Nonlocking beam finite elements for use with inelastic material models

A locking-assessment procedure for shear-deforming beam elements is propose d that is suitable for inelastic material behavior. By way of example, the procedure is used to motivate the formulation of a nonlocking element in th e context of an isotropic but inelastic (e.g., J(2)-flow theory with isotro pic hardening) constitutive model. In particular, constraints among the nod al degrees of freedom (dof) are introduced to ensure uniform, non-shear-loc king element behavior. The locking-assessment procedure distinguishes betwe en locking, stiffening, and uniform element behavior in the thin-beam limit by comparing the dimensions of the function spaces containing the bending strains, both in the presence and absence of the thin-beam constraints. Int er-dof constraints that lead to uniform behavior are seen to arise naturall y from this element-assessment procedure. Also, a novel cross-sectional num erical integration scheme is presented that is highly accurate in relation to the number of stress-sampling points on the cross section.