Abstract
Some elastic solids fail not through macro — fracture or plastic flow, but rather through growth of micro — defects. Modelling of such processes occurs through theories of continuous damage mechanics. Thermodynamic aspects of one such theory are discussed in this paper, focussing on limitations of admissible processes, energy dissipation in a loading — unloading cycle and the number of cycles leading to failure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Krajcinovic, D., Continuum damage mechanics, Appl.Mech.Rev.,v. 37, no. 1, 1–6, 1984
Krajcinovic, D., Continuum damage mechanics, Mechanics Today, to be published
Herrmann, G., On energetics of interacting defects, Proc. 3rd Symposium on Energy Engineering Sciences,Conf.–8510176, held at the Pennsylvania State Univ., University Park, Pa., Oct. 8–10, 1985
Gyarmaty, I., Non - equilibrium thermodynamics. Field theory and variational principles, Springer - V., Berlin - Heidelberg - New York, 1970
Prigogine, I. Introduction to thermodynamics of irreversible processes, Springfield, 1955
Meixner, J., Reik, H.G., Thermodynamik der irreversiblen Prozesse, in: Handbook der Physik, Bd. 3, TI. 2, Springer - V., Berlin - Göttingen - Heidelberg, 1959
Kachanov, L.M., Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, v. 8, (1958), 26–31
Grady, D.E., Kipp, M.E., Continuum modelling of explosive fracture in oil shale, Rock Mech. Min. Sci. Geomech. Abstr., v. 17 (1980), 147–157
Denkhaus, H.G., The load -deformation behaviour of rock in uni -axial compression, Rock Mechanics, Suppl. v. 2 (1973), 33–51
Walsh, J.B., The effects of cracks in the compressibility of rock, J. Geophys. Res., v. 70 (1965), 381–389
Davison, L., Stevens, A.L., Thermomechanical constitution for spalling elastic bodies, J. Appl. Phys., v. 44 (1976), 93–106
Cherepanov, G.P., Mechanics of brittle fracture, Nauka Publ., Moscow, 1974 (in Russian)
Lippmann, H., Ductility caused by progressive formation of shear cracks, in: Three–dimensional constitutive relations and ductile fracture, ed. by S. Nemat–Nasser, N.–Holland Publ. Co., Amsterdam, 1981, pp. 389–404
Mroz, Z., Mathematical models of inelastic concrete behaviour, in: Inelasticity and non–linearity in structural concrete, ed. by Cohn, M.Z., Univ. Waterloo Press, 1972, pp. 47–72
Ziegler, H., Some extremum principles in irreversible thermodynamics with applications to continuum mechanics, in: Progress in solid mechanics, v.IV, Ch.II, ed. by Sneddon, I. N., Hill, R., N. -Holland Publ. Co., Amsterdam, 1963
Chaboche, J. - L., Lemaitre, J., Mecanique des materiaux solides, Dunod, Paris, 1985
Krajcinovic, D., Ilankamban, R., Mechanics of solids with defective microstructure, J. Struct. Mech., v. 13 (1985), 267–282
Lippmann, H., Mechanik des plastischen Fließens, Springer - V., Berlin - Heidelberg - N.York, 1981
Budiansky, B., O’Connell, R., Elastic moduli of a cracked solid, Int. J. Solids Structures, v. 12 (1976), 8’1–97
Kachanov, L.M., Introduction to continuum damage mechanics, M. Nijhoff Publ., Dordrecht, 1986
Dems, K., Mroz, Z., Stability conditions for brittle–plastic structures with propagating damage surfaces, J. Struct. Mech., v. 13 (1985), 95–122
Hogland, R.G., Hahn, G.T., Rosenfield, A.R., Influence of micro -structure on fracture propagation in rock, Rock Mechanics, v. 5 (1973), 77–106
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Wien
About this chapter
Cite this chapter
Najar, J. (1987). Continuous Damage of Brittle Solids. In: Krajcinovic, D., Lemaitre, J. (eds) Continuum Damage Mechanics Theory and Application. International Centre for Mechanical Sciences, vol 295. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2806-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2806-0_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82011-7
Online ISBN: 978-3-7091-2806-0
eBook Packages: Springer Book Archive