On Hyperelastic Crease

Abstract

We present analyses of crease-formation and stability criteria for incompressible hyperelastic solids. A generic singular perturbation over a laterally compressed half-space creates a far-field eigenmode of three energy-release angular sectors separated by two energy-elevating sectors of incremental deformation. The far-field eigenmode braces the energy-release field of the surface flaw against the transition to a self-similar crease field, and the braced-incremental-deformation (bid) field has a unique shape factor that determines the creasing stability. The shape factor, which is identified by two conservation integrals that represent a subsurface dislocation in the tangential manifold, is a monotonically increasing function of compressive strain. For Neo-Hookean material, when the shape factor is below unity, the bid field is configurationally stable. When the compressive strain is 0.356, the shape factor becomes unity, and the bid field undergoes a higher-order transition to a crease field. At the crease-limit point, we have two asymptotic solutions of the crease-tip folding field and the leading-order far field with two scaling parameters, the ratio of which is determined by matched asymptotes. Our analyses show that the surface is stable against singular perturbation up to the crease limit point and becomes unstable beyond the limit. However, the flat state is metastable against a regular perturbation between the crease limit point and wrinkle critical point, which is a first-order instability point. We introduced a novel finite element method for simulating the bid field with a finite domain size. For Gent model, the strain-stiffening alters the shape factor dependence on the compressive strain, raising crease resistance. The new findings in crease mechanisms will help study ruga mechanics of self-organization and design soft-material structures for high crease resistance.