Using nurbsas response surface for membrane material behavior

This work proposes a NURBS for the determination of a smooth response surface relating biaxial strains and stresses from discrete test data. These NURBS surfaces are based on twoaxes of strain and one axis of stress. The constitutive material tensoris calculated with the derivatives of the NURBS surfaces and curves. The motivation of the proposed work came from the use of new materials inmembrane structures that requires complex material model stode scribe the comelx material behavior. A method for the establishment of a matrix of material coefficients from these surfaces is developed aiming its application infinite element models. There sponse surface stress-strain relation and the material matrixd erivedare compared to classical hyperelastic and Mooney-Rivlin material models. There sponse surface approa chusing NURBS all ows for aneasy implementation in anexistent FE code, requiring few changes. Asimilar application is found in the work of Bridgens and Gosling[1].This approach provides a direct correlation between stres sesands trains in the wider angeof possible stress paths the material is subject to.Curve fitting base donl east squares approximation is employed to generate NURBS surfaces for the experimental data. The advantage of this material model is that a smooth stress -strain response surface can be obtained directly from the experimental results.Ontheotherhand,inordertogenerate good NURBS surfaces the experimental data should provide anadequate point distribution. This could requireal argerange of experimental data. Wec onclude that this material model is a good alternative to conventional 1material models for complex material behavior.