Hamiltonian and Lagrangian theory of viscoelasticity

被引：0
|
作者：
A. Hanyga
M. Seredyńska
机构：
[1] University of Bergen,Department of Earth Sciences
[2] Polish Academy of Sciences,Institute of Fundamental Technological Research
来源：
Continuum Mechanics and Thermodynamics | 2008年 / 19卷
关键词：
Viscoelasticity; Poroelasticity; Relaxation; Energy conservation; Hamiltonian; Lagrangian; Poisson bracket; 46.35.+z; 45.20.dh; 45.20.Jj; 45.10.Hj;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
引用
收藏
相关论文
共 50 条
  • [21] LAGRANGIAN AND HAMILTONIAN METHODS IN MAGNETOHYDRODYNAMICS
    NEWCOMB, WA
    [J]. NUCLEAR FUSION, 1962, : 451 - 463
  • [22] Hamiltonian versus Lagrangian forms
    Trimarco, C
    [J]. TRENDS IN APPLICATIONS OF MATHEMATICS TO MECHANICS, 2000, 106 : 103 - 111
  • [23] LAGRANGIAN SUBMANIFOLDS AND HAMILTONIAN SYSTEMS
    WEINSTEIN, A
    [J]. ANNALS OF MATHEMATICS, 1973, 98 (03) : 377 - 410
  • [24] Commutativity in Lagrangian and Hamiltonian mechanics
    Sridhar, Ananth
    Suris, Yuri B.
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2019, 137 : 154 - 161
  • [25] LAGRANGIAN SUBMANIFOLDS AND HAMILTONIAN DYNAMICS
    TULCZYJEW, WM
    [J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 283 (01): : 15 - 18
  • [26] HAMILTONIAN AND LAGRANGIAN BOND GRAPHS
    BROWN, FT
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1991, 328 (5-6): : 809 - 831
  • [27] LAGRANGIAN AND HAMILTONIAN BRST FORMALISMS
    BATLLE, C
    GOMIS, J
    PARIS, J
    ROCA, J
    [J]. PHYSICS LETTERS B, 1989, 224 (03) : 288 - 290
  • [28] Lagrangian configurations and Hamiltonian maps
    Polterovich, Leonid
    Shelukhin, Egor
    [J]. COMPOSITIO MATHEMATICA, 2023, 159 (12) : 2483 - 2520
  • [29] Classical Mechanics Is Lagrangian; It Is Not Hamiltonian
    Curiel, Erik
    [J]. BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, 2014, 65 (02): : 269 - 321
  • [30] HAMILTONIAN-STRUCTURE OF THE THEORY OF GRAVITY WITH R+T2 TYPE OF LAGRANGIAN
    BLAGOJEVIC, M
    NIKOLIC, IA
    [J]. NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-BASIC TOPICS IN PHYSICS, 1983, 73 (02): : 258 - 273
12345