Reduced Quadrature for Isogeometric Methods in Nonlinear Solid Mechanics
Stony Brook University
A framework that improves one-point quadrature and, more generally, reduced integration in the context of isogeometric analysis for nonlinear solid mechanics is presented. The framework makes use of first- and higher-order Taylor expansion of the integrands involved in the principle of virtual work, and the analytical integration of the resulting correction terms. The formulation relies on the evaluation of stress gradients, for which the evolution equations and update algorithms are developed. Several numerical examples employing a variety of constitutive models are presented. The resulting formulations are especially effective in alleviating volumetric locking for the cases of nearly-incompressible and plastic deformations.