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Existence and stability for a visco‐plastic material with a fractional constitutive equation
Author(s) -
Fabrizio M.,
Lazzari B.,
Nibbi R.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4458
Subject(s) - mathematics , constitutive equation , plasticity , fractional calculus , semigroup , constant (computer programming) , mathematical analysis , exponential function , compatibility (geochemistry) , cauchy elastic material , exponential decay , thermodynamics , physics , materials science , finite element method , computer science , nuclear physics , programming language , composite material
The well posedness of the evolutive problem for visco‐plastic materials represented by two different fractional constitutive equations is proved. We show that, for these materials, we can observe permanent deformations. So that, as it is usual in plasticity, when the stress goes to zero, then the strain assumes a constant nonzero behavior. Moreover, we prove the compatibility of our models with the classical laws of thermodynamics. For the second model, described through a fractional derivative with an exponential kernel, we obtain the exponential decay of the solutions by means of the semigroup theory.