Elasticity

Elasticity - Physical Sciences 2 Fall 2007 Some Introductory Notes about Elasticity(supplement to the material in the textbook Introduction Many

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1 Physical Sciences 2, Fall 2007 Some Introductory Notes about Elasticity (supplement to the material in the textbook) Introduction Many common materials are soft, squishy, and flexible. We frequently stretch or deform materials, such as when we repair objects (a building, a patient, etc.) or when we manipulate living systems: forces produce deformations such as when we bend objects and break things. The coatings of many surfaces – including our skin, deformed balloons, and clothing – are wrinkled and stretched. To understand these observations, and to quantify them, we begin with Hooke’s law for the force-displacement characterization of a spring, and modify it slightly to describe the stress and strain in a material. We will see that we can then learn about and quantify how, and by how much, mechanical forces deform objects, whether they are steel structures, your bones, tissues or cells. Earlier in the course we referred to the idea that everything is a spring ; the characterization of the elastic response of materials is a wonderful example of this analogy. Dictionary definition (Webster’s 2 nd College Edition 1968): Elastic Adjective: 1. Having the property of immediately returning to its original size, shape, or position after being stretched, squeezed, flexed, expanded, etc; flexible, springy. 2. having the ability to recover easily from dejection, fatigue, etc. 3. readily changed or changing to suit circumstances; adaptable. Noun: 1. a loosely woven fabric made flexible by strands of rubber or a rubberlike synthetic running through it. 2. a band, garter, etc. of this material; 3. a rubber band.
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2 Figure 1: Applying a tensile force F to elongate a material. Springs and the elastic response We have learned that when a spring is stretched a length x a restoring force with magnitude k x (Hooke’s law) is exerted in the direction opposite to the displacement. Thus, we write that the force exerted by the spring is F spring =- k x . Alternatively, the force F applied to the spring to produce the displacement is (by Newton’s third law), F= k x. Suppose that we now consider an elastic (solid) material in the shape of a cylinder of initial length L 0 and cross sectional area A (see figure 1). Apply a force F to each end in order to extend the cylinder a small amount, which we will denote L . It is more
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This note was uploaded on 03/29/2012 for the course LS 2 taught by Professor Andrewa.biewener,petert.ellison,anddaniele.lieberman during the Fall '10 term at Harvard.

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Elasticity - Physical Sciences 2 Fall 2007 Some Introductory Notes about Elasticity(supplement to the material in the textbook Introduction Many

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