2023/02/14 by Timothy J. Healey, Healey, Timothy J.
Engineering · #Advanced Materials and Mechanics #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2302.07327
openalex publication_date 2023/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. Without bending energy, the stored-energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to the plane, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small-bending component of the model is the same as that in the classical von Kármán model. Here we prove the existence of energy minima for a general class of such models.