Parameter effects in linear embedding analysis

Abstract

There are different major strategies in continuum micromechanics such as mean field approaches, periodic microfield approaches, bounding methods, windowing methods and embedding methods. The most typical application for these is the material characterization of composites, simulating the response of the material under simple loading. This thesis focuses on studying the embedded cell method because it is the least well studied of the above approaches. Embedding is based on investigating a two- or multi-phase volume element (the core) that is surrounded by a homogeneous material to which the loads are applied. The idea behind this thesis is to better understand the effects of a number of modelling parameters relevant to embedding analysis. Only linear elastic behaviour of the composite materials is considered and simple load cases are used to get the characterization of the composites. Several composites reinforced by continuous aligned fibers were simulated during the thesis, with fiber volume fractions ranging from 15% to 60% and between 5 to 25 fibers per volume element. Three modelling parameters were studied. First, attention was focused on the effects of the fiber volume fraction and the material parameters prescribed to the embedding material. Next, the influence of the size of the embedding region was studied and, finally, specific shapes of the core were considered. The comparison of predictions was done, one the one hand, in terms of the macroscopic properties of the full model, the core and the embedding region, the Young's modulus, shear modulus, Poisson's number and coeffcient of thermal expansion being compared. On the other hand, the microscopic stress fields evaluated with the finite elements software ABAQUS were compared. To conclude, the results of this study provide new information to better comprehend how embedding models work and how the different parameters affect their results.