Abstract
AbstractIn this paper, the authors begin by observing that using the new definition of fractional derivative with an exponential kernel makes it is possible to obtain again some generalized constitutive equation of continuum mechanics as a Kelvin-Voight Maxwell standard linear solid. However, this equivalence holds only in a space of smooth solutions. In the second part, two different fractional derivatives to describe the behavior of some types of plastic materials are considered. Before a kernel with a negative power of the variable and then a kernel with a negative exponential are assumed. The problems related with 1D (one dimensional) stress and a 1D strain respectively are applied to the 3D (three dimensional) body as part of a discussion of the Poisson phenomenon.
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