Eigen strain
Eigen strain
(OP)
WHAT IS EIGEN STRAIN
HOW TO FIND EIGEN STRAIN?
HOW TO FIND EIGEN STRAIN?
Raj
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RE: Eigen strain
Ed.R.
RE: Eigen strain
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RE: Eigen strain
RE: Eigen strain
For the homogeneous part of the material the energy is due to e0. while for the inclusion or interface we have energy coming due to et which is eigen strain. So i had a question whats eigen strain and how do we compute it.
Thanks all for replies.
Raj
RE: Eigen strain
mse.mcmaster.ca/cncms/lectures/Lectures6_8.pdf
Haatajan called eigenstrain the "stress free strain". One example of such strain is the strain due to temperature changes. You may recall the following form of the 3D Hooke's
law:
e(i,j)=s(i,j)/2G-(nu/E)*delta(i,j)*s(kk)
where e(i,j) is the total strain, s(i,j) the stress; nu,E are Poisson ratio and Young's modulus, delta(i,j) is the Dirac delta function; s(kk) means sum (s(1,1)+s(2,2)+s(3,3)).
The eigenstrain e*(i,j) can be added directly to the right hand side of this equation,
e(i,j)=s(i,j)/2G-(nu/E)*delta(i,j)*s(kk)+e*(i,j)
If the 'stress free strain' is temperature induced, then sometimes we write
e*(i,j)=alpha*deltaT*delta(i,j)
where alpha is the expansion coefficient, deltaT is the temperature difference, and delta(i,j) is again the Dirac delta function.
It seems strange to have a 'stress free strain', but you can see such strain quite easily of course by heating up something that isn't constrained, like heating up a bar laying on a table, and observing how it grows in length. Because it is growing unconstrained (assuming the growth is uniform; sometimes material inhomogeneity prevents uniform growth), you know that there is no change in the stress in the bar, yet you also know the strain is changing because you observe the length changes.