Las teorías de la plasticidad sobre el flujo con grandes deformaciones suelen comenzar con uno de los siguientes supuestos:.

El primer supuesto se utilizó ampliamente para simulaciones numéricas del comportamiento de los metales, pero gradualmente ha sido reemplazado por la teoría multiplicativa.

Kinematics of multiplicative plasticity

The concept of multiplicative decomposition of the strain gradient into elastic and plastic parts was first proposed independently by B. A. Bilby"),[3]​ E. Kröner,[4]​ in the context of crystal plasticity") and extended to continuous plasticity by Erasmus Lee.[5]​ The decomposition assumes that the total strain gradient (F) can be decomposed as:.

where F is the elastic (recoverable) part and F is the plastic (unrecoverable) part of the deformation. The space velocity gradient is given by.

where an overlapping point indicates a derivative with respect to time. The above can be written as.

The quantity.

it is called plastic velocity gradient and is defined in an intermediate stress-free configuration (incompatible&action=edit&redlink=1 "Compatibility (mechanical) (not yet drafted)")). The symmetric part (D) of L is called plastic strain rate, while the antisymmetric part (W) is called plastic twist:.

Typically, plastic spin is ignored in most descriptions of finite plasticity.

Elastic regime

Elastic behavior in the finite strain regime is usually described by a hyperelastic model. Elastic strain can be measured using a right elastic Cauchy-Green strain tensor defined as:.

The logarithmic or Hencky strain tensor can then be defined as.

The symmetrized Mandel stress tensor") is a convenient stress measure for finite plasticity and is defined as.

where S is the second Piola-Kirchhoff stress"). A possible hyperelastic model in terms of logarithmic deformation is [6]​.

where W is a strain energy density function, J = det(F), μ is a modulus and dev indicates the deviatoric part of a tensor.

The application of the Clausius-Duhem inequality") leads, in the absence of plastic spin, to the finite strain flow rule.

Loading-unloading conditions

It can be shown that the loading and unloading conditions are equivalent to the Karush-Kuhn-Tucker conditions.

The consistency condition is identical to that of the case of small deformations.

Las teorías de la plasticidad sobre el flujo con grandes deformaciones suelen comenzar con uno de los siguientes supuestos:.

El primer supuesto se utilizó ampliamente para simulaciones numéricas del comportamiento de los metales, pero gradualmente ha sido reemplazado por la teoría multiplicativa.

Kinematics of multiplicative plasticity

The concept of multiplicative decomposition of the strain gradient into elastic and plastic parts was first proposed independently by B. A. Bilby"),[3]​ E. Kröner,[4]​ in the context of crystal plasticity") and extended to continuous plasticity by Erasmus Lee.[5]​ The decomposition assumes that the total strain gradient (F) can be decomposed as:.

where F is the elastic (recoverable) part and F is the plastic (unrecoverable) part of the deformation. The space velocity gradient is given by.

where an overlapping point indicates a derivative with respect to time. The above can be written as.

The quantity.

it is called plastic velocity gradient and is defined in an intermediate stress-free configuration (incompatible&action=edit&redlink=1 "Compatibility (mechanical) (not yet drafted)")). The symmetric part (D) of L is called plastic strain rate, while the antisymmetric part (W) is called plastic twist:.

Typically, plastic spin is ignored in most descriptions of finite plasticity.

Elastic regime

Elastic behavior in the finite strain regime is usually described by a hyperelastic model. Elastic strain can be measured using a right elastic Cauchy-Green strain tensor defined as:.

The logarithmic or Hencky strain tensor can then be defined as.

The symmetrized Mandel stress tensor") is a convenient stress measure for finite plasticity and is defined as.

where S is the second Piola-Kirchhoff stress"). A possible hyperelastic model in terms of logarithmic deformation is [6]​.

where W is a strain energy density function, J = det(F), μ is a modulus and dev indicates the deviatoric part of a tensor.

The application of the Clausius-Duhem inequality") leads, in the absence of plastic spin, to the finite strain flow rule.

Loading-unloading conditions

It can be shown that the loading and unloading conditions are equivalent to the Karush-Kuhn-Tucker conditions.

The consistency condition is identical to that of the case of small deformations.