Multiscale approach to the behaviour and damage of the heterogeneous elastic–viscoplastic materials

Both natural and man-made materials, often exhibit heterogeneous structure, depending on the scale of observation. This heterogeneous aspect acts as an important factor on their macroscopic mechanical behaviour response. One of the most reliable ways to obtain a quantitative relation between different scales is the use of the homogenisation methods. The fundamental assumption in these methods is the existence of a unit cell that is representative for the microstructure of the material under consideration, the so-called representative volume element (RVE). Modelling the mechanical behaviour of heterogeneous elastic–viscoplastic solids under finite strains framework, by using numerical homogenisation methodology is the main goal purchased in this work. Generally, the macroscopic quantities are formulated as average values of the corresponding microscopic state variables. The average of a quantity is taken over the region occupied by the unit cell [R. Hill, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids 11 (1963) 357–372]. The method which is proposed here, has been validated by comparing results of F.E. simulations with the experimental results. The composite elements consist of a polymeric continuous matrix of polymethylmethacrylate filled with rubber particles, to obtain the so-called RT-PMMA (rubber toughened PMMA). An hyper-elastic–viscoplastic description was developed to account for both finite strains and time and history dependence mechanical behaviour that exhibits most of polymers. With regard to the influence of the damage in such kinds of composites materials, the evolution of the cavitation mechanism, identified as one of the possible damage process, is also examined.