Effect of Periodic Boundary Conditions on Elastic Properties of Unidirectional Composites

Synopsis: Over the last three decades, the growth of composite materials as an engineering material of choice for design and construction in automobile and aero industries has been remarkable. Their many design advantages like weight savings, ease of production, recyclability, etc are amongst the many reasons for this growth. To encourage widespread adoption of composite materials in other areas of precision engineering, detailed studies of their mechanical behaviour for different loading histories must be carried out. As well as experimental data sets of these materials, the modern trend in engineering is the development of predictive tools for confirming experimental findings. Finite element modelling (FEM) is one of such numerical tools for exploring microscale properties of composites. An FEM tool requires a Representative Volume Element (RVE) of the test material and on this is based any numerical predictions.

A key component of a numerical scheme is choice of relevant boundary conditions for simulating the loading cases imposed on real composite structures. Typical implementations of boundary conditions are: (a) Dirichlet Implementation - a displacement based boundary condition (b) Neumann Implementation – a traction/force based boundary condition (c) Periodic Boundary conditions (d) Combinations of Dirichlet and Neumann Implementations.

This project is based on the Periodic Boundary Conditions which require that homogeneous deformation of corresponding parallel faces/surfaces of a chosen RVE. There are different approaches for imposing the Periodic Boundary Conditions on RVEs and these include: (a) Kouznetsova none-to-node coupling (b) Gosz Node-to-node coupling (c) Tyrus Polynomial Interpolation and (d) Ludovic Polynomial Interpolation approaches. These strategies have been made popular by the authors who published them and it is unknown which of them is the best. It is necessary to investigate the effect of a chosen PBC implementation in the understanding of predicted effective properties of a chosen unidirectional fibre reinforced polymeric composite.

Objectives: This project is aimed at development of  a numerical framework incorporating four implementations of periodic boundary conditions on a given RVE. It is based on 2D RVEs of a continuous fibre reinforced polymeric composite. Such RVEs will be used within a simple FEM model of the composite to determine their elastic properties. Results will be compared with experiments. The challenge in this project will be creating numerical algorithms based on the four implementations and running parametric studies based on these to assess their effect on the elastic and constitutive response of the composite.

Prerequisites: Students choosing this topic should have a good understanding of the theory of mechanics of materials. This project will particularly suit students who enjoy programming in MATLAB and Python as well as show a willingness to learn the use of ABAQUS finite element solver.

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