Plasticity and Constitutive Relations in Soil Mechanics

After early attempts to describe the behavior of beams under load, equations of equilibrium were first formulated correctly in 1827. Isotropic elastic behavior was described shortly after. Plasticity studies were initiated and failure conditions were established in the period 1860 to 1920. By 1900, correct equations of plasticity for soils had been proposed, and solutions had been obtained to a number of practical cases by graphical integration. Punch or footing problems were examined in the 1920s. By 1950, the mathematical bases of plasticity for metals were firmly established. Since that time, they have been extended by many investigators to account for the peculiarities of soil behavior, including yielding under hydrostatic stresses. The present state of incremental plasticity theory, necessitating the use of computers for solutions, requires consideration of three basic conditions: A yield criterion, a hardening law, and a flow rule.