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An idealized uniaxial stress-strain curve showing elastic and plastic deformation regimes for the deformation theory of plasticity There are several mathematical descriptions of plasticity. [ 12 ] One is deformation theory (see e.g. Hooke's law ) where the Cauchy stress tensor (of order d-1 in d dimensions) is a function of the strain tensor.
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness ...
Poisson's ratio of a material defines the ratio of transverse strain (x direction) to the axial strain (y direction)In materials science and solid mechanics, Poisson's ratio (symbol: ν ()) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading.
The strain can be decomposed into a recoverable elastic strain (ε e) and an inelastic strain (ε p). The stress at initial yield is σ 0 . Work hardening , also known as strain hardening , is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation.
In materials science and engineering, the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress, . This is a scalar value of stress that can be computed from the Cauchy stress tensor .
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
Other models may also include the effects of strain gradients. [3] Independent of test conditions, the flow stress is also affected by: chemical composition, purity, crystal structure, phase constitution, microstructure, grain size, and prior strain. [4] The flow stress is an important parameter in the fatigue failure of ductile materials.
In those situations the plastic strain rate is calculated in the same manner as in rate-independent plasticity. In other situations, the yield stress model provides a direct means of computing the plastic strain rate. Numerous empirical and semi-empirical flow stress models are used the computational plasticity.