Restrictions to the Energy Density in Energetic Models of Carbon Fiber Reinforced Carbon

Abstract

In this contribution an energetic model for multi-phase materials is developed describing the influence of microstructure on different length scales as well as the evolution of phase changes. Restrictions on the energy functional are discussed. In such a nonconvex framework, interfacial contributions serve for relaxing the total energy. Such models can be applied to describe the macroscopic material properties of carbon fiber reinforced carbon where phase transitions between regions of different texture of the carbon matrix are observed on a nanoscale as well as columnar microstructures on microscale.

Energy functionals for microstructured multi‐phase materials

“…Moreover, the interface energy ε inter , the elastic energy density W and the dissipation distance have to be defined. First choices for ε inter and W have been proposed in [5]: there, sharp interfaces have been assumed between the different phases and a constant surface tension dependent on the adjacent phases as well as a non-convex three-well contribution to the elastic energy density. For such models, no analysis seem to exist up to date.…”

“…Assuming a given solution of the thermal conductivity equation, the first step in extending energetic models to thermomechanical problems has been recently proposed [4]. An application of modeling the macroscopic behaviour of CFC under thermomechanical load is presented in [5].…”