Nonlinear Composites

When the investigations are conducted with the aim of determining effective nonlinear elastic parameters, a concept of secant modulus is used. But at each step the linearized problem is solved with the help of the MEFM which has none of the disadvantages of Mori-Tanaka’s method (for details see Chapter 8). In the modified approach the nonlinear dependence of elastic properties on the strain field is taken into account and one assumes that the effective strain for the phase being considered equals the second moment of strains averaged over this phase [129], [130], [1058]. In doing so the exact estimates [602], [860] (as distinct from those contained in [80], [910], [1075]) in relation to the average in volume of anisotropic components single-point second moments of the stress fields are used. A similar approach was employed previously in [129], [130] for estimating the overall moduli of nonlinear elastic composites. Finally, the application of the proposed theory to the case of different problems will be considered (following Buryachenko [131]): the effective moduli, the yield surface, the power-law creep response and the elastoplastic deformation of composites with compressible and incompressible matrix are predicted. The approach described here has been applied for simulating the monotonic and cyclic thermomechanical behavior of a multiphase model material. Onset of plastic deformations, overall hardening behavior, shake down, and ratchetting are studied.