Irreducible Orthogonal Decomposition of Tensors of any finite order in dimensions 2 and 3 in Deviatoric Tensors

The goal of this thesis is to understand the deviatoric decomposition of tensors of higher order in 2 and 3 dimensions. In the first chapter an introduction to tensor algebra will be given. Chapter 2 and 3 concentrate on establishing a recursive formula for the deviatoric decomposition in 2D and 3D, respectively. This recursive formula is the key to prove by induction the existense of a deviatoric decomposition for any tensor. Useful examples will also be given at the end of each chapter.:Introduction 1. Introduction to Tensor Algebra 2. Orthogonal Irreducible Decomposition for 2D Tensors 3. Orthogonal Irreducible Decomposition for 3D Tensors 4. Conclusion Bibliography 5. Declaration of Originalit