A stabilized non-ordinary peridynamic model for linear piezoelectricity

Rakici, Semsi; Kim, Jinseok

doi:10.1016/j.apm.2023.10.010

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2024

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“…Mathematics plays a pivotal role in the field of contact mechanics by providing diverse contact conditions. Contemporary research in this field also encompasses behavior laws that establish connections between mechanical and electrical effects, known as piezoelectricity [7,8]. This area is extensively explored in engineering structures, due to its temperature-dependent characteristics.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

Fadlia,

Dalah,

Torres

2024

Mathematics

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We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is represented by a system of partial differential equations, and establishing its solution involves several key steps. Initially, we obtain a variational formulation of the model, which comprises three systems: a hemivariational inequality, an elliptic equation, and a parabolic equation. Subsequently, we demonstrate the existence of a unique weak solution to the model. The proof relies on various arguments, including those related to evolutionary inequalities, techniques for decoupling unknowns, and certain results from differential equations.

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Section: Introductionmentioning

confidence: 99%