Direction of Stress (Force) Stress and Strain Compression Tension Shear Course Text: Hamill & Knutzen (Ch 2) Nordin & Frankel (Ch 1) or Hall (Ch. 4) Axial compression of the spinal unit results in a loss of height measured between the vertebrae. As the disc material itself is essentially incompressible, height decrease must result in a radial bulge of the disc and a corresponding axial disc bulge (an inward deformation of the vertebral end plates). Bending Tension Compression 1 Stress analysis of the proximal end of the femur (Koch) Torsion Strength & Stiffness Neutral Axis Ø Strength Shear Ø Defined by the failure point. Also can be assessed by energy storage (area under curve). Ø Stiffness (modulus of elasticity) Ø determined by the slope of the load deformation curve 2 Stiffness Stress Stiffness = "force "displ. Strain Force/Area Δlength original length Force Δy ! Same units as pressure Δx Ratio, no units. Displacement Elastic Response Stress/Strain Curves Failure Yield Stress Elastic Region Plastic Region Metal (ductile) Glass (brittle) Bone Strain 3 Young’s Modulus Flexible, Strong Stiff, Strong fiberglass steel Young’s Modulus is the ratio of: stress / strain (stiffness) Young’s Modulus Tendon 2 x 109 Bone 1.7 x 1010 Carbon Steel 2 x 1011 6 Soft rubber c.10 Tensile Strength 1 x 108 1.8 x 108 3 x 109 iron gold silk spider web BONE copper oak glass lead Flexible, Weak Stiff, Weak Question a) In a fall a ligament has 2500 N of tensile force exerted on it. If the area of the crosssectional area of the ligament is 2 cm2 what is the tensile stress on the ligament? b) If the force rises to 3000 N and 10% of the collagen fibers fail (break), what would the tensile stress be now? c) What may happen to the ligament in this situation? Relate your answer to the stress strain curve for human ligament tissue. 4 Viscosity Ø The mechanical response of human tissues to applied force is not simply elastic. Ø Human tissues also have fluid in them and hence they have a viscous response also. Ø Viscosity can be thought of as the "internal friction” when a fluid is subject to shearing. Ø In simple terms viscosity is related to the the "thickness" of the fluid. Viscoelastic Characteristics of Human Bone Load Fracture Quick Slow Fracture Deformation Viscoelastic Characteristics Load a Lo d (d or ef ) m U nl d oa ur et n) (r Hysteresis loop (shaded area) represents lost energy (heat) Thixotropy Ø By agitating or heating a material you can make it less viscous. Ø Obviously the example is the last bit of tomato ketchup in the bottle (which you can make less viscous by shaking it). Not really applicable to many materials. Ø Although heating steel will make it more flexible such that it may flow, it would take a lot of shaking to disrupt the molecular bonds! Ø With human tissue, the warm-up prior to athletic events does increase flexibility, but could reduce connective tissue strength (more later). Deformation 5 Qualitative Tissue Tolerance Graph Acute Trauma Tissue strength (conditioning) is also a factor in risk of injury Keep the big picture in mind. If you have little movement/ exercise then the tissues become more susceptible to injury due to poor conditioning. Risk of Injury Load Injury Threshold Tolerance Chronic Repetitive Injury Repetition Loading and Growth Ø Loading suppresses catabolic enzymes (regulation) Ø Mechanical loading is essential for maturation Ø Disuse is an issue…loose bone mass at a rate of 1.5% a month too little too much Movement (repetition), force (lifting) physical activity, sitting or standing Hippocrates (460-377 B.C.) “All parts of the body which have a function, if used in moderation and exercises in labours to which each are accustomed, thereby become healthy and well-developed: but if unused and left idle, they become liable to disease, defective in growth, and age quickly. This is especially the case with joints and ligaments, if one doe not use them.” LeVay 1990. p30. 6 Acute vs. Chronic Injuries Acute Force If you had a force vs time graph the area under the curve would be an impulse (Ft => the cumulative loading of that tissue) Chronic Cumulative Loading Ø Assessing the effect of cumulative loading is a difficult thing. Ø If there is adequate recovery time then even high cumulative loads may be safe. Ø On the other hand a one time high peak force over a very short period of time (low cumulative load) may exceed the strength of the tissue and cause injury. Time Biomechanical Factors Tissue Biomechanics Ø Kumar (1999) proposed a theory of overexertion that states overexertion can be created by exceeding the normal physical and physiological in any one of: force (Fx), exposure time (Dy), range of motion (Mz). Ø The weighting of these three functions is obscure but Kumar symbolically represents overexertion (OE) with the equation below. Ø Any deformation or residual deformation alters the mechanical response of the tissue reducing its stress bearing capacity. Ø Tissues that frequently get injured due to occupational and athletic biomechanical hazards are ligaments, tendons, muscle and nerves (cartilage and bones are injured infrequently in occupational settings but more frequently in sports due to impacts and falls). Ø We will look more closely at human tissue’s mechanical response to loading in the next chapter. OE = ! ( Fx, Dy, Mz ) 7