The upper bound theorem provides one of the major methods for analyzing metal-forming processes. However, most solutions assume the friction law that postulates that the friction stress equals a fraction of the shear yield stress. Meanwhile, Coulomb’s friction law is often required in applications. The finite element method is usually used in this case. The present paper develops a procedure for applying the upper bound theorem in conjunction with Coulomb’s friction law to evaluate the compression force in a cylinder compression. Moreover, the derivation is based on the concept of the work function, rather than the conventional approach based on the yield criterion and its associated flow rule. The two adopted work functions ensure that any physically reasonable ratios of the shear yield stress to the tensile yield stress are satisfied for materials with no strength-differential effect by choosing the parameters in these functions. Numerical results illustrate the general derivation.
Lyamina et al. (Fri,) studied this question.