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?

mp-672: CdS (Hexagonal, P6_3mc, 186)

Understanding Yield Stress Measurements

Elastic Limit - FasterCapital

Charting the complete elastic properties of inorganic crystalline compounds

Probing the frequency-dependent elastic moduli of lattice materials - ScienceDirect

Offset Yield Strength

A nonlinear stress–strain relation (solid line) characterizes most

Materials, Free Full-Text

Self-assembled three dimensional network designs for soft electronics

Elasticity in solids is caused by