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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.
Plasticity theory is based on plastic behaviour, and calculates a lower bound on the load that a structure can carry (the load at which it collapses will not be lower than that calculated). This allows a structure to be designed so it will always be able to carry the chosen magnitude of load, even if the exact way it does so is not understood.
It is a part of plasticity theory that mostly applies to ductile materials, ... Distortional component is responsible for shear deformation or change in shape.
Typical flow plasticity theories (for small deformation perfect plasticity or hardening plasticity) are developed on the basis on the following requirements: The rock has a linear elastic range. The rock has an elastic limit defined as the stress at which plastic deformation first takes place, i.e., σ = σ 0 {\displaystyle \sigma =\sigma _{0}} .
The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure.
Different deformation modes may occur under different conditions, as can be depicted using a deformation mechanism map. Permanent deformation is irreversible; the deformation stays even after removal of the applied forces, while the temporary deformation is recoverable as it disappears after the removal of applied forces.
His 1950 The Mathematical Theory of Plasticity work [3] forms the foundation of plasticity theory. Hill is widely regarded as among the foremost contributors to the foundations of solid mechanics over the second half of the 20th century. His early work was central to founding the mathematical theory of plasticity.