Journal article
Parameter Estimation of Hyperelasticity Relations of Generalized Polynomial-Type with Constraint Conditionss
Publication Details
Authors: | Hartmann, S. |
Publication year: | 2001 |
Journal: | International Journal of Solids and Structures |
Pages range : | 7999-8018 |
Volume number: | 38 |
ISSN: | 0020-7683 |
Abstract
In this article the identification of the material parameters occurring in isotropic and incompressible hyperelasticity relations of generalized polynomial-type is discussed. The underlying strain-energy function depends on the first and second invariant of the left Cauchy-Green tensor in the form of a polynomial. The material parameters are the polynomial coefficients. This leads in several identification processes to linear least-square problems. However, in most applications the parameters are not restricted to a range of validity. This article points out that the assumption of merely positive material parameters leads to a non-negative strain-energy function in any process which is underpinned by requirements with respect to gradient and convexity behaviour in certain deformations. Furthermore, it is shown that for positive material parameters no non-monotonic behaviour occurs in simple deformation processes under consideration outside the identification region. The second topic of the article deals with some identification applications of tension-torsion tests, which are carried out by Haupt and Sedlan (Archive of Applied Mechanics, 2000), taking into account the inequality constraints emphasized. Under certain assumptions, this naturally leads to new, specific models, Furthermore, it is shown that the parameter estimation becomes much less sensitive than in the unconstrained case. (C) 2001 Elsevier Science Ltd. All rights reserved.
In this article the identification of the material parameters occurring in isotropic and incompressible hyperelasticity relations of generalized polynomial-type is discussed. The underlying strain-energy function depends on the first and second invariant of the left Cauchy-Green tensor in the form of a polynomial. The material parameters are the polynomial coefficients. This leads in several identification processes to linear least-square problems. However, in most applications the parameters are not restricted to a range of validity. This article points out that the assumption of merely positive material parameters leads to a non-negative strain-energy function in any process which is underpinned by requirements with respect to gradient and convexity behaviour in certain deformations. Furthermore, it is shown that for positive material parameters no non-monotonic behaviour occurs in simple deformation processes under consideration outside the identification region. The second topic of the article deals with some identification applications of tension-torsion tests, which are carried out by Haupt and Sedlan (Archive of Applied Mechanics, 2000), taking into account the inequality constraints emphasized. Under certain assumptions, this naturally leads to new, specific models, Furthermore, it is shown that the parameter estimation becomes much less sensitive than in the unconstrained case. (C) 2001 Elsevier Science Ltd. All rights reserved.
