Advanced materials (e.g., composites) are subject to stresses and strains at the microscopic, mesoscopic, and macroscopic level. This extends to components, especially if manufactured with complex methods, such as additive manufacturing. The determination of mechanical properties of such materials and of the life duration of such components is particularly important, but also extremely challenging, in view of their microstructural complexity. Typical examples are composite materials (especially multi-phase) and functional materials such as those for filter applications. For components it is of great interest to determine (and possibly measure) internal stresses in a non-destructive manner, in order to connect the internal stresses with their performance and lifetime.

One aspect of relevance is the multi-scale character of the problem. For example, in composite materials internal stresses do not only appear at macro level (due to machining, heat treatments, operating conditions, etc.) but also at micro-level, i.e., among the different constituent phases. Those stresses are a consequence of the microstructure; they also evolve under applied loads (thermal, mechanical chemical, etc.), and need to be monitored. Diffraction methods are particularly suited to tackle the non-destructive determination of internal stresses, and micromechanical methods are available to calculate them analytically. Both methods can cast further light onto the mechanisms of load partition among the different constituents.

The present course is targeted at systematically rationalizing the experimental and theoretical aspects of stress analysis in complex materials such as multi-phase composites (thereby including pores as a phase).

Classic experimental determination of mechanical and thermal properties through uniaxial, bending, instrumented indentation tests, impulse excitation, and thermal conductivity will also be treated. It will be shown how thermal properties are connected to mechanical behavior, and which additional information they can yield, especially under the light of the so-called cross property connections in materials.

Several micromechanical schemes will be treated, and advanced applications of those micromechanical methods will be made by calculation of stress partition in multiphase materials and non-linearity in porous ceramics and rocks, as well as by determination of equivalent elastic constants in multi-phase materials.

In parallel, different numerical approaches will be covered, the main emphasis being put on Finite Element based methods, with special attention being given to issues connected to evaluating local stress and strain fields.

Both analytical and numerical methods will be merged into the so-called Inverse Analysis (IA), which aims at extracting information from experimental data through simulation and modeling (i.e. minimization of discrepancy between experimentally measured quantities and their computed counterpart).

It will be pointed out how models give a framework to assess quantities that are not directly measurable within the experiment by measuring something else, which is more accessible.

The target audience are mainly Mechanical Engineers and Materials Scientists, but Physicists and Geologists may well use the material dealt with.