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Eigen strain
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Taken at face value -- as per the sentiment of EdR's post -- I would say that this is a value based on an eigenvalue extraction. If this is a standard modal extraction, then all displacments, and hence strains, are relative and therefore meaningless in a true magnitude sense. If this is from a buckling solution, however, then there maybe valid strains known as eigenstrains. Please supply approximately 99.9999999% more of the problem scope. Or a crystal ball.
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Eigen strains- i happen to come across while i was reading some material on material interfaces and inclusions.
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
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
Another interpretation of eigenstrain, which I found a website at McMaster University, lecture notes from Mikko Haatajan:
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.
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.
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