Intro to Tissue Mechanics

forces and moments have…

direction & magnitude

forces that do not align with the center of mass

torque

external forces

gravity, external resistance (weight, bands, etc.), frictional, water (drag)

internal forces

muscle (tendon), ligmaments, skin, fascia

deformable bodies change shape in response to…

forces

change in shape

deformation (aka strain)

deformation may be…

instantaneous or time-dependent

instantaneous

elastic (temporary) or plastic (permanent)

time-dependent

viscoelastic or viscoplastic

extent of deformation depends on…

• applied force (magnitude, direction, & duration)

• characteristics of the material being deformed (material properties & size and shape)

• environmental factors (temp. & humidity)

types of internal forces that cause deformation

• tensile

• compressive

• shear

• bending

• torsion

what causes deformation and failure

stress

stress

force / area

strain

new shape / original shape

-change in shape

-also called deformation

Poisson effect

deformation can spread across dimensions to resist change in total volume

Poisson Ratio

v = -(lateral strain) / (longitudinal strain)

elastic deformation is…

reversible

plastic deformation…

persists (irreversible)

stress-strain curve

illustrates what happens when a “fresh” material is stressed to failure

stress (curve)

internal force distributed across (any) cross section

strain (curve)

resulting change in shape

elastic region

reversible deformation tends to have a roughly linear relationship between stress and strain

plastic region

irreversible changes in the material

failure point

where objects/materials/tissues will break/tear completely

O (curve)

origin; material at rest

P (curve)

proportionality limit; between O and P the stress and strain are linear

E

elastic limit; sometimes we can get a bit past the proportionality limit while still being fully reversible

Y

yield point; elongation can occur without an increase in load (this is the start of the plastic region)

σy - the yield strength of the material

U

the highest stress point on the diagram; σu - the ultimate strength of the material

R

rupture or failure point

Stiffness

measures as the slope of the elastic region of the stress/strain curve (aka Young’s or Elastic modulus)

elastic modulus

stress/strain; the slope of the elastic region of the stress strain curve

higher modulus means…

the material is stiffer (more stress required for strain)

lower modulus means…

the material is more flexible

stiffness

the slope of the elastic region of the stress/strain curve

compliance

the reciprocal of stiffness; the ease of deformings

strength

load at ultimate stress point; this is often at or just before the failure point

toughness

area under the curve; how much energy it can absorb before failure

elasticity

property of solids; the ability to recover size and shape after a load is removed (time-independent)

viscosity

property of fluids; resistance to flow

viscoelasticity

a continuous load will cause continuous deformation; time-dependent and rate-dependent

time-dependent properties of viscoelastic materials

• creep and recovery

• stress relaxation

creep and recovery

time-dependent deformation under constant load

stress relaxation

decreasing stress over time under constant strain

hysteresis

stress-strain relationships for viscoelastic materials differ between loading and unloading

rebound resilience

the proportion of energy you get back during unloading

lower hysteresis =

faster response to imposed loads

uncrimping

when collagen fibers go from being “wavy” to straight with an applied stress

elastic deformation (tissue)

the ability of the material to return to its resting length after a load has been applied

creep and recovery (tissue)

elongation after a constant load is applied for a given length of time

stress relaxation

when the elongation is taken to maximum, and the stress is reduced (6-8 hours for this to occur in most cases)

stress reaction

when the tissue responds to repeated stresses to make itself stronger (i.e., Wolff’s Law)

generalized descriptions of material properties

• instantaneous resistance to load (e.g., soft, hard, stiff)

• how easily they fail (e.g., strong, weak)

• how they behave before failure (e.g., brittle, ductile)

material testing considerations

• material properties of tissues

• tissue storage & condition

• measurement of cross-sectional area

• grip

• tissue geometry

• load application

• temperature

acute failure

failure from one large insult (macrotrauma)

• to change failure point, increase strength of material

fatigue failure

failure from repeated/cyclic (smaller) loads)

• to change failure point, increase endurance of material

shatter

typical of high impact (acute failure) to brittle materials

• poor prognosis, complicated recovery

crack (or tear) propagation

more common from fatigue failure

• shredding of tissue; bone stress fracture

key concerns for fracture mechanics

• number of defects present

• size of the defects

• location of the defects