A Variational Model for Micro-Cracking and Failure in Short Fiber-Reinforced Composites
Short fiber-reinforced composites made of short fibers embedded in brittle matrices (e.g., fiber-reinforced concretes) usually exhibit ductile failure, which is characterized by a stress-hardening phase of micro- and multi-cracking, followed by a stress-softening stage of micro-crack opening. Within each crack, bridging fibers enhance the strength, and improve the ductility.
The aim of the seminar is to present a variational model for the description of the failure process observed in short fibre-reinforced composites, stretched by tensile loads. The key idea of the model is to schematize the composite as a mixture of two phases, a brittle phase, representative of the matrix, and an elasto-plastic phase, accounting for the fibers reinforcement, which are coupled by elastic bonds. The model is characterized by three different internal lengths, accounting for the process zone sizes of micro- and macro- cracks and for the spacing between adjacent micro-cracks.
Different modeling levels of increasing complexity are discussed, allowing to highlight the internal lengths influence on the micro-crack patterning and on the macro-failure evolution, to establish strategies for parameters calibration, and to investigate the model ability to reproduce failure in real engineering problems.