I have a 1.5 mm thick plastic sheet part which hast to be bent at a joint 0.3 mm thick by ~ 10 Deg. I know (found from design drawing) compressed and stretched lengths of the joint. How can I find the length of the joint in non-bent (flat) position so that when it is bent the compressed and stretched joint lengths have the initial known lengths ?

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  • $\begingroup$ I think my problem is similar to mechanical beam problems where one end is fixed, since I also assume that right end is fixed. Furthermore, I have taken that compressed and stretched lengths form concentric circular arcs and assumed that the neutral axis which does not change in length (based on the answer to engineering question #2693) goes trough the middle of the joint, is also circular arc and concentric with the above compressed/stretched arcs. From the construction I can find the lengths of this neutral line which is then the length of the joint in non-bent (flat) position. $\endgroup$ – miquo Jul 21 '16 at 21:54

If we can assume that the material behaves in an elastic linear way and that the joint is only loaded by bending, then as you commented the neutral line lies in the middle and that deformation on the two extreme fibres is equal but in opposite directions. Then, original length is just the average of both deformed lengths.

Of course, to get this result we must assume too that the conditions for the Euler–Bernoulli beam theory holds, and according to your diagram we might approaching its limits (short span compared to width, not very small deformation...) but I think it's still a good approximation.

However, if the material is not linear elastic, location of neutral fibre depends on the constitutive equation of the material (the stress-strain diagram), and the original length may not be the average of both deformed lengths, specially if the constitutive equation is not symmetrical.

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  • $\begingroup$ In my case it is a printed circuit board (PCB). If I understand correctly I should look at the stress-strain diagram for PCB's to make sure that I am in the linear (elastic) region for my approximation to be valid. But how do I know where on the stress-strain curve will I end up given my bending angle and geometry ? $\endgroup$ – miquo Aug 3 '16 at 21:49
  • $\begingroup$ You can find the initial and final length assuming elasticity, as explained above. From them, you can compute strain and check if that strain is in the linear region of the stress-strain diagram. $\endgroup$ – Pere Aug 3 '16 at 22:02

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