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;
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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.
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