Material model based on NURBS response surfaces

•The NURBS application aims to provide a material model with smooth response surface for biaxial strains and stresses.•The material tensor is calculated using the derivatives from the NURBS surfaces.•Material model based on NURBS is validated on classical models and the methodology is also applied for an aluminum.

The development of new and complex models is typically required to gain an understanding of advanced materials and structures. The accuracy of a structural response obtained from finite element analysis is highly dependent on the extent to which a material model represents actual material behavior. This study proposes the application of rational surfaces to provide a smooth response surface for membrane material behavior. Constitutive material tensor is calculated by using the derivatives of rational surfaces. The surfaces possess two axes of strain and an axis of stress. The methodology is validated based on classical hyperelastic models. A set of results from an aluminum testing program illustrates the response surface construction procedure from the test results. The results indicate that it is easy to implement an extension of finite element codes to include the response surface approach based on NURBS.