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 non zero 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.

Fabrizio, M., Lazzari, B., Nibbi, R. (2017). Existence and stability for a visco-plastic material with a fractional constitutive equation. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 40(18), 6306-6315 [10.1002/mma.4458].

Existence and stability for a visco-plastic material with a fractional constitutive equation

Fabrizio, Mauro;Lazzari, Barbara;Nibbi, Roberta
2017

Abstract

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 non zero 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.
2017
Fabrizio, M., Lazzari, B., Nibbi, R. (2017). Existence and stability for a visco-plastic material with a fractional constitutive equation. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 40(18), 6306-6315 [10.1002/mma.4458].
Fabrizio, Mauro; Lazzari, Barbara; Nibbi, Roberta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/615503
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