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The title is basically my question. Viscoelastic materials are characterized by a constitutive equation between stress and strain involving a convolution integral. This integral is weighted with a relaxation kernel (or memory kernel).

Usually, the memory kernel is convex and decreasing (actually, it is often an exponential), but I was wondering if there exist materials for which the memory kernel is nonconvex.

Thank you very much to anyone willing to respond!

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    $\begingroup$ I know very little about this topic, but from searching around, this book has a section nonconvex kernels. Hopefully they give some sort of example. $\endgroup$
    – Tyberius ♦
    Oct 2, 2020 at 21:14
  • $\begingroup$ Lorenzo, was the book helpful? $\endgroup$
    – Nike Dattani
    Oct 6, 2020 at 22:06
  • $\begingroup$ Hi! Sorry, but unfortunately I couldn't find anything worth it in the book. The only thing I've found is a sentence in this paper (link.springer.com/article/10.1007/s00397-005-0443-6) by Hanyga: "Complete monotonicity is not a universal feature of weakly dissipative viscoelastic systems. [... see formula (10) ...] Oscillatory relaxation appears in seawater with damped bubble oscillations. It can also be generated by including mass in spring-dashpot models." However, I couldn't find much literature supporting the sentence. $\endgroup$
    – ALive
    Oct 8, 2020 at 7:36
  • $\begingroup$ That's very interesting question. Sorry I did not see your reply to my comment, because you didn't tag me with @NikeDattani. Only the person that asked the question gets notifications on comments, otherwise you need to tag the user you're talking to. Do you know of any materials with a non-monotonic memory kernel? A parabola can be convex but non-monotonic; have you ever seen such convex but non-monotonic memory kernel? $\endgroup$
    – Nike Dattani
    Oct 15, 2020 at 1:04
  • $\begingroup$ @NikeDattani, unfortunately I come from the mathematics field, so I don't know anything on materials. In particular, no, I don't know anything about viscoelastic materials with nonmonotonic kernel. However, I'm pretty sure the kernel HAS to be monotonic. Having a nonmonotonic kernel would mean that the material "weights" events happened in the long past more than events happened in recent past, which does not seem very physical. $\endgroup$
    – ALive
    Oct 16, 2020 at 7:47

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