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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.
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.
This equation defines the yield surface as a circular cylinder (See Figure) whose yield curve, or intersection with the deviatoric plane, is a circle with radius , or . This implies that the yield condition is independent of hydrostatic stresses.
The normalized strain-rate and temperature in equation (1) are defined as ... is the effective plastic strain-rate of the quasi-static test used to determine the ...
The exact equation to represent flow stress depends on the particular material and plasticity model being used. Hollomon's equation is commonly used to represent the behavior seen in a stress-strain plot during work hardening: [2] =
The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain—that is, the stress–strain curve—in materials near their yield points. It is especially applicable to metals that harden with plastic deformation (see work hardening), showing a smooth elastic-plastic transition.
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.
The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations.The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form.