condensed matter - Why the elastic limit of solid corresponds to a

In all the force-extension graphs I saw, the elastic limit corresponds to a larger extension than the limit of proportionality. Is this true for all cases? If so, what are the underlying reasons?

Elasticity of Solids

Plasticity (physics) - Wikipedia

Mathematics, Free Full-Text

PDF) A Brief Review of Elasticity and Viscoelasticity

Fast dynamics and high effective dimensionality of liquid fluidity

Elasticity of Solids

Condensed matter physics - Wikipedia

Elastic Limit - FasterCapital

Elasticity of Solids

What Is Elastic Limit? Definition, Importance, How It Works, and Examples

Instability in dynamic fracture and the failure of the classical theory of cracks