We analyze complex bodies with active microstructure described by a vector field with val- ues ν ∈ R3, which complements the displacement u ∈ R3. We consider linear elastic consti- tutive structures for macroscopic and microstructural stresses, diffusion of microstructures, and a viscoelastic-substrate-type effect, which has a regularizing influence that we eliminate at a later stage of our analysis. For weak solutions of the balance equations, we prove decay inequalities in W1,2 and also for the p-power of the norms of u and ν in Lp spaces under slip-without-friction-type boundary conditions.

Energy Decay in the Dynamics of Complex Bodies with Spreading Microstructures Represented by 3D Vectors / Diego Berti, Luca Bisconti, Paolo Maria Mariano. - In: JOURNAL OF ELASTICITY. - ISSN 0374-3535. - STAMPA. - ---:(In corso di stampa), pp. 1-25. [10.1007/s10659-022-09921-4]

Energy Decay in the Dynamics of Complex Bodies with Spreading Microstructures Represented by 3D Vectors

Diego Berti;Luca Bisconti;Paolo Maria Mariano
In corso di stampa

Abstract

We analyze complex bodies with active microstructure described by a vector field with val- ues ν ∈ R3, which complements the displacement u ∈ R3. We consider linear elastic consti- tutive structures for macroscopic and microstructural stresses, diffusion of microstructures, and a viscoelastic-substrate-type effect, which has a regularizing influence that we eliminate at a later stage of our analysis. For weak solutions of the balance equations, we prove decay inequalities in W1,2 and also for the p-power of the norms of u and ν in Lp spaces under slip-without-friction-type boundary conditions.
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Diego Berti, Luca Bisconti, Paolo Maria Mariano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1285197
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