NS

#4 - Material, Structural and Tissue Mechanics

Material, Structural and Tissue Mechanics


  • The study of mechanical properties of biological tissues relies on:

    • Material Properties:

      • How a material behaves under loading conditions.

      • Mass, density, stiffness, strength

    • Structural Properties:

      • How the gross geometric configuration affects loading behaviours

        • size, shape (length, diameter)

  • Stress

    • Stress (σ) = Force / Area

      • A measure of a material’s internal resistance to axial load (either compression or tensile)

      • Measured in Pascals (Pa) = 1 N / m2 or MegaPascals = 1N/mm2

      • [1 N = 0.225 lbs force; 1 Pa = 145x10-6 lb/sq in]

  • Material failure - Stress Risers

    • Stress Riser: Discontinuity leading to uneven distribution of stresses.

    • Increases chance of tissue failure

      • “Sisceptibility to tissue failure is directly related to distribution of forces through tissue.”

    • Even distribution is optimal

    • Examples of discontinuities/stress risers??

      • Fractures (existing, past)

      • Occult tissue/fibrosis

      • Screws (current, past)

      • Tumour, infection

      • Osteotendinous junctions

  • Material Failure

  • Strain

    • Strain (ε): a measure of deformation

  • Stress-Strain Curves: Material Property

  • Stress-Strain Considerations: Toughness

    • “Toughness”: total failure energy = area under curve

  • Characteristics of an Idealized Stress-Strain Curve for Biologic Tissues: Uniaxial Loading

  • Elastic Limit (“C”)

  • Permanent Set

  • What is the physiologic/biomechanical impact of permanent set?


  • Clinical Impact of permanent set and plastic deformation??

  • Length-Tension Relationship in Muscle

What are the clinical implications of this?

How might we identify this clinically?


Clinical Implications of Plastic Deformation


  • Load-Deformation Curve: Structural Property


  • Structural Stiffness ~ A/L

  • Clinical Implications: Strength training increases Cross-sectional area of patellar tendon in cyclists

  • Material Mechanics:

    • Comparison of Structural vs Material Properties

  • Biologic Stress Strain Curves are Direction-dependent

    • Isotropic = loading characteristics/properties of a material are the same in all direction.

    • Anisotropic = loading characteristics/properties of a material are directionally dependent.

  • Biological Tissues are ANISOTROPIC

    • Exhibit a preferred direction of loading.

    • Examples include tendons, ligament, bone.

  • Effect of Anisotropy on tendon biomechanical properties

  • Reduced strain-to-failure

  • Decreased stiffness

  • Smaller region of plastic deformation (more brittle)

  • What is the clinical relevance/application of this concept?

  • Clinical Application of Anisotropicity

    • Pronation (pes planus)

      • Calcaneovalgus

    • Leads to shear forces at achilles tendon insertion

  • Ductile vs. Brittle

  • Fluid Mechanics and Friction

    • Branch of mechanics dealing with the properties and behaviour of liquids (and gases)

    • Several branches of mechanics in biology rely on principles of Fluid Mechanics:

      • Performance biomechanics

      • Biotribology: study of wear and tear on joints

      • Tissue Mechanics (disc, tendon, bone)

  • ****VERY IMPORTANT METHOD OF DISSIPATING ENERGY****

  • Friction:

    • Resistance at the interface of two bodies

    • Static Friction: from a standing position (v=0)

What is the clinical relevance/application of this equation?

  • Dynamic Friction:

  • Rheology - study of flow of matter

    • Viscosity

      • Resistance to flow of a liquid

      • Related to forces of attraction of particles within the liquid

      • Related to the material properties of the fluid

      • Fluid “internal” friction

      • Fluid “shear stiffness” or “shear stress”

  • What can alter the viscosity (internal friction) of a liquid?

    • Temperature

    • Rate of flow**

  • Inertia and Drag of Fluids

    • Fd = ½pv^2CdA

      • Fd = Drag force

      • P = density of fluid

      • V = velocity

      • C = Drag coefficient

      • A = X-sectional AREA body

  • Rate of Flow ~ Viscosity

  • Shear Stress: fluid ‘stiffness’, resistance to flow = slope of a stress-strain curve of a liquid

  • Viscosity vs Shear rate: Newtonian Vs Non-Newtonian


Clinical Conditions that alter interstitial fluid viscosity

  • Altered macromolecular structure/content (collagen, proteoglycans, glycosaminoglycans, elastin, glycation end products)

    • Age

      • Increased glycation (cross-links between collagen molecules)

      • Altered high-weight molecules in the extracellular matrix (GAG, PG)

    • Inflammation/Edema

      • Protein accumulation (fibrin, globulins)

      • Glucpsaminoglycans

    • Dehydration

      • Electrolyte imbalance - alters change density (hydophilic)

      • Concentration of remaining proteins

    • Pathological matrix remodelling

      • Fibrosis

      • Diabetic glycation

      • Degenerative diseases (cartilage, tendonosis)

  • What relevance does this slide have to injury prevention?

  • Viscoelastic Tissue Mechanics

    • Viscoelastic Tissue

      • Biological tissues are viscoelastic

        • Tendon, ligament, cartilage, bone

      • Interaction of fluid (viscous) and solid (elastic) phases

        • High friction forces at interface of fluid: elastic components

      • Friction and viscosity are important principles in understanding tissue mechanics and injury

      • ***Integriy of solid/fluid phases critical to tissue function***

        • Ehlers-danlos syndrome, Marfan Syndrome

    • RATE IF LOADING of BIOLOGIC TISSUES significantly alters internal tissue stresses because it impacts viscosity



  • Viscoelasticity

    • Elastic Tissue

  • Viscoelastic Tissue

  • Viscoelasticity - hysteresis

  • Elastic vs Viscoelastic

  • Theological Models to study Viscoelastic Tissues

    • Rheology: Study of deformation and flow of matter

      • Used to model biological (viscoelastic) tissue

      • Interrelate stress, strain, and strain rate

    • Two model components:

      • Linear spring

        • Elastic component

      • Dashpot

        • Viscous component






  • Rheological Models: Linear spring

    • Elastic properties of tissue

    • Strain Rate INDEPENDENT

  • Rheological Models: Dashpot

    • Represents ‘viscous’ component of viscoelastic tissue

    • Loading response is strain rate development

  • Rate of Loading Increases internal tissue stress

  • Viscoelastic Tissues exhibit Unique Mechanical Behaviours:

  1. Stress-Relaxation

  2. Creep




  • Biologic Tissues demonstrate:

    • Stress-Relaxation: CONSTANT DEFORMATION

  • Viscoelastic Creep:

    • Increasing strain with CONSTANT STRESS

  • Clinical Applications of Creep

  • Initial-Cycles (First-Cycle) Effect

    • Loading history (history dependence) of biologic tissues has significant effect on mechanical properties

    • Repeart Loads lead to tissue ‘fatigue’ - reduced hysteresis effect

      • More pronounced with aging and OA

    • Decreased ‘stiffness’

      • Due to plastic deformation (permanent set)

      • Decreased ability to withstand further applied forces.

    • In load-time curve

      • Upward shift (less ‘stress-relaxation’) with increasing repetition (n)

      • Steady state = ‘preconditioned’

    • Continued loading to predisposes to tissue ‘ failure’.


Tissue Loading


  • Uniaxial Loading: Poisson Effect

  • Bending: Area Moment of Inertia:

    • = resistance of a beam to bending about its neutral axis

  • Solid Cylinder


  • Hollow Cylinder

  • What is the trade-off between Bone, Mass, Radius in a solid vs hollow bone with the same Area Moment of Inertia

  1. If we keep the area moment of inertia the same, what is the difference in radius of a hollow bone vs a solid bone?

  2. In keeping area moment of inertia the same, what is the difference in mass between a hollow bone vs solid bone?

  • What is the trade-off between Mass and Radius of a solid vs hollow bone?


  • Comparison of Solid vs Hollow Bone Strength vs Mass

    • Assume bone dimensions of:

      • Radius = 10cm

      • Length = 40cm

      • Density (cortical bone) p = 1.9 g/cm^3

  • Hollow Bone:

    • What outer radius is needed to maintain area moment of inertia for hollow bone?

  • Summary: for two bones with equal area moment of inertia….

    • Solid Bone:

      • Radius = 10cm

      • Length = 40cm

      • Weight = 23.9kg

      • I = 7850cm^4

    • Hollow Bone:

      • Inner Radius = 10cm

      • Outer Radius = 11.9cm

      • Cortical Thickness = 1.9cm

      • Length = 40cm

      • Weight = 9.9kg

      • I = 7859cm^4

    • Net Weight Difference = 14 kg

    • 19% increase in radius

    • 59% lighter

  • Bending

    • Long bones mechanically considered as ‘beams’

    • Stress (both tensile and compressive) are maximal the further from the neutral axis

  • Three Point Bending




  • Failure in 3 vs 4-point Bending

  • Torsion: Helical Stress

  • Cantilever Bending:

    • = compressive force offset from the longitudinal axis creating both bending moment and compression