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Mathematics and Mechanics of Solids
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Frame-Invariant Polyconvex Strain-Energy Functions for Some Anisotropic Solids

David J. Steigmann

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

We present a set of simple sufficient conditions for the polyconvexity and coercivity of strainenergy functions for transversely isotropic and orthotropic elastic solids. The formulation is based on appropriate function bases for the right stretch tensor in the polar decomposition of the deformation gradient and furnishes numerical analysts with a priori existence criteria for boundary-value problems.

Key Words: Finite elasticity • anisotropy • convexity

Mathematics and Mechanics of Solids, Vol. 8, No. 5, 497-506 (2003)
DOI: 10.1177/10812865030085004
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J. Merodio and K. R. Rajagopal
On Constitutive Equations For Anisotropic Nonlinearly Viscoelastic Solids
Mathematics and Mechanics of Solids, April 1, 2007; 12(2): 131 - 147.
[Abstract] [PDF]