FE-FORMULATION OF A NONLOCAL PLASTICITY THEORY

A nonlocal continuum plasticity theory is presented. The nonlocal fiel d introduced here is defined as a certain weighted average of the corr esponding local field, taken over all the material points in the body. Hereby, a quantity with the dimension of length occurs as a material parameter. When this so-called internal length is equal to zero, the l ocal classical plasticity theory is regained. In the present model, th e yield function will depend on a nonlocal field. The consistency cond ition and the integration algorithm result in integral equations for d etermination of the field of plastic multipliers. The integral equatio ns are classified as Fredholm equations of the second kind and the exi stence of a solution will be commented upon. After discretization, a m atrix equation is obtained, and an algorithm for finding the solution is proposed. For a generalized von Mises material, a plane boundary va lue problem is solved with a FE-method. Since the nonlocal quantities are integrals, C-0-continuous elements are sufficient. The solution st rategy is split into a displacement estimate for equilibrium and the i ntegration of constitutive equations. In the numerical simulations she ar band formation is analysed and the results display mesh insensitivi ty.