Room 1
Plastically compressible material obeying a pressure-dependent yield condition and its associated flow rule is confined between two plates which are inclined at an angle 2á and which intersect in a line. The line of intersection is a hinge and the angle á slowly decreases with increasing time. The material undergoes a plane strain deformation in planes perpendicular to the hinged line of intersection. There is no material flux at the line of intersection. Velocity and stress boundary conditions are prescribed on the plates, including the maximum friction law. The maximum friction law postulates that the friction stress is equal to the maximum possible shear stress supported by the material. The porosity is uniformly distributed at the initial instant. An exact analytic solution (the solution is reduced to subsequent calculation of several ordinary integrals) to the problem formulated is obtained by an inverse method. The qualitativebehaviour of the solution depends on the angle between the plates. In particular, a rigid zone can occur in the vicinity of the friction surface and the porosity can vanish after a certain amount of deformation. The solution is compared with the corresponding solutions based on the classical theory of rigid perfectly plastic solids and several models of incompressible pressure-dependent materials. In particular, in contrast to other solutions, the regime of sticking always occurs at the friction surface.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons