Energy Dissipation in Solids due to Material Inelasticity, Viscous Coupling, and Algorithmic Damping
Publication: Journal of Engineering Mechanics
Volume 145, Issue 9
Abstract
Presented is a study on energy dissipation in dynamic inelastic systems due to material inelasticity, viscous damping, and algorithmic damping. Formulation for plastic dissipation is based on thermodynamics, with consideration of plastic free energy. Computation of viscous energy dissipation of the Rayleigh type is developed and discussed. Energy dissipation due to algorithmic damping is discussed as well, and compared with the previous two, physical energy dissipation mechanisms. Energy dissipation due to all three dissipation mechanisms is illustrated and discussed in relation to single-element tests and dynamic wave propagation problems.
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Acknowledgments
This work was supported in part by the US DOE.
References
Argyris, J., and H.-P. Mlejnek. 1991. Dynamics of structures. Amsterdam, Netherlands: North Holland.
Bathe, K.-J. 2007. “Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme.” Comput. Struct. 85 (7): 437–445. https://doi.org/10.1016/j.compstruc.2006.09.004.
Besseling, J. F., and E. Van Der Giessen. 1994. Mathematical modeling of inelastic deformation. Vol. 5 of Applied mathematics and mathematical computation. Boca Raton, FL: CRC Press.
Caughey, T. 1960. “Classical normal modes in damped linear systems.” J. Appl. Mech. 27 (2): 269–271. https://doi.org/10.1115/1.3643949.
Chung, J., and G. Hulbert. 1993. “A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized- method.” J. Appl. Mech. 60 (2): 371–375. https://doi.org/10.1115/1.2900803.
Collins, I. F., and G. T. Houlsby. 1997. “Application of thermomechanical principles to the modelling of geotechnical materials.” Proc. R. Soc. London. Ser. A 453 (1964): 1975–2001. https://doi.org/10.1098/rspa.1997.0107.
Collins, I. F., and P. A. Kelly. 2002. “A thermomechanical analysis of a family of soil models.” Geotechnique 52 (7): 507–518. https://doi.org/10.1680/geot.2002.52.7.507.
Farren, W., and G. Taylor. 1925. “The heat developed during plastic extension of metals.” Proc. R. Soc. London. Ser. A 107 (743): 422–451. https://doi.org/10.1098/rspa.1925.0034.
Feigenbaum, H. P., and Y. F. Dafalias. 2007. “Directional distortional hardening in metal plasticity within thermodynamics.” Int. J. Solids Struct. 44 (22–23): 7526–7542. https://doi.org/10.1016/j.ijsolstr.2007.04.025.
Gonzalez, O. 2000. “Exact energy and momentum conserving algorithms for general models in nonlinear elasticity.” Comput. Methods Appl. Mech. Eng. 190 (13–14): 1763–1783. https://doi.org/10.1016/S0045-7825(00)00189-4.
Hall, J. F. 2006. “Problems encountered from the use (or misuse) of Rayleigh damping.” Earthquake Eng. Struct. Dyn. 35 (5): 525–545. https://doi.org/10.1002/eqe.541.
Hilber, H. M., T. J. R. Hughes, and R. L. Taylor. 1977. “Improved numerical dissipation for time integration algorithms in structural dynamics.” Earthquake Eng. Struct. Dyn. 5 (3): 283–292. https://doi.org/10.1002/eqe.4290050306.
Hughes, T. 1987. The finite element method: Linear static and dynamic finite element analysis. Upper Saddle River, NJ: Prentice-Hall.
Jeremić, B., et al. 2018. Nonlinear finite elements: Modeling and simulation of earthquakes, soils, structures and their interaction. Davis, CA: Univ. of California, and Lawrence Berkeley National Laboratory.
Jeremić, B., G. Jie, M. Preisig, and N. Tafazzoli. 2009. “Time domain simulation of soil–foundation–structure interaction in non-uniform soils.” Earthquake Eng. Struct. Dyn. 38 (5): 699–718. https://doi.org/10.1002/eqe.896.
Krenk, S. 2006. “Energy conservation in Newmark based time integration algorithms.” Comput. Methods Appl. Mech. Eng. 195 (44–47): 6110–6124. https://doi.org/10.1016/j.cma.2005.12.001.
Krenk, S. 2014. “Global format for energy-momentum based time integration in nonlinear dynamics.” Int. J. Numer. Methods Eng. 100 (6): 458–476. https://doi.org/10.1002/nme.4745.
Mason, J., A. Rosakis, and G. Ravichandran. 1994. “On the strain and strain rate dependence of the fraction of plastic work converted to heat: An experimental study using high speed infrared detectors and the Kolsky bar.” Mech. Mater. 17 (2–3): 135–145. https://doi.org/10.1016/0167-6636(94)90054-X.
Newmark, N. M. 1959. “A method of computation for structural dynamics.” J. Eng. Mech. Div. 85 (3): 67–94.
Ostadan, F., N. Deng, and J. M. Roesset. 2004. “Estimating total system damping for soil-structure interaction systems.” In Proc., Third UJNR Workshop on Soil-Structure Interaction. Alexandria, VA: U.S. National Science Foundation.
Rittel, D. 2000. “An investigation of the heat generated during cyclic loading of two glassy polymers. Part I: Experimental.” Mech. Mater. 32 (3): 131–147. https://doi.org/10.1016/S0167-6636(99)00051-4.
Rittel, D., and Y. Rabin. 2000. “An investigation of the heat generated during cyclic loading of two glassy polymers. Part II: Thermal analysis.” Mech. Mater. 32 (3): 149–159. https://doi.org/10.1016/S0167-6636(99)00052-6.
Rosakis, P., A. Rosakis, G. Ravichandran, and J. Hodowany. 2000. “A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals.” J. Mech. Phys. Solids 48 (3): 581–607. https://doi.org/10.1016/S0022-5096(99)00048-4.
Ryan, H. 1994. “Ricker, Ormsby, Klander, Butterworth: A choice of wavelets.” Can. Soc. Explor. Geophysicists Recorder 19 (7): 8–9.
Simo, J. C., and K. K. Wong. 1991. “Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum.” Int. J. Numer. Methods Eng. 31 (1): 19–52. https://doi.org/10.1002/nme.1620310103.
Veveakis, E., J. Sulem, and I. Stefanou. 2012. “Modeling of fault gouges with Cosserat continuum mechanics: Influence of thermal pressurization and chemical decomposition as coseismic weakening mechanisms.” J. Struct. Geol. 38 (May): 254–264. https://doi.org/10.1016/j.jsg.2011.09.012.
Watanabe, K., F. Pisanò, and B. Jeremić. 2017. “A numerical investigation on discretization effects in seismic wave propagation analyses.” Eng. Comput. 33 (3): 519–545. https://doi.org/10.1007/s00366-016-0488-4.
Yang, H., Y. Feng, H. Wang, and B. Jeremić. Forthcoming. “Energy dissipation analysis for inelastic reinforced concrete and steel beam-columns.” Eng. Struct.
Yang, H., S. K. Sinha, Y. Feng, D. B. McCallen, and B. Jeremić. 2018. “Energy dissipation analysis of elastic-plastic materials.” Comput. Methods Appl. Mech. Eng. 331 (Apr): 309–326. https://doi.org/10.1016/j.cma.2017.11.009.
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©2019 American Society of Civil Engineers.
History
Received: Sep 24, 2018
Accepted: Dec 5, 2018
Published online: Jun 17, 2019
Published in print: Sep 1, 2019
Discussion open until: Nov 17, 2019
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