Finite Element Discretization of Spatial Discontinuities Due to Localization

The paper addresses spatial discontinuities of the velocity gradients and the ability of finite elements to capture jump conditions within a single element or within the element assembly of the solution domain. To this end the theory of localization within the classical flow theory of elastoplasticity is adopted in which spatial discontinuities of the second order develop in the field of velocity gradients due to discontinuous bifurcation. The prominent role of element design and orientation will be demonstrated on the element level, when triangular and quadrilateral elements based on linear and quadratic displacement expansions are subjected to the `Weak Localization Test' of elastoplastic bifurcation. This element test will be complemented on the structural level with the bifurcation analysis of an elastic perfectly plastic J2-panel which is subjected to uniaxial tension for which the analytic bifurcation mode is known for comparison