5.1 Derivation of Elasticity Equations

The equations that model displacements in an elastic body, such as a metal block, can be derived using Newton's second law. If we focus on an arbitrary small volume images of this body and set the mass times the acceleration equal to the sum of the internal and external forces acting on images, we get

Here images is the density, and (images, images, images) is the displacement vector. That is, the body element that is at (images) when the elastic body is unloaded and in equilibrium is displaced to (images, , ) at time . Thus (, , ) is the acceleration vector. The stresses are the elements ...

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