LADDER MODELS FOR THE CONSTITUTIVE BEHAVIOR OF HETEROGENEOUS MATERIALS WITH DAMAGE

Many materials which are used in engineering applications, such as fiber reinforced plastic composites, metal matrix composites and also more traditional materials such as concrete, belong to a large class of multiphase, inhomogeneous solids. When these components are used for structural applications, the evaluation of structural safety and durability can only be carried out by performing numerical analyses which use a representative constitutive law of the homogenized medium, partially losing a detailed description of the microstructure. Naturally, the better constitutive models are those retaining a larger number of relevant features present in the behavior at the microstructural level, though this attention for detail cannot be pushed beyond a limit which is assigned by the random variations in the microgeometry. It is the intent of this work to describe a procedure in which simplified constitutive models for random composites can be defined from the mechanical behavior of each component. The derivation of the overall properties does 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 parameters governing the interaction between the different phases are obtained from a purely topological description of the material. In the second part of this work, attention is devoted to the constitutive behavior 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 matrix phase (mortar). Finally, some results are given for a binary composite incorporating a softening and a linearly elastic phase for two simple loading histories.