Concept

Finite strain theory

Related lectures (32)

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Covers strain-displacement relations, equilibrium equations, and energy functional in nonlinear beam theory with small strain and moderate rotation.

Relative Deformation in 3D: Strain Matrix

Explores relative deformation in 3D through strain matrix and displacement gradient, emphasizing constraints, stress-strain relations, and equilibrium equations.

Nonlinear Beam Theory: Mechanics of Slender Structure

Covers strain-displacement relations, simplifications, constitutive relations, equilibrium equations, and circular rings.

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Elastic Deformation: Material Properties

Explores material properties, stress, strain, and deformation gradient in elastic deformation.

Generalized Hooke Law: Deformation and Stiffness Matrices

Explores the Generalized Hooke Law, stiffness matrices, and deformation effects in materials.

Deformation Analysis: Small Strain and Kinematics

Explores small strain theory, kinematics, and compatibility conditions in solid mechanics.

Continuum Mechanics: Forces and Deformation

Explores the laws of dynamics, stress, energy conservation, and deformation in continuum mechanics.

Nonlinear Beam Theory

Covers stress-strain relations, constitutive relations, and buckling of a circular ring in nonlinear beam theory.

Mechanics of Kirchhoff Rods I

Explores the mechanics of slender structures, introducing concepts like finite strain and finite rotation theory.

Linear Elasticity: 3D

Covers linearity between stress and strain in 3D and isotropic linear elasticity equations.

Plates: Pure Bending, Wrinkling, and Plate Buckling

Explores the mechanics of slender structures, focusing on plates in pure bending, wrinkling, and plate buckling.

Continuum Mechanics: Forces and Deformation

Covers the basics of continuum mechanics, including forces transmission, energy conservation, and body motion geometry.

Shells II: Mechanics of Slender Structure

Covers the expression of energy, dimensional reduction, equilibrium equations, and the relationship between covariant and contravariant components in shell mechanics.

Finite & Infinite Deformation: Key Distinction

Explains the geometric interpretation of eigen vectors and values in material deformation.

3D Linear Elasticity & Beams

Covers 3D linear elasticity, stress, strain, beams' behavior under loads, and torsion.

Continuum Mechanics: Kinematics and Deformation Analysis

Covers kinematics and deformation in continuum mechanics, focusing on displacement vectors and the deformation gradient tensor.

Energy Equilibrium and Newton CG Method

Covers continuum mechanics, linear elasticity, force balance, divergence, finite element discretization, energy minimization, and Newton's method.

Lagrange Representation

Covers the Lagrange representation and the continuity equation for deformations, emphasizing the possibility of large deformations.