Finite Element Modeling of Strain Localization Induced by Geometric Irregularities

The concentration of deformation into zones of intense shearing, known as shear bands, is a common phenomenon in inelastic deformation. The modeling of this phenomenon by the finite element method is hampered by a number of factors; the lack of a priori knowledge of the location, direction, and onset of the localized zones, and the inability of conventional isoparametric elements to model the high strain gradients which occur in these zones. This study develops new techniques for the finite element modeling of strain localization. Special isoparametric elements with enhanced strain fields derived from incompatible modes are developed to model the high gradients which occur during strain localization. The incompatible modes are modified to insure that the derived element stiffness satisfies the patch test, thereby preserving the convergence properties of the parent element. Use of these elements in place of conventional isoparametric elements allows equivalent results to be obtained with much less computational effort. Additionally, simple criteria predict the onset, direction, and location of the strain localization, allowing the enhanced elements to be used only when and where they are needed, further reducing the computational effort. Numerical experiments elucidate the effectiveness of the new formulation.David Taylor Research Center, Metals and Welding DivisionResearch Contracts N61533-88-C-0035 and N61533-90-K-005