Effect of Voids and Internal State Variables in Elasticity of Porous Bodies with Dipolar Structure

Marin Marin, Sorin Vlase, Iana Fudulu and Georgiana Precup
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Marin Marin: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania
Sorin Vlase: Department of Mecanical Engineering, Transilvania University of Brasov, 500036 Brasov, Romania
Iana Fudulu: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania
Georgiana Precup: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania

Mathematics, 2021, vol. 9, issue 21, 1-14

Abstract: In this study, we will prove that the presence of the voids and of the internal state variables in an elastic body with dipolar structure have no effect on the result of uniqueness regarding the solution of the initial-boundary value problem from this context. First, we put down the basic equations and conditions which define the initial-boundary value problem in the context. Then, by means of three theorems, we prove some auxiliary estimates that underlie the result of uniqueness. Finally, by means of these estimates and by using the Gronwall’s inequality, we prove our main result.

Keywords: elastic body; dipolar structure; internal state variables; uniqueness; Gronwall’s inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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