Material Model Based on Response Surfaces of NURBS Applied to Isotropic and Orthotropic Materials

A finite element analysis depends on the material model used to represent the material behavior of a physical phenomenon. Some materials expose a constitutive behavior that cannot be represented by analytical models. Complex material behavior requires the use of appropriate material models able to represent the response under a wide range of load conditions. This contribution uses a response surface based on non-uniform rational B-splines (NURBS) surfaces to define direct biaxial stress–strain relations. For the application in a finite element method, an approach is suggested to compute the matrix of material coefficients from these surfaces. The method was developed for a plane stress condition, which can be used for membranes, beams and thin plates. Two applications of this method are shown: a large strain elastoplastic material behavior with von Mises yield criterion and a linear elastic orthotropic material behavior (Münsch-Reinhardt). The advantage of this material model is that from results of experimental tests, any kind of material can be modeled by fitting the response surface parameters subjected to monotonic load. This approach might be a good alternative to model new fabrics and polymers used in membrane structures.