Bounds for the overall properties of composites with time-dependent constitutive law

This paper deals with the search, via variational methods, of bounds on the overall mechanical properties of composite materials, with the constitutive laws of the constituents governed by linear operators, generally non-symmetric with respect to the chosen bilinear form. For these types of problems, by virtue of a symmetrization technique derived by Tonti (1984), we provide a minimum formulation, then used to derive bounds for the overall properties of composites having a linear time-dependent constitutive law. Some of the examples already known in the literature prove to be special cases of the theory proposed here, such as the results derived by Cherkaev and Gibiansky (1994) and Milton (1990), those obtained by Rafalski (1969a, 1969b) and Reiss and Haug (1978), and those provided by Carini and Mattei (2015). •We derive a minimum formulation for the problem on the RVE of a composite with non-symmetric local constitutive law operator.•The minimum formulation so derived is used to determine bounds on the effective properties of the composite.•The general formulation here provided proves to be an extension of other well-known theories.•By suitably setting the variables involved we rederive bounds already proposed in the literature.