NortonHoffForm

NortonHoffForm is a term used in continuum mechanics to describe a class of rate-dependent constitutive forms used to model visco-plastic behavior in materials. It combines elements of the Norton creep law with a Hoff-type yield criterion, yielding a simple, widely used form for the plastic flow rule in finite element analyses of soils, rocks, polymers, and metals.

Mathematical form: The plastic strain rate is assumed to follow a power-law in the driving stress: ε̇_p = A [⟨‖σ'‖ − σ_y⟩]^n, where σ' is the deviatoric stress, ‖σ'‖ its equivalent stress, σ_y is the yield stress (potentially dependent on hardening variables), A is a material constant, and n > 0 is the rate-sensitivity exponent. The operator ⟨x⟩ denotes the positive part (x if x > 0, otherwise 0). Variants may use a different yield function f(σ) and may include non-associative flow rules or additional internal variables for hardening or damage.

Characteristics and use: The NortonHoffForm is rate-dependent and path-dependent, providing a smooth transition from elastic to plastic behavior and compatibility with standard return-mapping algorithms in finite element codes. It is often chosen for problems where creep, relaxation, or rate effects are significant.

Applications: It is widely used in geotechnical engineering, rock mechanics, and polymer science to model time-dependent yielding, creep, and visco-plastic flow, especially where there is a power-law relationship between stress and plastic strain rate.

See also: Norton creep law, Hoff yield criterion, viscoplasticity, power-law fluids, Drucker-Prager model.