An Eulerian formulation for large deformations of anisotropic elastic and viscoelastic solids and viscous fluids

详细信息    查看全文

• 作者：M. B. Rubin ; B. Nadler
• 关键词：Eulerian formulation ; Anisotropy ; Nonlinear ; Hyperelasticity ; Viscous fluids
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：28
• 期：1-2
• 页码：515-522
• 全文大小：419 KB
• 参考文献：1.Besseling, J.F.: A thermodynamic approach to rheology. In: Parkus, H., Sedov, L.I. (eds). Proceedings of IUTAM Symposium on Irreversible Aspects of Continuum Mechanics, Vienna, pp. 16–53. Springer, Wein, 1968 (1966)
  2.Ericksen J.L.: Anisotropic fluids. Arch. Ration. Mech. Anal. 4, 231–237 (1960)MathSciNet CrossRef
  3.Eringen A.C.: Simple microfluids. Int. J. Eng. Sci. 2, 205–217 (1964)MathSciNet CrossRef
  4.Eringen A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)MathSciNet
  5.Flory P.: Thermodynamic relations for highly elastic materials. Trans. Faraday Soc. 57, 829–838 (1961)MathSciNet CrossRef
  6.Frank R.C.: On the theory of liquid crystals. Discuss. Faraday Soc. 25, 19–28 (1958)CrossRef
  7.Gilman, J.J.: Physical nature of plastic flow and fracture. In: Plasticity: Proceedings of the Second Symposium on Naval Structural mechanics, pp. 43–99 (1960)
  8.Oseen C.W.: Theory of liquid crystals. Trans. Faraday Soc. 29, 883–899 (1933)CrossRef
  9.Rubin M.B., Papes O.: Advantages of formulating evolution equations for elastic–viscoplastic materials in terms of the velocity gradient instead of the spin tensor. J. Mech. Mater. Struct. 6, 229–243 (2011)CrossRef
  10.Rajagopal K.R., Srinivasa A.R.: Modeling anisotropic fluids within the framework of bodies with multiple natural configurations. J. Non-Newton. Fluid Mech. 99, 109–124 (2001)CrossRef
  11.Rubin M.B.: Plasticity theory formulated in terms of physically based microstructural variables – Part I: Theory. Int. J. Solids Struct. 31, 2615–2634 (1994)CrossRef
  
• 作者单位：M. B. Rubin (1)
  B. Nadler (2)
  
  1. Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, 32000, Haifa, Israel
  2. Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Engineering Thermodynamics and Transport Phenomena
  Mechanics, Fluids and Thermodynamics
  Structural Materials
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0959

文摘

An Eulerian formulation has been developed for the constitutive response of a group of materials that includes anisotropic elastic and viscoelastic solids and viscous fluids. The material is considered to be a composite of an elastic solid and a viscous fluid. Evolution equations are proposed for a triad of vectors m _i that represent the stretches and orientations of material line elements in the solid component. Evolution equations for an orthonormal triad of vectors s _i are also proposed to characterize anisotropy of the fluid component. In particular, for an elastic solid it is shown that the material response is totally characterized by the functional form of the strain energy and by the current values of m _i , which are measurable in the current state of the material. Moreover, it is shown that the proposed Eulerian formulation removes unphysical arbitrariness of the choice of the reference configuration in the standard formulation of constitutive equations for anisotropic elastic solids. Keywords Eulerian formulation Anisotropy Nonlinear Hyperelasticity Viscous fluids