Plastic limit theorems

Plastic limit theorems in continuum mechanics provide two bounds^[1] that can be used to determine whether material failure is possible by means of plastic 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.^[2]

^ Drucker, D. C.; Prager, W.; Greenberg, H. J. (1952). "Extended limit design theorems for continuous media". Quarterly of Applied Mathematics. 9 (4): 381–389. doi:10.1090/qam/45573. ISSN 0033-569X.
^ Chen, W. F.; Scawthorn, C. R. (1970). "Limit Analysis and Limit Equilibrium Solutions in Soil Mechanics". Soils and Foundations. 10 (3): 13–49. Bibcode:1970SoFou..10...13C. doi:10.3208/sandf1960.10.3_13. ISSN 1881-1418.

[DruckerPrager1952-1] Drucker, D. C.; Prager, W.; Greenberg, H. J. (1952). "Extended limit design theorems for continuous media". Quarterly of Applied Mathematics. 9 (4): 381–389. doi:10.1090/qam/45573. ISSN 0033-569X.

[ChenScawthorn1970-2] Chen, W. F.; Scawthorn, C. R. (1970). "Limit Analysis and Limit Equilibrium Solutions in Soil Mechanics". Soils and Foundations. 10 (3): 13–49. Bibcode:1970SoFou..10...13C. doi:10.3208/sandf1960.10.3_13. ISSN 1881-1418.

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