Plasticity theory

Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. 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.

In flow plasticity theories it is assumed that the total strain in a body can be decomposed additively (or multiplicatively) into an elastic part and a plastic part. The elastic part of the strain can be computed from a linear elastic or hyperelastic constitutive model. However, determination of the plastic part of the strain requires a flow rule and a hardening model.

Typical flow plasticity theories (for small deformation perfect plasticity or hardening plasticity) are developed on the basis of the following requirements:

The above requirements can be expressed in three dimensions as follows.

In metal plasticity, the assumption that the plastic strain increment and deviatoric stress tensor have the same principal directions is encapsulated in a relation called the flow rule. Rock plasticity theories also use a similar concept except that the requirement of pressure-dependence of the yield surface requires a relaxation of the above assumption. Instead, it is typically assumed that the plastic strain increment and the normal to the pressure-dependent yield surface have the same direction, i.e.,

where ${\displaystyle d\lambda >0}$ is a hardening parameter. This form of the flow rule is called an associated flow rule and the assumption of co-directionality is called the normality condition. The function ${\displaystyle f}$ is also called a plastic potential.

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