The modern theory of elasticity generalizes Hookes law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the proportionality factor may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers. In this general form, Hookes law and Newtons laws of static equilibrium make it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length.
Posted on: Tue, 30 Dec 2014 23:52:12 +0000
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