BENG 226 Foundations of Biomechanics, Spring Quarter, 2016

Week of

Topic

Instructor

Handouts

PDF Lecture Notes

Interactive Video

Mar 29

Foundations of Biomechanics.
Introduction to Biomechanics, Deforming and Flowing Continua, Tensors and Tensor Analysis

McCulloch

Continuum Mechanics Preliminaries
Tensor Notation
Tensor Calculus

Introduction to Biomechanics
Deforming & Flowing Continua
Review of Matrices
Review of Vectors
Tensors
Tensor Analysis

Introduction|(YouTube)
Deforming & Flowing Continua|(YouTube)
Review of Matrices|(YouTube)
Review of Vectors|(YouTube)
Tensors|(YouTube)
Tensor Properties and Operations|(YouTube)

Apr 5

Stress and Kinematics.
Stress, Strain and Rate of Deformation.

McCulloch

Kinematics Summary

Stress
Cauchy's Formula
Stress Equilibrium
Equilibrium Derivation
Deformation Gradient
Polar Decomposition
Strain
Flow

Stress
Cauchy's Formula
Stress Equilibrium
Equilibrium Derivation
Deformation Gradient
Polar Decomposition
Strain
Flow
Strain and Flow Examples

Apr 12

Governing Laws.
Conservation Laws and Constitutive Laws for Solids and Fluids.

McCulloch

Conservation Laws

Conservation of Mass
Conservation of Momentum
Conservation of Energy
Newtonian Viscous Fluids
Hookean Elastic Solids

Conservation of Mass
Conservation of Momentum
Conservation of Energy
Newtonian Viscous Fluids
Hookean Elastic Solids

Apr 19

Analysis of Blood Flow.
Navier-Stokes equation, Poiseuille flow, Flow in elastic vessels, Pulsatile flow

McCulloch

Handout

Navier-Stokes equations
Arterial Blood flow
Flow in elastic vessels and Pulsatile flow

Navier-Stokes equations
Arterial Blood flow
Flow in elastic vessels and Pulsatile flow

Apr 26

Soft Tissue Mechanics.
Finite deformations. Hyperelasticity.

McCulloch

Handout
Hyperelasticity Handout

Soft Tissue Mechanics
Finite Deformation Elasticity

Soft Tissue Mechanics
Finite Deformation Elasticity

May 3

Finite Element Modeling of Tissue Mechanics. Finite element approximations. Finite element basis functions. Boundary conditions. Non-homogeneous strain analysis.

McCulloch

Introduction to the Finite Element Method
More on the Finite Element Method

Introduction to the Finite Element Method

May 10

Nonlinear Stress Analysis
Solving nonlinear boundary value problems in soft tissue elasticity.

McCulloch

FE Stress Analysis
Continuity documentation/Strain tutorial

May 17

Growth and Remodeling
Modeling volumetric finite growth and remodeling. Residual stresses. Hypertrophy and mechanotransduction mechanisms

McCulloch

Rodriguez et al, 1994

Mechanics of Growth and Remodeling

May 24

Muscle Mechanics
Striated muscle structure and mechanics. Excitation-contraction coupling. Molecular motors. Crossbridge models.

McCulloch

Muscle Mechanics
The Crossbridge model

May 31

Cardiac Mechanics
Cardiac muscle structure and function. Modeling cardiac excitation-contraction coupling. Ventricular pump function.

McCulloch

Cardiac Muscle
Ventricular Mechanics

Jun 7th

FINAL EXAM (Closed Book and notes)
3:00-6:00 pm PFBH room 161