TOPICS
Search

Strain Tensor


The infinitesimal strain tensor of a displacement field u is the symmetric part of its derivative,

 e(u)=(Du+(Du)^T)/2.

Its trace is the divergence of u. This is the linearized strain used in the isotropic elasticity system, rather than the finite-deformation strain of a large displacement. For an affine displacement u(x)=Ax+b, the strain is the constant symmetric matrix (A+A^T)/2. The stress tensor relates this strain to boundary traction.


See also

Isotropic Elasticity System, Stress Tensor, Symmetric Matrix

Explore with Wolfram|Alpha

References

Uhlmann, G. and Wang, J.-N. "Complex Spherical Waves for the Elasticity System and Probing of Inclusions." SIAM J. Math. Anal. 38, 1967-1980, 2007. https://doi.org/10.1137/060651434.

Cite this as:

Weisstein, Eric W. "Strain Tensor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrainTensor.html

Subject classifications