# Computational Continuum Mechanics

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#### Computational Continuum Mechanics

Computational Continuum Mechanics as a full-fledged course is a very interesting but challenging subject. Usually, its application within the nonlinear finite element codes is not clear to the student. Computational continuum mechanics tries to bridge this gap.

Hence, it can be treated as an applied version of the continuum mechanics course. It assumes no prior exposure to continuum mechanics. The course starts with a sufficient introduction to tensors, kinematics, and kinetics. Then, the course applies these concepts to set up the constitutive relations for nonlinear finite element analysis of simple hyperelastic material.

This is followed by the linearization of the weak form of the equilibrium equations followed by discretization to obtain the finite element equations, in particular, the tangent matrices and residual vectors are discussed. Finally, the Newton-Raphson solution procedure is discussed along with line search and arc length methods to enhance the solution procedure.

INTENDED AUDIENCE: Masters student and research scholars

### What Will You Learn?

• Week 1:Introduction – origins of nonlinearity
• Week 2:Mathematical Preliminaries -1: Tensors and tensor algebra
• Week 3:Mathematical Preliminaries -2: Linearization and directional derivative, Tensor analysis
• Week 4:Kinematics – 1: Deformation gradient, Polar decomposition, Area and volume change
• Week 5:Kinematics – 2: Linearized kinematics, Material time derivative, Rate of deformation, and spin tensor
• Week 6:Kinetics – 1: Cauchy stress tensor, Equilibrium equations, Principle of virtual work
• Week 7:Kinetics – 2: Work conjugacy, Different stress tensors, Stress rates
• Week 8:Hyperelasticity - 1: Lagrangian and Eulerian elasticity tensor
• Week 9:Hyperelasticity - 2: Isotropic hyperelasticity, Compressible Neo-Hookean material
• Week 10:Linearization: Linearization of internal virtual work, Linearization of external virtual work
• Week 11:Discretization: Discretization of Linearized equilibrium equations – material and geometric tangent matrices
• Week 12:Solution Procedure: Newton-Raphson procedure, Line search, and Arc length method

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