Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations
Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives of second order, like those in Burgers’ model, are used to describe the complicated response of fluid like materials that are endowed with a complex microstructure that allows them to possess tw...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | Fluids |
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| Online Access: | http://www.mdpi.com/2311-5521/3/4/69 |
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| author | Josef Málek Kumbakonam R. Rajagopal Karel Tůma |
| author_facet | Josef Málek Kumbakonam R. Rajagopal Karel Tůma |
| author_sort | Josef Málek |
| collection | DOAJ |
| description | Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives of second order, like those in Burgers’ model, are used to describe the complicated response of fluid like materials that are endowed with a complex microstructure that allows them to possess two different relaxation mechanisms as well as other non-Newtonian characteristics. Such models are used in geomechanics, biomechanics, chemical engineering and material sciences. We show how to develop such rate-type fluid models that include the classical Burgers’ model as well as variants of Burgers’ model, using a thermodynamic approach based on constitutive assumptions for two scalar quantities (namely, how the material stores energy and how the energy is dissipated) and appealing to the concept of natural configuration associated with the placement of the body that evolves as the body deforms. |
| first_indexed | 2024-12-12T21:54:22Z |
| format | Article |
| id | doaj.art-3a1fd085affe48b7b007de2a4136e13e |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-12-12T21:54:22Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-3a1fd085affe48b7b007de2a4136e13e2022-12-22T00:10:41ZengMDPI AGFluids2311-55212018-09-01346910.3390/fluids3040069fluids3040069Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural ConfigurationsJosef Málek0Kumbakonam R. Rajagopal1Karel Tůma2Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8, CZ 186 75, Czech RepublicDepartment of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USAFaculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8, CZ 186 75, Czech RepublicViscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives of second order, like those in Burgers’ model, are used to describe the complicated response of fluid like materials that are endowed with a complex microstructure that allows them to possess two different relaxation mechanisms as well as other non-Newtonian characteristics. Such models are used in geomechanics, biomechanics, chemical engineering and material sciences. We show how to develop such rate-type fluid models that include the classical Burgers’ model as well as variants of Burgers’ model, using a thermodynamic approach based on constitutive assumptions for two scalar quantities (namely, how the material stores energy and how the energy is dissipated) and appealing to the concept of natural configuration associated with the placement of the body that evolves as the body deforms.http://www.mdpi.com/2311-5521/3/4/69Burgers modelrate-type fluid modelsviscoelasticitysecond law of thermodynamicsthermodynamics |
| spellingShingle | Josef Málek Kumbakonam R. Rajagopal Karel Tůma Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations Fluids Burgers model rate-type fluid models viscoelasticity second law of thermodynamics thermodynamics |
| title | Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations |
| title_full | Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations |
| title_fullStr | Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations |
| title_full_unstemmed | Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations |
| title_short | Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations |
| title_sort | derivation of the variants of the burgers model using a thermodynamic approach and appealing to the concept of evolving natural configurations |
| topic | Burgers model rate-type fluid models viscoelasticity second law of thermodynamics thermodynamics |
| url | http://www.mdpi.com/2311-5521/3/4/69 |
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