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Discuss stress and strain of materials in terms of Hooke's law. Please be detailed.

Discuss stress and strain of materials in terms of Hooke's law. Please be detailed.

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Expert Solution

the relevant state of the medium around a point must be represented by two second-order tensors, the strain tensor (in lieu of the displacement ) and the stress tensor (replacing the restoring force ).The analogous of Hooke's spring law for continuous media is then

where is a fourth-order tensor (that is, a linear map between second-order tensors) usually called the stiffness tensor or elasticity tensor. One may also write it as

Hooke's law only holds for some materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke's law is valid for it throughout its elastic range

genius_generous answered 2 years ago
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