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Week of
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Topic
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Instructor
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Handouts
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PDF Lecture Notes
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Interactive Video
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Mar 29
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Foundations of Biomechanics.
Introduction to Biomechanics, Deforming and Flowing Continua, Tensors and Tensor Analysis
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McCulloch
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Continuum Mechanics Preliminaries
Tensor Notation
Tensor Calculus
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Introduction to Biomechanics
Deforming & Flowing Continua
Review of Matrices
Review of Vectors
Tensors
Tensor Analysis
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Introduction|(YouTube)
Deforming & Flowing Continua|(YouTube)
Review of Matrices|(YouTube)
Review of Vectors|(YouTube)
Tensors|(YouTube)
Tensor Properties and Operations|(YouTube)
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Apr 5
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Stress and Kinematics.
Stress, Strain and Rate of Deformation.
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McCulloch
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Kinematics Summary
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Stress
Cauchy’s Formula
Stress Equilibrium
Equilibrium Derivation
Deformation Gradient
Polar Decomposition
Strain
Flow
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Stress
Cauchy’s Formula
Stress Equilibrium
Equilibrium Derivation
Deformation Gradient
Polar Decomposition
Strain
Flow
Strain and Flow Examples
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Apr 12
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Governing Laws.
Conservation Laws and Constitutive Laws for Solids and Fluids.
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McCulloch
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Conservation Laws
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Conservation of Mass
Conservation of Momentum
Conservation of Energy
Newtonian Viscous Fluids
Hookean Elastic
Solids
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Conservation of Mass
Conservation of Momentum
Conservation of Energy
Newtonian Viscous Fluids
Hookean Elastic Solids
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Apr 19
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Analysis of Blood Flow.
Navier-Stokes equation, Poiseuille flow, Flow in elastic vessels, Pulsatile flow
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McCulloch
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Handout
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Navier-Stokes equations
Arterial Blood flow
Flow in elastic vessels and Pulsatile flow
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Navier-Stokes equations
Arterial Blood flow
Flow in elastic vessels and Pulsatile flow
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Apr 26
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Soft Tissue Mechanics.
Finite deformations. Hyperelasticity.
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McCulloch
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Handout
Hyperelasticity Handout
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Soft Tissue Mechanics
Finite Deformation Elasticity
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Soft Tissue Mechanics
Finite Deformation Elasticity
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May 3
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Finite Element Modeling of Tissue Mechanics. Finite element approximations. Finite element basis functions. Boundary conditions. Non-homogeneous strain analysis.
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McCulloch
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Introduction to the Finite Element Method
More on the Finite Element Method
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Introduction to the Finite Element Method
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May 10
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Nonlinear Stress Analysis
Solving nonlinear boundary value problems in soft tissue elasticity.
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McCulloch
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FE Stress Analysis
Continuity documentation/Strain tutorial
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May 17
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Growth and Remodeling
Modeling volumetric finite growth and remodeling. Residual stresses. Hypertrophy and mechanotransduction mechanisms
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McCulloch
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Rodriguez et al, 1994
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Mechanics of Growth and Remodeling
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May 24
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Muscle Mechanics
Striated muscle structure and mechanics. Excitation-contraction coupling. Molecular motors. Crossbridge models.
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McCulloch
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Muscle Mechanics
The Crossbridge model
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May 31
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Cardiac Mechanics
Cardiac muscle structure and function. Modeling cardiac excitation-contraction coupling. Ventricular pump function.
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McCulloch
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Cardiac Muscle
Ventricular Mechanics
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Jun 7th
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FINAL EXAM (Closed Book and notes)
3:00-6:00 pm PFBH room 161
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