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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 ...
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 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.
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.
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.
In a molecule, strain energy is released when the constituent atoms are allowed to rearrange themselves in a chemical reaction. [1] The external work done on an elastic member in causing it to distort from its unstressed state is transformed into strain energy which is a form of potential energy.
Plastic deformation of a thin metal sheet. Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. [1] Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material.