Effective Limiting Surfaces in the Theory of Nonlinear Composites
In contrast to the extensive work on the elastic behavior of composites, only a limited number of studies for the nonlinear range have been published (for references see , ). Standard methods of successive approximation may be used in nonlinear problems of composites with random structure, linearized problems being solved at each stage. The well-known concept of secant moduli has been combined with the hypothesis of the homogeneity of the increments of the plastic or creep strains , , , , , , . Since the widely used method of average strains is capable of estimating only the average stresses in the components, its use for the linearization of functions describing nonlinear effects, e.g., strength (, ), yielding , damage accumulation (, ; see also the theories combining the damage accumulation and life-fraction rule , ), hardening , creep , and dynamic viscoplasticity  may be problematical. Due to the significant inhomogeneity of the stress fields in the components (especially in the matrix), such linearization entails physical inconsistencies, which was discussed in detail in ,  within the context of predicting the flow behavior of porous media. Alternatively, for linearizing nonlinear functions (such as the yield or strength criterion, dissipative function) physically consistent assumptions for the dependence of these functions on the second moment of stresses are employed.
KeywordsEnergy Release Rate Yield Surface Fracture Probability Interface Stress Integral Equation Method
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