Bounding the Effective Yield Behavior of Mixtures

The yield surface of a mixture of elastic/plastic materials is examined through mathematical techniques. A variational principle is derived from the local yield behavior (which may be anisotropic) and is used to generate upper bounds on the effective yield surface of the mixture. These bounds effectively reduce estimates on the nonlinear problem of yield to estimates on the elastic properties of mixtures oflinearly elastic“reference materials.” Upper bounds obtained from the variational principle are shown to be tighter than previous bounds, provided one uses a linear bound which is tighter than the arithmetic-mean bound. Finally, explicit bounds are derived for the yield surface of anisotropic mixtures of two von Mises type materials when one phase takes the form of ellipsoidal inclusions embedded in a matrix of the second phase, and difficulties arising in applications to polycrystals are discussed.