en.wikipedia.org/wiki/Hooke%27s_law
1 correction found
The strain tensor ε merely specifies the displacement of the medium particles in the neighborhood of the point
This confuses strain with displacement. In continuum mechanics, the displacement field specifies particle displacement; the strain tensor measures local deformation, i.e. relative changes in length/angle derived from spatial derivatives of displacement.
Full reasoning
In continuum mechanics, displacement and strain are different quantities.
- The displacement field (u(x)) gives the motion of material points.
- The strain tensor is derived from spatial derivatives of displacement and measures local deformation (changes in length and angle), not displacement itself.
MIT OpenCourseWare’s notes on strain explicitly state that deformation is described by the displacement field and then derive the strain–displacement relations from it. NPTEL’s continuum mechanics notes likewise explain that deformation at a point is related to the displacement of a neighborhood, and that the linear strain tensor is the symmetric part of the displacement gradient that describes the deformation of that neighborhood, while other parts correspond to translation and rotation.
So the article sentence is incorrect because it says the strain tensor “specifies the displacement” of particles. A more accurate statement would be that the strain tensor specifies the local deformation/relative displacement in the neighborhood of a point, not the particle displacement itself.
2 sources
- MIT OpenCourseWare – Lecture: Strain; Transformation of Strain Components
"Strain - displacement relations: Deformation described by displacement field u(x) = ui(x)ei." The notes then define strain components from derivatives of the displacement field.
- NPTEL – Review of Stress, Linear Strain and Elastic Stress-Strain Relations
The notes state that deformation at a point is related to the displacement of a neighborhood; displacement contains translation, rotation, and deformation; and the symmetric part of the displacement gradient is the linear strain tensor that describes deformation when it is small.