Finite-Element Analysis of Elastoplastic Discontinuities

In the present paper we address the question of whether localized failure due to elastoplastic bifurcation can be captured within the fixed‐mesh approach. To this end, the theoretical framework of localization analysis of elastoplastic solids is revisited, and examples of weak discontinuities are presented for an elastic perfectly plastic Huber‐Mises material with focus on plane stress. The prominent role of finite‐element design (standard displacement versus enriched formulation) and orientation (aligned versus misaligned geometry) is demonstrated first at the element level, when a single element is uniformly stretched to the yield limit and subjected to localization at all Gauss points. The weak localization test probes the directional properties of the finite element when spatial discontinuities in the strain field are to be captured. This element test is subsequently extended to the structural level and is illustrated with the eigenanalysis of a flat steel bar that is uniformly stretched to the yield limit in uniaxial tension. The effect of mesh alignment is examined with a layer of finite elements that is gradually rotated towards the spatial discontinuity of elastoplastic bifurcation analysis.