A viscoelastic material with nonconvex memory

I’m new here, so I hope a question like this is allowed.

I’m currently researching in the field of partial differential equations with memory. A PDE with memory is usually of the form: $$u_{tt} – Delta u + int_0^t g(t-s)Delta u(s) ds = 0$$ where $g : mathbb R^+ to mathbb R^+$ is the so-called memory kernel, which is a decreasing summable function.

Equations like this usually comes from the field of viscoelasticity, where the stress-strain relationship involves a convolution integral.

Now, usually $g$ is also convex (actually, often $g$ is a decreasing exponential). I wanted to know whether there exists some kind of viscoelastic material in which the memory kernel is not convex.

Thank you in advance to everyone who will respond to this question!