A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material
Purpose – The 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...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2025-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2021-0174/full/pdf |
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| _version_ | 1832590069417902080 |
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| author | Abdelmoumene Djabi |
| author_facet | Abdelmoumene Djabi |
| author_sort | Abdelmoumene Djabi |
| collection | DOAJ |
| description | Purpose – The 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/approach – The 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. Findings – The 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/value – The 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. |
| format | Article |
| id | doaj-art-9ef5144962d0470aa82dbd093f88f02f |
| institution | Kabale University |
| issn | 1319-5166 2588-9214 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj-art-9ef5144962d0470aa82dbd093f88f02f2025-01-24T04:22:17ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142025-01-01311618110.1108/AJMS-08-2021-0174A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic materialAbdelmoumene Djabi0Applied Mathematics Laboratory, Ferhat Abbas- Setif 1 University, Setif, AlgeriaPurpose – The 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/approach – The 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. Findings – The 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/value – The 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.https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2021-0174/full/pdfConductive foundationFixed pointFrictional contactNormal damped responseThermo-piezoelectricVariational inequality |
| spellingShingle | Abdelmoumene Djabi A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material Arab Journal of Mathematical Sciences Conductive foundation Fixed point Frictional contact Normal damped response Thermo-piezoelectric Variational inequality |
| title | A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material |
| title_full | A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material |
| title_fullStr | A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material |
| title_full_unstemmed | A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material |
| title_short | A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material |
| title_sort | frictional contact problem with normal damped response conditions and thermal effects for a thermo electro viscoelastic material |
| topic | Conductive foundation Fixed point Frictional contact Normal damped response Thermo-piezoelectric Variational inequality |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2021-0174/full/pdf |
| work_keys_str_mv | AT abdelmoumenedjabi africtionalcontactproblemwithnormaldampedresponseconditionsandthermaleffectsforathermoelectroviscoelasticmaterial AT abdelmoumenedjabi frictionalcontactproblemwithnormaldampedresponseconditionsandthermaleffectsforathermoelectroviscoelasticmaterial |