Suppose we have an ideal homogeneous, isotropic sheet S of rubber that we stretch in some given fashion. Using the simplest mathematical model (a 2D version of Hooke's law?), what is the potential energy it stores from this deformation? In case it simplifies things, we can assume that it is stretched over a convex surface K in 3-space, say by a mapping f: S -> K, and in such a way that no distances along S are decreased along K. I.e., for all x,y in S, we have d_K(f(x),f(y)) >= d_S(x,y). ---------------------------------------------------- Or, it may be sufficient to know the elastic potential energy density for a linear mapping L of an infinitesimal square Q in the tangent space T_x(S) onto an infinitesimal parallelogram P in the tangent space T_f(x)(K) for arbitrary x in S. (The non-decreasing distance condition can be enforced by assuming all such L satisfy D \sub L(D), where D is the unit disk in T_x(S).) --Dan ________________________________________________________________________________________ It goes without saying that .