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We consider a class of models motivated by previous numerical studies ofwrinkling in highly stretched, thin rectangular elastomer sheets. The modelused is characterized by a finite-strain hyperelastic membrane energy perturbedby small bending energy. Without bending energy, the stored-energy density isnot rank-one convex for general spatial deformations but reduces to apolyconvex function when restricted to the plane, i.e., two-dimensionalhyperelasticity. In addition, it grows unbounded as the local area ratioapproaches zero. The small-bending component of the model is the same as thatin the classical von K\'arm\'an model. Here we prove the existence of energyminima for a general class of such models.

An Existence Theorem for a Class of Wrinkling Models for Highly Stretched Elastic Sheets