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In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation , from which the stress and strain can be determined (see tensile testing ).
In the above definitions of engineering stress and strain, two behaviors of materials in tensile tests are ignored: the shrinking of section area; compounding development of elongation; True stress and true strain are defined differently than engineering stress and strain to account for these behaviors. They are given as
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics , stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other ...
The Considère construction for prediction of the onset of necking, expressed as the gradient of the (true) stress-strain curve falling to the true stress, for a material conforming to the Ludwik-Hollomon relationship, with the parameter values shown. The condition can also be expressed in terms of the nominal strain:
The nominal stress = is the transpose of the first Piola–Kirchhoff stress (PK1 stress, also called engineering stress) and is defined via = = = or = = = This stress is unsymmetric and is a two-point tensor like the deformation gradient.
This type of stress may be called (simple) normal stress or uniaxial stress; specifically, (uniaxial, simple, etc.) tensile stress. [13] If the load is compression on the bar, rather than stretching it, the analysis is the same except that the force F and the stress σ {\displaystyle \sigma } change sign, and the stress is called compressive ...
True strain, also known as logarithmic strain or natural strain, provides a more accurate measure of large deformations, such as in materials like ductile metals [3] ´ = (/) = (+) The compressive strength therefore corresponds to the point on the engineering stress–strain curve (,) defined by = =,