Microscopic constitutive theory of stress overshoot, yielding, and strain hardening in amorphous materials

We develop a microscopic constitutive theory for the nonlinear deformation of metallic and polymer glasses based on nonaffine elasticity coupled to irreversible many-body relaxation.

The theory predicts the full stress--strain response, from linear elasticity through stress overshoot and yielding to steady plastic flow.

We show that stress overshoot originates from the competition between a nonaffine elastic instability induced by strain-driven loss of mechanical connectivity at the atomic/molecular level, and viscous dissipation associated with structural relaxation.

For polymer glasses, finite chain extensibility naturally accounts for strain hardening at large deformation.

The stretched-exponential relaxation exponent is obtained independently from stress or modulus relaxation measurements and provides the primary dynamical input to the theory.

Using a small set of physically meaningful parameters, the model quantitatively reproduces experimental stress--strain curves for metallic glasses, polycarbonate, PMMA, and epoxy resins over a broad range of strain rates.

These results establish a unified microscopic framework linking relaxation dynamics, yielding, plastic flow, and strain hardening in amorphous solids.