Ceramic matrix composites (CMCs) combine the outstanding high temperature properties of monolithic ceramics with a quasi-ductile, non-brittle mechanical behaviour. CMCs are therefore perfect candidate for high-temperature energy- and transport application such as components for the combustion chamber of stationery and air-plane turbines. In view of an industrial application of CMCs, material models are needed that are as simple as possible to enable an efficient numerical implementation as well as a straightforward and unique experimental parameter determination. On the other side the damage mechanisms are quite complex, involving effects such as the anisotropic damage initiation and evolution, transverse damage effects, damage deactivation under compression as well as residual (plastic) strains, making the formulation of CMC material models for industrial application even more challenging.

In this talk, we will present a damage model for CMCs with a special focus on the formulation of the so-called damage effect. In the literature this damage effect is often derived by applying the idea of effective stress together with some equivalence requirements between damaged and undamaged materials, but sometimes the motivation also remains unclear. This approach often violates fundamental mechanical relations such as the damage growth criteria introduced in previous contributions.

Here we will follow a more rigorous way to formulate the damage effect fulfilling the damage growth criterion by making use of the representation theory of invariant tensor functions. Starting from a very general damage effect equation, we reduce the number of material parameters by applying some general mechanical requirements as well as some special material symmetry conditions. In the second part of the talk, we will use microstructural simulations to validate the model and compare the accuracy with existing models from the literature.