Abstract
Whenever effective material responses are determined, there is a degree of microscale uncertainty. For example in the case of overall isotropic responses, we have uncertainties in the effective constitutive parameters, such as μ* + δμ* and κ* + δκ*. In this communication bounds on the resulting uncertainty in a class of polyconvex macroscale finite deformation stored energy functions, which employ the uncertain material parameters, are determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Ball, J. M. (1977). Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63, 337–403.
Ciarlet, P. G. (1993). Mathematical elasticity. Elsevier.
Ogden, R. W, (1999). Nonlinear elasticity. Dover reissue.
Hill, R. (1952). The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. (Lond.) A65, 349–354.
Voigt, W. (1889). Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper. Wied. Ann. 38, 573–587
Reuss, A. (1929). Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. angew. Math. Mech. 9, 19–58.
Hashin, Z. and Shtrikman, S. (1962). On some variational principles in anisotropic and nonhomogeneous elasticity. Journal of the Mechanics and Physics of Solids. 10, 335–342.
Hashin, Z. and Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids. 11, 127–140.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zohdi, T.I. Propagation of Microscale Material Uncertainty in a Class of Hyperelastic Finite Deformation Stored Energy Functions. International Journal of Fracture 112, 13–17 (2001). https://doi.org/10.1023/A:1022672021519
Issue Date:
DOI: https://doi.org/10.1023/A:1022672021519