Parameter estimation of hyperelasticity relations of generalized polynomial-type with constraint conditions

In this article the identification of the material parameters occurring in isotropic and incompressible hyperelasticity relations of generalized polyn omial-type is discussed. The underlying strain-energy function depends on t he first and second invariant of the left Cauchy-Green tensor in the form o f a polynomial. The material parameters are the polynomial coefficients. Th is leads in several identification processes to linear least-square problem s. However, in most applications the parameters are not restricted to a ran ge of validity. This article points out that the assumption of merely posit ive material parameters leads to a non-negative strain-energy function in a ny process which is underpinned by requirements with respect to gradient an d convexity behaviour in certain deformations. Furthermore, it is shown tha t for positive material parameters no non-monotonic behaviour occurs in sim ple deformation processes under consideration outside the identification re gion. The second topic of the article deals with some identification applic ations of tension-torsion tests, which are carried out by Haupt and Sedlan (Archive of Applied Mechanics, 2000), taking into account the inequality co nstraints emphasized. Under certain assumptions, this naturally leads to ne w, specific models, Furthermore, it is shown that the parameter estimation becomes much less sensitive than in the unconstrained case. (C) 2001 Elsevi er Science Ltd. All rights reserved.