Hamiltonian and Lagrangian theory of viscoelasticity

Hanyga, A.; Seredynska, M.
March 2008
Continuum Mechanics & Thermodynamics;Mar2008, Vol. 19 Issue 8, p475
Academic Journal
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.


Related Articles

  • DILATATION AND DISTORTIONAL WAVES IN MICRO-ISOTROPIC, MICRO-ELASTIC MEDIUM. Chandulal, A.; Sambaiah, K. // Bulletin of Pure & Applied Sciences-Mathematics;2010, Vol. 29E Issue 2, p309 

    In this paper, the propagation of dilatation and distortional waves in micro-isotropic, microelastic medium has been discussed. Frequency equations have been deduced in both the cases. It is found that additional waves are propagating in the medium. The classical results are obtained as a...

  • Study of wave propagation in nanowires with surface effects by using a high-order continuum theory. Song, F.; Huang, G. L.; Varadan, V. K. // Acta Mechanica;Jan2010, Vol. 209 Issue 1/2, p129 

    A high-order continuum model is developed to study wave propagation in nanowires. By using the model, heterogeneous nanostructure effects can be captured especially for high wave frequency cases. Surface stress effects are also included by using the incremental deformation approach. The...

  • Constant of Motion, Lagrangian and Hamiltonian of the Gravitational Attraction of Two Bodies with Variable Mass. López, G. // International Journal of Theoretical Physics;Apr2007, Vol. 46 Issue 4, p806 

    The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the reference system in the body with much higher mass, it is...

  • Unified formalism for nonautonomous mechanical systems. Barbero-Liñán, María; Echeverría-Enr&;#x00ED;quez, Arturo; Diego, David Martín de; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso // Journal of Mathematical Physics;Jun2008, Vol. 49 Issue 6, p062902 

    We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and nonregular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk [“Generalized Hamiltonian dynamics I. Formulation on T*QxTQ,” J....

  • Low dimensional features of the Hamiltonian Mean Field model. Facchini, Angelo; Ruffo, Stefano // AIP Conference Proceedings;1/11/2008, Vol. 970 Issue 1, p109 

    The order parameter of the Hamiltonian Mean Field (HMF) model, which describes the motion of N globally coupled rotors, is a two-component vector (Mx = ΣiN cos(θi)/N,My = ΣiN sin(θi)/N). Its dynamics is found to be “cyclic”: the vector approaches a fixed norm and rotates...

  • Higher order constrained Hamiltonian systems. Grillo, Sergio D. // Journal of Mathematical Physics;Aug2009, Vol. 50 Issue 8, p082901 

    In this paper we study a Hamiltonian formulation of the higher order constrained systems (HOCSs), defined previously in Lagrangian terms. We shall focus on second order constraints in positions, i.e., second order HOCSs, which correspond, on the Hamiltonian side, to first order constraints in...

  • High order normal form construction near the elliptic orbit of the Sitnikov problem. Di Ruzza, Sara; Lhotka, Christoph // Celestial Mechanics & Dynamical Astronomy;Dec2011, Vol. 111 Issue 4, p449 

    We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action-angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and...

  • Dynamics of a prestressed incompressible layered half-space under moving load. Babich, S.; Glukhov, Yu.; Guz, A. // International Applied Mechanics;Mar2008, Vol. 44 Issue 3, p268 

    The paper addresses a plane problem: a concentrated force acts on a plate resting on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is assumed to be incompressible and isotropic in the natural state. The...

  • Measurement of the compression isentrope for 6061-T6 aluminum to 185 GPa and 46% volumetric strain using pulsed magnetic loading. Hayes, D.B.; Hall, C.A.; Asay, J.R.; Knudson, M.D. // Journal of Applied Physics;11/15/2004, Vol. 96 Issue 10, p5520 

    The Z accelerator at Sandia National Laboratories was used to measure the compression isentrope of 6061-T6 aluminum to 185 GPa. The isentropic compression experimental technique uses a rapidly increasing, planar magnetic field to simultaneously subject multiple planar aluminum samples of...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics