Integration of Tresca and Mohr–Coulomb constitutive relations in plane strain elastoplasticity

This paper considers the problem of integrating the constitutive relations for Tresca and Mohr–Coulomb materials under conditions of plane strain. In the case of a Tresca material, we show that the constitutive law may be integrated exactly by assuming the strain rates dϵ/dλ to be constant. We also derive a semi‐analytic method for integrating both types of constitutive law which assumes that the quantities dϵ/dλ are constant. This approach is motivated by the fact that the exact variation of the strains during a time interval is unknown and leads to a single non‐linear equation in λ which can be solved efficiently to yield the unknown stresses. Finally, we compare the results from the analytic and semi‐analytic methods with those from a variety of numerical integration schemes.