Homogenisation of heterogeneous viscoplastic materials.

Heterogeneous materials have been used extensively in the past few decades, since their mechanical properties, such as strength, stiffness and toughness are being improved continuously. Experimental work has clearly demonstrated the significant influence of the micromechanical phenomena on the resulting overall macroscopic deformation behaviour of the material. Nevertheless, more fundamental studies are needed for a better understanding of the deformation behaviour of these materials. Relations between the microstructural phenomena and the macroscopic deformation behaviour are indispensable when predicting macroscopic properties from the microstructure. Homogenisation provides a way in determining this relation. The homogenisation process aims at replacing the heterogeneous material with an equivalent continuum model, for which a closed-form constitutive equation is derived. Assuming statistical homogeneity of the heterogeneous material, it is possible to identify an element whose mechanical behaviour is representative for the heterogeneous material as a whole, a so-called representative volume element (RVE). In the homogenisation method proposed in this paper, finite element calculations are performed on the microstructural level, and therefore no simplifying assumptions concerning the microstructure of the material are required. First, the proposed homogenisation strategy is validated numerically. Here, the obtained homogenised values are used to simulate various loading histories on a perforated plate. The obtained global behaviour is confronted with direct finite element calculations on the complete heterogeneous structure. From this, we have concluded that the proposed homogenisation method results in a fairly accurate and time-efficient prediction of the mechanical behaviour of the heterogeneous structure. Experiments have been used as well to evaluate the method. Thermoplastic sheets with an arbitrary distributed hole pattern, are subjected to tensile and shear loadings. First, the material is characterised by standard techniques. Then, the RVE is defined, after which an effective parameter set for this RVE is obtained. This parameter set is then used to model the mechanical behaviour of the experimentally tested perforated plate