Abstract
We consider a viscoelastic–viscoplastic continuum damage model for polycrystalline ice. The focus lies on the thermodynamics particularities of such a constitutive model and restrictions on the constitutive theory which are implied by the entropy principle. We use Müller’s formulation of the entropy principle, together with Liu’s method of exploiting it with the aid of Lagrange multipliers.
Similar content being viewed by others
References
Carathéodory C.: Untersuchungen über die Grundlagen der Thermodynamik. Mathematische Annalen 67(3), 355–386 (1909)
Duddu R., Waisman H.: A temperature dependent creep damage model for polycrystalline ice. Mech. Mater. 46, 23–41 (2012)
Hutter K.: The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics. Acta Mech. 27(1), 1–54 (1977)
Karr D.G., Choi K.: A three-dimensional constitutive damage model for polycrystalline ice. Mech. Mater. 8(1), 55–66 (1989)
Keller, A., Hutter, K.: A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distributed fiber bundle models. Part I: Constitutive models. Submitted to Continuum Mechanics and Thermodynamics
Keller, A., Hutter, K.: On the thermodynamic consistency of the equivalence principle in continuum damage mechanics. J. Mech. Phys. Solids 59(5), 1115–1120 (2011). doi:10.1016/j.jmps.2011.01.015. http://www.sciencedirect.com/science/article/B6TXB-523CDY6-2/2/bda2f1b70e114f23d673d5cbff6f7e1d
Lemaitre J., Lippmann H.: A course on damage mechanics, vol. 2. Springer, Berlin (1996)
Liu I.S.: Method of Lagrange multipliers for exploitation of entropy principle. Arch. Ration. Mech. Anal. 46(2), 131–148 (1972)
Mahrenholtz, O., Wu, Z.: Determination of creep damage parameters for polycrystalline ice. Advances in Ice Technology (3rd Int. Conf. Ice Tech./Cambridge USA), pp. 181–192 (1992)
Müller I.: Die Kältefunktion, eine universelle Funktion in der Thermodynamik viskoser wärmeleitender Flüssigkeiten. Arch. Ration. Mech. Anal. 40(1), 1–36 (1971)
Pralong, A., Funk, M.: Dynamic damage model of crevasse opening and application to glacier calving. J. Geophys. Res. 110, (B01309) (2005). doi:10.1029/2004JB003104
Pralong A., Hutter K., Funk M.: Anisotropic damage mechanics for viscoelastic ice. Contin. Mech. Thermodyn. 17(5), 387–408 (2006). doi:10.1007/s00161-005-0002-5
Rist, M., Murrell, S.: Ice triaxial deformation and fracture. J. Glaciol. 40(135), 305–318 (1994)
Sinha N.K.: Crack-enhanced creep in polycrystalline material: Strain-rate sensitive strength and deformation of ice. J. Mater. Sci. 23(12), 4415–4428 (1988)
Szyszkowski W., Glockner P.: On a multiaxial constitutive law for ice. Mech. Mater. 5(1), 49–71 (1986)
Weiss J., Gay M.: Fracturing of ice under compression creep as revealed by a multifractal analysis. J. Geophys. Res. 103(B10), 24005–24024 (1998)
**ao J., Jordaan I.: Application of damage mechanics to ice failure in compression. Cold Reg. Sci. Technol. 24(3), 305–322 (1996)
Zheng Q.: Theory of representations for tensor functions—a unified invariant approach to constitutive equations. Appl. Mech. Rev. 47(11), 545–587 (1994)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Andreas Öchsner.
Rights and permissions
About this article
Cite this article
Keller, A., Hutter, K. A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distributed fiber bundle models. Part II: Thermodynamics of a rank-4 damage model. Continuum Mech. Thermodyn. 26, 895–906 (2014). https://doi.org/10.1007/s00161-014-0335-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00161-014-0335-z