| Abstract: | 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 d?/dλ to be constant. We also derive a semi-analytic method for integrating both types of constitutive law which assumes that the quantities d?/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. |
