Abstract
Conewise linear elastic (CLE) materials are proposed as the proper generalization to two and three dimensions of one-dimensionalbimodular models. The basic elements of classical smooth elasticity are extended tononsmooth (or piecewise smooth) elasticity. Firstly, a necessary and sufficient condition for a stress-strain law to becontinous across the interface of the tension and compression subdomains is established. Secondly, a sufficient condition for the strain energy function to be strictlyconvex is derived. Thirdly, the representations of the energy function, stress-strain law and elasticity tensor are obtained fororthotropic, transverse isotropic andisotropic CLE materials. Finally, the previous results are specialized to apiecewise linear stress-strain law and it is found out that the pieces must be polyhedral convex cones, thus the CLE name.
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Curnier, A., He, QC. & Zysset, P. Conewise linear elastic materials. J Elasticity 37, 1–38 (1994). https://doi.org/10.1007/BF00043417
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DOI: https://doi.org/10.1007/BF00043417