Providing the fundamentals of nonlinear mechanics of continuous media. Explaining kinematics and dynamics of continuum in the case of finite deformation, general principles of continuum mechanics and the basic postulates of constitutive relationship theory.

A proper understanding and working knowledge of the matter required for developing theoretical and computational models used in the analysis of deformable bodies in domain of geometric and/or physical non-linearity.

Introduction to tensor analysis. Kinematics of continuum, material (‘Lagrangian’) and spatial (‘Eulerian’) description. Deformation gradients, deformation tensors and strain tensors. Principle values and principle directions of deformation and strain tensors. Length change, volume and area changes. Polar decomposition theorem, stretch tensors and rotation tensor. Finite and infinitesimal deformations. Motion, material derivatives and time rates. Deformation rates, spin and vorticity. Dynamics of continuum, stress tensor and concept pseudo stress. Balance principles. Reynolds' transport theorems. Conservation of mass. Balance of linear and angular momentum. The first and second Cauchy’s laws of motion. Variational principles. Principle of objectivity, objective rates. Introduction to continuum thermodynamics. Basic principle of constitutive relationships.