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The Quarterly Journal of Mechanics and Applied Mathematics 2000 53(1):73-89; doi:10.1093/qjmam/53.1.73
© 2000 by Oxford University Press
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Computation of form-invariant response functions in elasticity

P LabordeA1 and F PetitjeanA2

( A1 Mathématiques pour l'Industrie et la Physique (MIP) - CNRS/UPS/INSAT, 118 route de Narbonne, 31062 Toulouse Cedex 4, France A2 CISI, Agence de Saclay, 91190 Gif/Yvette, France )

Our aim is to determine the stress-strain response function of a given elastic material. This tensor function is considered in its canonical form derived from the form-invariance condition under the material symmetry group. Using a suitable formalism, we define specific identifiable models which are consistent with given nonlinear strain-stress diagrams. Some useful results in the theory of invariants are revisited. We especially focus on the isotropic and orthotropic symmetry properties in conjunction with typical constitutive nonlinearities, for example, difference of behaviour in tension and in compression.


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