strainstress

Strainstress is not a standard term in classical continuum mechanics, but it is sometimes used informally to refer to the interdependent relationship between strain and stress in a material or to the study of their coupling within constitutive models. In standard terminology, stress and strain are separate physical fields linked by a material’s constitutive law.

Stress is the internal force per unit area within a material, described by the stress tensor sigma. Strain measures deformation, described by the strain tensor epsilon. For small deformations, linear elastic models relate stress and strain through constitutive equations, such as Hooke’s law for isotropic materials: sigma = lambda tr(epsilon) I + 2 mu epsilon, where lambda and mu are Lamé constants. In nonlinear and more general materials, the relationship becomes sigma = f(epsilon, history, temperature, rate), capturing effects like plasticity, viscoelasticity, and anisotropy.

The term strainstress is sometimes used to emphasize the coupled nature of the relationship or to denote the set of stress–strain relationships that characterize a material’s response. A related concept is the strain energy density W(epsilon), with the stress given by sigma = dW/depsilon in hyperelastic materials. In viscoelastic and plastic materials, the stress depends on the history of strain, requiring time-dependent or internal-variable formulations.

In practice, the fundamental data come from stress–strain curves obtained in mechanical tests such as tension, compression, or indentation. These curves inform constitutive models used in engineering design, finite element analysis, and materials research. When precision is required, standard terminology (stress, strain, constitutive model, stress–strain relationship) is preferred over nonstandard terms like strainstress.