LADDER MODELS FOR THE CONSTITUTIVE BEHAVIOR OF HETEROGENEOUS MATERIALS WITH DAMAGE

Many materials which are used in engineering applications, such as fib er reinforced plastic composites, metal matrix composites and also mor e traditional materials such as concrete, belong to a large class of m ultiphase, inhomogeneous solids. When these components are used for st ructural applications, the evaluation of structural safety and durabil ity can only be carried out by performing numerical analyses which use a representative constitutive law of the homogenized medium, partiall y losing a detailed description of the microstructure. Naturally, the better constitutive models are those retaining a larger number of rele vant features present in the behavior at the microstructural level, th ough this attention for detail cannot be pushed beyond a limit which i s assigned by the random variations in the microgeometry. It is the in tent of this work to describe a procedure in which simplified constitu tive models for random composites can be defined from the mechanical b ehavior of each component. The derivation of the overall properties do es not rely on a linear elastic analysis of the microstructure but, as it is done in a more refined way in finite element studies, the param eters governing the interaction between the different phases are obtai ned from a purely topological description of the material. In the seco nd part of this work, attention is devoted to the constitutive behavio r of concrete, which is a binary composite with random distribution of phases. Some of the features characterizing the softening response of this material are incorporated in a new constitutive model for the ma trix phase (mortar). Finally, some results are given for a binary comp osite incorporating a softening and a linearly elastic phase for two s imple loading histories.