دورية أكاديمية
Analytical continuum mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids
| العنوان: | Analytical continuum mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids |
|---|---|
| المؤلفون: | Auffray, Nicolas, Dell'Isola, F., Eremeyev, V., Madeo, A., Rosi, G. |
| المساهمون: | Laboratoire de Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est Marne-la-Vallée (UPEM)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Ingegneria Strutturale e Geotecnica (DISG), Università degli Studi di Roma "La Sapienza" = Sapienza University Rome (UNIROMA), Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University Magdeburg (OVGU), Southern Federal University Rostov-on-Don (SFEDU), Laboratoire de Génie Civil et d'Ingénierie Environnementale (LGCIE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), International Research Centre on Mathematics & Mechanics of Complex Systems (M&MoCS), Università degli Studi dell'Aquila = University of L'Aquila (UNIVAQ) |
| المصدر: | ISSN: 1081-2865 ; Mathematics and Mechanics of Solids ; https://hal.science/hal-00836085Test ; Mathematics and Mechanics of Solids, 2013. |
| بيانات النشر: | HAL CCSD SAGE Publications |
| سنة النشر: | 2013 |
| المجموعة: | HAL Lyon 1 (University Claude Bernard Lyon 1) |
| مصطلحات موضوعية: | [PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph] |
| الوصف: | International audience ; In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | hal-00836085; https://hal.science/hal-00836085Test; https://hal.science/hal-00836085/documentTest; https://hal.science/hal-00836085/file/1305.6744v1.pdfTest |
| الإتاحة: | https://hal.science/hal-00836085Test https://hal.science/hal-00836085/documentTest https://hal.science/hal-00836085/file/1305.6744v1.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.84E190AE |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |