Isogeometric analysis of nearly incompressible large strain plasticity

• We study the performance of IsoGeometric Analysis for large strain incompressible plasticity.
• High order standard NURBS elements exhibit spurious stresses and F-bar NURBS elements produce good results.
• Displacements and reaction forces are misleading measures of element performance.
• Mesh locking is not a relevant issue for higher order NURBS.

We study the behavior of NURBS-based Isogeometric Analysis on problems of large-deformation plasticity. We evaluate the performance of standard NURBS elements and elements based on the F¯ formulation of Elguedj et al. (2008) [1]. Our experience shows that standard measures of evaluation employed in the literature, namely, displacements at selected locations and graphs of reaction forces versus displacements, are often misleading metrics in problems of plasticity. On the other hand, stress distributions, in the form of contour plots, are, in our experience,revealing measure of element performance. We also determine that the concept of “mesh locking”, which has dominated investigations of low-order elements, is not a relevant issue for higher-order NURBS elements for problems of large-deformation plasticity. However, standard higher-order NURBS elements of type Qk, of continuity class Ck-1,k⩾2Ck-1,k⩾2, typically exhibit spurious stress oscillations, whereas the F¯ elements of type Qk/Qk-1 produce good results in all cases.