  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.
