Two-Field Weak Solutions for a Class of Contact Models
Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacemen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/369 |
| _version_ | 1797486368568377344 |
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| author | Andaluzia Matei Madalina Osiceanu |
| author_facet | Andaluzia Matei Madalina Osiceanu |
| author_sort | Andaluzia Matei |
| collection | DOAJ |
| description | Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacement field and the Cauchy stress tensor. The two-field weak solutions are sought into product spaces involving variable convex sets. Both models lead to variational systems which can be cast in an abstract setting. After delivering some abstract results, we apply them in order to study the weak solvability of the mechanical models as well as the data dependence of the weak solutions. |
| first_indexed | 2024-03-09T23:33:12Z |
| format | Article |
| id | doaj.art-74874bdfa1b2413dbb8264479f47223d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:33:12Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-74874bdfa1b2413dbb8264479f47223d2023-11-23T17:06:24ZengMDPI AGMathematics2227-73902022-01-0110336910.3390/math10030369Two-Field Weak Solutions for a Class of Contact ModelsAndaluzia Matei0Madalina Osiceanu1Department of Mathematics, University of Craiova, A.I.Cuza 13, 200585 Craiova, RomaniaDoctoral School of Sciences, University of Craiova, A.I.Cuza 13, 200585 Craiova, RomaniaTwo contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacement field and the Cauchy stress tensor. The two-field weak solutions are sought into product spaces involving variable convex sets. Both models lead to variational systems which can be cast in an abstract setting. After delivering some abstract results, we apply them in order to study the weak solvability of the mechanical models as well as the data dependence of the weak solutions.https://www.mdpi.com/2227-7390/10/3/369nonlinear constitutive lawbipotentialtwo-field weak solutionwell-posedness |
| spellingShingle | Andaluzia Matei Madalina Osiceanu Two-Field Weak Solutions for a Class of Contact Models Mathematics nonlinear constitutive law bipotential two-field weak solution well-posedness |
| title | Two-Field Weak Solutions for a Class of Contact Models |
| title_full | Two-Field Weak Solutions for a Class of Contact Models |
| title_fullStr | Two-Field Weak Solutions for a Class of Contact Models |
| title_full_unstemmed | Two-Field Weak Solutions for a Class of Contact Models |
| title_short | Two-Field Weak Solutions for a Class of Contact Models |
| title_sort | two field weak solutions for a class of contact models |
| topic | nonlinear constitutive law bipotential two-field weak solution well-posedness |
| url | https://www.mdpi.com/2227-7390/10/3/369 |
| work_keys_str_mv | AT andaluziamatei twofieldweaksolutionsforaclassofcontactmodels AT madalinaosiceanu twofieldweaksolutionsforaclassofcontactmodels |