Lectures related to Biomechanical Tissues: Non-linear Constitutive Laws

Introduction to Structural Mechanics

Covers the basics of structural mechanics, including static forces, stress, strain, and structural elements like bars, cables, trusses, and beams.

Linear Elasticity: 3D

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

Normal Stresses: Internal Stress and Strain

Introduces internal stress and strain, material properties, and design considerations for axial loads and direct shear.

3D Linear Elasticity & Beams

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

Stiffness vs Strength: Deformation and Load

Covers stiffness, strength, strain, stress, and strain measurement in structural mechanics.

Generalized Hooke Law: Deformation and Stiffness Matrices

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

Introduction to Structural Mechanics: Stress and Strain

Covers stress equilibrium, strain, and constitutive equations in 2D and 3D.

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

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

Plates I: Deformation, Strain, Stress, and Wrinkling

Covers deformation, strain, stress, and wrinkling in plates under pure bending, exploring applications and bending stiffness.

Plasticity: Bending of an Elastic-Perfectly-Plastic Beam

Covers the bending of an elastic-perfectly-plastic beam and its key characteristics.

Nonlinear Beam Theory: Mechanics of Slender Structure

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

Rheology: Constitutive Law and Cats

Explores the rheology of materials, drawing parallels between cats' behavior and material properties.

Material Properties and Stress-Strain Curves

Explores material properties, stress-strain curves, stress concentration, and failure criteria in structural mechanics.

Introduction to Structural Mechanics

Covers the fundamentals of structural mechanics, including axial loading, stress, strain, and generalized uniaxial loading.

Mechanical Testing: Tensile Properties

Explains stress-strain curves and necking phenomenon in mechanical testing.

Deformations and Constraints

Covers relative deformations, flexibility matrix, stress relations, and internal forces in structures.

Deformation and Strain Tensors

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

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Orthotropic Continuum Damage Models

Explores orthotropic continuum damage models, stress-strain behavior, crack representation, and concrete simulation.