DISCONTINUOUS DISPLACEMENT APPROXIMATION FOR CAPTURING PLASTIC LOCALIZATION

It is proposed to capture localized plastic deformation via the inclus ion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that w hich is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a 'co nstitutive' property rather than a geometric feature of the finite ele ment mesh. In this way the spurious mesh sensitivity, which is obtaine d when the displacement approximation is continuous, can be avoided. A nother consequence is that the interfacial relation between the elemen ts is derived directly from the conventional constitutive properties o f the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontin uous bifurcation but will also serve as the tangent stiffness tensor o f the interface (up to within a scalar factor). An analytical investig ation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a 'shear' band for a general plasticity model. The significance of proper mesh alignment i s demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper conc ludes with a numerical simulation of the gradual development of a shea r band in a soil slope.