Plastic limit theorems in
continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles.
Continuum mec ...
provide two bounds
that can be used to determine whether material failure is possible by means of
plastic
Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding ...
deformation for a given external loading scenario. According to the theorems, to find the range within which the true solution must lie, it is necessary to find both a stress field that balances the external forces and a velocity field or flow pattern that corresponds to those stresses. If the upper and lower bounds provided by the velocity field and stress field coincide, the exact value of the
collapse load is determined.
Limit theorems
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.
Upper limit theorem:
The body (or bodies) will collapse if there is any compatible pattern of plastic deformation for which the rate of work done by the external loads exceeds the internal plastic dissipation.
References
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Continuum mechanics
Physics theorems