On dynamic contact problem with generalized Coulomb friction, normal compliance and damage

Gasiński, Leszek; Kalita, Piotr

doi:10.3934/eect.2020049

Cited by 3 publications

(2 citation statements)

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“…Duvaut and Lions were the first to work on the mathematical theory of contact mechanics; They introduced variational formulations of contact problems and provided existence and uniqueness results. Subsequently, several new works have focused on the resolution of these variational problems such as the work of Refs [1][2][3][4][5][6]. However, mathematical theory of contact problems is a very broad field of study where many issues remain to be investigated.…”

Section: Introductionmentioning

confidence: 99%

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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material

Djabi

2023

AJMS

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PurposeThe paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.Design/methodology/approachThe author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.FindingsThe author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.Originality/valueThe author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

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Section: Introductionmentioning

confidence: 99%

“…General models of energy can be found in Refs [1]. a generalized Coulomb friction version is given in Refs [3,20]. Indeed, the authors used the normal damped response conditions for a lubricated foundation; see, for instance [21,22].…”

Section: Introductionmentioning

confidence: 99%