T-splines for isogeometric analysis of two-dimensional nonlinear problems

Nonlinear behaviors are commonplace in many complex engineering applications, e.g., metal forming, vehicle crash test and so on. This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems, to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials. By applying the adaptive refinement capability of T-splines during the iteration process of analysis, the numerical simulation accuracy of the nonlinear model could be increased dramatically. The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes. In addition, T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features. Several numerical examples have been tested to validate the accuracy and convergence of the proposed method. The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.