12. Inelastic Composite Materials

Initial applications of elastic–plastic and other inelastic constitutive relations in predicting overall response of heterogeneous materials had focused on polycrystalline metals, modeled as a multiphase system of randomly orientated single crystal grains which were assigned certain yield conditions and slip mechanisms. Early work includes the slip theory of Batdorf and Budiansky (1949), the rigid-plastic single crystal system of Bishop and Hill (1951), the elastic–plastic K.B.W. model of Kröner (1961) and the self-consistent approximation by Hershey (1954) and by Budiansky and Wu (1962). Further developed by Hill (1965c, 1967) and implemented by Hutchinson (1970), the SCM approximation extended the elasticity form of the method to polycrystals and two-phase composites. That and numerous other extensions of elastic micromechanical methods to inelastic systems provide an interface with the latter. However, they often assume uniform elastic and inelastic deformation in each grain, or in the entire matrix of a particulate or fibrous composite, according to a specified constitutive relation. Since local deformation is not uniform, the overall response predicted by such theories is not supported by experiments, as shown in Sect. 12.2.2. Nonuniform local deformation was examined on composite cylinders under axisymmetric and thermal loads, and in shakedown state, by Dvorak and Rao (1976a, b), Tarn, et al. (1975). General loading effects were investigated with models which constrained only longitudinal deformation by elastic fibers (Dvorak and Bahei-El-Din 1979, 1980, 1982). More recent work, supported by numerical methods, has focused on realistic aspects of deformation mechanisms of polycrystals and composites, as reviewed by Dawson, Hutchinson, Torquato and others in a report on research trends in solid mechanics (Dvorak 1999).