Deformation Behavior of Ductile Solids Containing Anisotropic Damage
Publication: Journal of Engineering Mechanics
Volume 119, Issue 7
Abstract
Many materials of interest contain initial crack‐like defects. Often these cracks are oriented more or less regularly and hence, they contribute to an anisotropic material behavior. We have applied a second‐order tensorial representation of damage, and treat the cracks as a continuum phenomenon on a suitable macroscopic scale. Our model accounts for the progressive failure of damaging materials due to the growth of these defects. The main emphasis of the presented work is put on the propagation of sets of cracks in mode II. This case occurs when the loading axis does not coincide with the plane of the initial cracks. Thus, our model is not restricted to proportional loading. Assuming the existence of a Helmholz free‐energy function and a dissipation potential in the space of affinities we have derived a constitutive equation and a damage propagation law by means of the thermodynamic principles of irreversible processes. Within the framework of the small deformation theory, the proposed formulation considers both brittle and ductile materials.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ashby, M. F., and Hallam, S. D. (1986). “The failure of brittle solids containing small cracks under compressive stress states.” Acta metall., 34(3), 497–510.
2.
Chow, C. L., and Lu, T. J. (1989). “On evolution laws of anisotropic damage.” Engrg. Fract. Mech., 34(3), 679–701.
3.
Coleman, B. D., and Gurtin, M. E. (1967). “Thermodynamics with internal state variables.” J. Chem. Phys., 47(2), 597–613.
4.
Ilankamban, R., and Krajcinovic, D. (1987). “A constitutive theory for progressively deteriorating brittle solids.” Int. J. Solids Struct., 23(11), 1521–1534.
5.
Kawamoto, T., Ichikawa, Y., and Kyoya, T. (1988). “Deformation and fracturing 1349 behaviour of discontinuous rock mass and damage mechanics theory.” Int. J. Num. Anal. Meth. Geom., 12(1), 1–30.
6.
Kobayashi, S. (1972). “Fracture criteria for rock‐like materials.” Proc. Kyoto Conf. on the Strength of Materials, 1–11.
7.
Krajcinovic, D. (1983). “Constitutive equations for damaging materials.” J. Appl. Mech., 50(June), 355–360.
8.
Lemaitre, J. (1971). “Evaluation of dissipation and damage in metals, submitted to dynamic loading.” Proc. ICM1, Kyoto, Japan.
9.
Mròz, Z. (1973). Mathematical models of inelastic material behaviour. Univ. of Waterloo, 120–146.
10.
Murakami, S. (1988). “Mechanical modeling of material damage.” J. Appl. Mech., 55(June), 280–286.
11.
Murakami, S., and Ohno, N. (1981). “A continuum theory of creep and creep damage.” Creep in structures, Springer‐Verlag, Berlin, Germany, pp. 422–444.
12.
Paterson, M. S. (1978). Experimental rock deformation—The brittle field, Springer‐Verlag, Berlin, Germany.
13.
Rabotnov, Y. N. (1969). Creep problems in structural members. North Holland, Amsterdam, The Netherlands.
14.
Rice, J. R. (1971). “Inelastic constitutive relations for solids: An internal‐variable theory and its application to metal plasticity.” J. Mech. Phys. Solids, 19, 433–455.
15.
Rivlin, R. S., and Ericksen, J. L. (1955). “Stress‐deformation relations for isotropic materials.” J. Rational Mech. and Anal., 4, 323–425.
16.
Simo, J. C., and Ju, J. W. (1987). “Strain‐ and stress‐based continuum damage models—I. Formulation.” Int. J. Solids Struct., 23(7), 821–840.
17.
Singh, U. K., Digby, P. J., and Stephansson, O. J. (1987). “Constitutive equation for progressive failure of brittle rock.” Constitutive laws for engineering materials, Elsevier, 923–930.
18.
Stumvoll, M. (1991). “Numerical model for discontinuous rock mass considering damage propagation under non‐proportional and compressive loading,” PhD Thesis, University of Innsbruck, Austria.
19.
Stumvoll, M., Kyoya, T., Ichikawa, Y., and Swoboda, G. (1991). “A damage model for discontinuous rock mass based on thermodynamic principles.” Proc. Comp. Method. and Adv. in Geomech., Balkema, 427–434.
20.
Suaris, W. (1987). “A damage theory for concrete incorporating crack growth characteristics.” Constitutive Laws for Engineering Materials, Elsevier, 931–938.
21.
Truesdell, C., and Noll, W. (1965). “The non‐linear field theories of mechanics.” Encyclopedia of Physics 3, Springer, Berlin, Germany.
22.
Truesdell, C., and Toupin, R. (1960). “The classical field theories.” Encyclopedia of Physics 3, Springer, Berlin, Germany, p. 257.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 7 • July 1993
Pages: 1331 - 1352
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: May 8, 1992
Published online: Jul 1, 1993
Published in print: Jul 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.