Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening
This paper presents the weak formulation of a quasi-static evolution model for two deformable bodies with unidirectional adhesive unilateral contact on which external loads act. Small deformations and linearized elastoplasticity with hardening are assumed. The adhesion component is rate-dependent or...
- Autores:
-
Peñas Galezo, Ramiro
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad del Atlántico
- Repositorio:
- Repositorio Uniatlantico
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniatlantico.edu.co:20.500.12834/825
- Acceso en línea:
- https://hdl.handle.net/20.500.12834/825
- Palabra clave:
- Contact, delamination, unilateral, unidirectional, doubly non-linear problem, strongly monotone operator
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc/4.0/
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Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| title |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| spellingShingle |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening Contact, delamination, unilateral, unidirectional, doubly non-linear problem, strongly monotone operator |
| title_short |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| title_full |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| title_fullStr |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| title_full_unstemmed |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| title_sort |
Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening |
| dc.creator.fl_str_mv |
Peñas Galezo, Ramiro |
| dc.contributor.author.none.fl_str_mv |
Peñas Galezo, Ramiro |
| dc.subject.keywords.spa.fl_str_mv |
Contact, delamination, unilateral, unidirectional, doubly non-linear problem, strongly monotone operator |
| topic |
Contact, delamination, unilateral, unidirectional, doubly non-linear problem, strongly monotone operator |
| description |
This paper presents the weak formulation of a quasi-static evolution model for two deformable bodies with unidirectional adhesive unilateral contact on which external loads act. Small deformations and linearized elastoplasticity with hardening are assumed. The adhesion component is rate-dependent or rate-independent according to the choice of the viscosity coefficient of the glue; elastoplasticity is considered rate-independent. The weak formulation is expressed as a doubly non-linear problem with unbounded multivalued operators, as a function of internal and boundary displacements, plastic and symmetric strain tensors, and the bonding field and its gradient. This paper differs from other formulations by coupling the equations defined inside and on the boundary of the solids in functional form. In addition to this novelty, we verify the existence of solutions by a path other than that displayed in similar articles. The existence of solutions is demonstrated after considering a succession of doubly non-linear problems with an unbounded operator, and verifying that the solution of one of the problems is also a solution to the objective problem. The proof is supported by previous results from non-linear Partial differential equations theory with monotone operators. |
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2021 |
| dc.date.issued.none.fl_str_mv |
2021-07-16 |
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2021-01-05 |
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2022-11-15T19:36:35Z |
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2022-11-15T19:36:35Z |
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https://hdl.handle.net/20.500.12834/825 |
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10.1177/16878140211039138 |
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Universidad del Atlántico |
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Repositorio Universidad del Atlántico |
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https://hdl.handle.net/20.500.12834/825 |
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10.1177/16878140211039138 Universidad del Atlántico Repositorio Universidad del Atlántico |
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eng |
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Matemáticas |
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Sede Norte |
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Advances in Mechanical Engineering |
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Peñas Galezo, Ramiro2f05fd4f-2742-4452-9bcf-237a893e75762022-11-15T19:36:35Z2022-11-15T19:36:35Z2021-07-162021-01-05https://hdl.handle.net/20.500.12834/82510.1177/16878140211039138Universidad del AtlánticoRepositorio Universidad del AtlánticoThis paper presents the weak formulation of a quasi-static evolution model for two deformable bodies with unidirectional adhesive unilateral contact on which external loads act. Small deformations and linearized elastoplasticity with hardening are assumed. The adhesion component is rate-dependent or rate-independent according to the choice of the viscosity coefficient of the glue; elastoplasticity is considered rate-independent. The weak formulation is expressed as a doubly non-linear problem with unbounded multivalued operators, as a function of internal and boundary displacements, plastic and symmetric strain tensors, and the bonding field and its gradient. This paper differs from other formulations by coupling the equations defined inside and on the boundary of the solids in functional form. In addition to this novelty, we verify the existence of solutions by a path other than that displayed in similar articles. The existence of solutions is demonstrated after considering a succession of doubly non-linear problems with an unbounded operator, and verifying that the solution of one of the problems is also a solution to the objective problem. The proof is supported by previous results from non-linear Partial differential equations theory with monotone operators.application/pdfenghttp://creativecommons.org/licenses/by-nc/4.0/Attribution-NonCommercial 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Advances in Mechanical EngineeringFormulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardeningPúblico generalContact, delamination, unilateral, unidirectional, doubly non-linear problem, strongly monotone operatorinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1BarranquillaMatemáticasSede Norte1. Roubı´cˇek T, Manticˇ V and Panagiotopoulos CG. A quasistatic mixed-mode delamination model. Discrete Contin Dyn Syst 2013; 6: 591–610.2. Kocˇvara M, Mielke A and Roubı´cˇek T. A rateindependent approach to the delamination problem. Math Mech Solids 2006; 11: 423–4473. Roubı´cˇek T, Scardia L and Zanini C. Quasistatic delamination problem. Continuum Mech Thermodyn 2009; 21: 223–2354. Bonetti E, Rocca E, Rossi R, et al. A rate-independent gradient system in damage coupled with plasticity via structured strains. ESAIM Proc Surv 2016; 54: 54–69.5. Rossi R and Roubı´cˇek T. Thermodynamics and analysis of rate-independent adhesive contact at small strains. Nonlinear Anal Theory Methods Appl 2011; 74: 3159–31906. Panagiotopoulos CG, Manticˇ V and Roubı´cˇek T. Two adhesive-contact models for quasistatic mixed-mode delamination problems. Math Comput Simul 2018; 145: 18–337. Fremond M. Contact with adhesion. In: Italiana UM (ed.) Phase change in mechanics. Berlin: Springer-Verlag, 2012, pp.109–113.8. Han W and Sofonea M. Quasistatic contact problem in viscoelasticity and viscoplasticity. Providence, RI: American Mathematical Society, 20029. Chau O, Ferna´ndez JR, Shillor M, et al. Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion. J Comput Appl Math 2003; 159: 431–46510. Bonetti E, Bonfanti G and Rossi R. Global existence for a contact problem with adhesion. Math Methods Appl Sci 2008; 31: 1029–1064.11. Colli P and Visintin A. On a class of doubly nonlinear evolution equations. Commun Partial Differ Equ 1990; 15: 737–756.12. Colli P. On some doubly nonlinear evolution equations in Banach spaces. Jpn J Ind Appl Math 1992; 9: 181–203.13. Akagi G. Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces. J Differ Equ 2006; 231: 32–5614. Barbu V. Nonlinear differential equations of monotone types in Banach spaces. Springer Monographs in Mathematics. New York, NY: Springer, 2010.15. Stefanelli U. A variational principle for hardening elastoplasticity. SIAM J Math Anal 2008; 40: 623–652.16. Liero M and Mielke A. An evolutionary elastoplastic plate model derived via G-convergence. Math Model Methods Appl Sci 2011; 21: 1961–1986.17. Mielke A. Chapter 6. Evolution of rate-independent systems. In: Dafermos CM and Feireisl E (eds) Handbook of differential equations: evolutionary equations, vol. 2. Amsterdam: Elsevier/North Holland, 2005, pp.461–559.18. Wang L. On Korn’s inequality. J Comput Math 2003; 31: 321–324.19. Heitbreder T, Ottosen NS, Ristinmaa M, et al. Consistent elastoplastic cohesive zone model at finite deformations – variational formulation. Int J Solids Struct 2017; 106–107: 284–29320. Xu H and Komvopoulos K. Surface adhesion and hardening effects on elastic–plastic deformation, shakedown and ratcheting behavior of half-spaces subjected to repeated sliding contact. Int J Solids Struct 2013; 50: 876–886.21. Roubı´cˇek T. Nonlinear partial differential equations with applications. Basel: Birkha¨user Verlag, 2005, 321–356 p.22. Temam R. Mathematical problems in plasticity. Paris: Gauthier-Villars, 1985, 1–99 p23. Adams RA and Fournier JJF. Sobolev spaces. Vol. 140. 2nd ed. Amsterdam: Academic Pres, 200324. Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York, NY: Springer-Verlag, 201125. Krabbenhøft K. A variational principle of elastoplasticity and its application to the modeling of frictional materials. Int J Solids Struct 2009; 46: 464–47926. Evans L. Partial differential equations. 2nd ed. Providence, RI: American Mathematical Society, 1998, 662 p27. Showalter RE. Monotone operators in Banach space and nonlinear partial differential equations. Math Surv Monogr 1997; 49: 282.http://purl.org/coar/resource_type/c_6501ORIGINAL16878140211039138.pdf16878140211039138.pdfapplication/pdf310068https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/825/1/16878140211039138.pdff0a83517228652dc6a13f1aa0a20508eMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/825/2/license_rdf24013099e9e6abb1575dc6ce0855efd5MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81306https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/825/3/license.txt67e239713705720ef0b79c50b2ececcaMD5320.500.12834/825oai:repositorio.uniatlantico.edu.co:20.500.12834/8252022-11-15 14:36:36.291DSpace de la Universidad de Atlánticosysadmin@mail.uniatlantico.edu.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 |