Deformation (mechanics)

Deformation (mechanics)

Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body.

The figure on the right shows a schematic of the deformation of a straight wire into a closed loop of almost identical length. Though there appears to be a large change in the macroscopic shape of the wire, the volume change and distortion (shape change) of material elements in the wire is small. Most of the deformation is caused by relative rigid body motions, without volume or shape changes, of adjacent elements (material points) in the wire. For this reason, contrary to macroscopic intuition, the continuum mechanics definition of deformation includes rigid body motions ( footnote 4, p. 48).

A deformation may be caused by external loads, body forces (such as gravity or electromagnetic forces), or temperature changes within the body.

Strain is a description of deformation in terms of relative displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.

In a continuous body, a deformation field results from a stress field induced by applied forces or is due to changes in the temperature field inside the body. The relation between stresses and induced strains is expressed by constitutive equations, e.g., Hooke's law for linear elastic materials. Deformations which are recovered after the stress field has been removed are called elastic deformations. In this case, the continuum completely recovers its original configuration. On the other hand, irreversible deformations remain even after stresses have been removed. One type of irreversible deformation is plastic deformation, which occurs in material bodies after stresses have attained a certain threshold value known as the elastic limit or yield stress, and are the result of slip, or dislocation mechanisms at the atomic level. Another type of irreversible deformation is viscous deformation, which is the irreversible part of viscoelastic deformation.

In the case of elastic deformations, the response function linking strain to the deforming stress is the compliance tensor of the material.