A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space

Abstract

AbstractIn this paper an inverse mechanical formulation and a Limited‐Broyden‐Flechter‐Goldfarb‐Shanno method for shape optimization are compared. Both methods deal with the determination of the undeformed shape of an hyperelastic part knowing its deformed configuration and the applied loads. We consider anisotropic hyperelastic materials that are formulated in the logarithmic strain space. Beside the theoretical aspects, we present a numerical example. We established that no difference could be found between the node coordinates on the undeformed sheets computed with both methods. However the convergence to the solution is faster for the inverse mechanical formulation compared to the L‐BFGS algorithm. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)