CONEWISE LINEAR ELASTIC-MATERIALS

Conewise linear elastic (CLE) materials are proposed as the proper gen eralization to two and three dimensions of one-dimensional bimodular m odels. The basic elements of classical smooth elasticity are extended to nonsmooth (or piecewise smooth) elasticity. Firstly, a necessary an d sufficient condition for a stress-strain law to be continuous across the interface of the tension and compression subdomains is establishe d. Secondly, a sufficient condition for the strain energy function to be strictly convex is derived. Thirdly, the representations of the ene rgy function, stress-strain law and elasticity tenser are obtained for orthotropic, transverse isotropic and isotropic CLE materials. Finall y, the previous results are specialized to a piecewise linear stress-s train law and it is found out that the pieces must be polyhedral conve x cones, thus the CLE name.