truestraintruestress

Truestraintruestress is a coined term in materials science that refers to the coupled relationship between true strain and true stress during large plastic deformations. It is not a formal model, but a framing used to discuss how stress and strain evolve together under realistic loading paths where cross-sectional area changes and strain rates matter.

Definitions: True strain εt is defined as εt = ln(l/l0), where l is the instantaneous length and l0 the reference length. True stress σt is defined as σt = F/A, with F the axial force and A the current cross-sectional area. In large deformations these quantities differ from engineering (nominal) measures, and their interplay becomes important for accurate predictions.

Concept: The idea of truestraintruestress emphasizes the dynamic, path-dependent evolution of stress and strain, including effects such as necking, strain hardening, and rate sensitivity. The term highlights that changes in geometry influence stress while the material response influences further deformation.

Mathematical framework: In constitutive modeling, σt is linked to εt (and possibly its rate) via a constitutive law, such as plasticity or visco-plastic models. Analyses may track σt(εt) or σt(εt, ε̇t, T) to capture the coupled behavior.

Applications: The concept is relevant in metal forming, sheet stamping, extrusion, and finite element simulations that employ large-strain formulations to predict force, displacement, and forming limits.

See also: True stress, True strain, engineering stress, engineering strain, plasticity, large-strain mechanics.