Summary
Continuum damage theories can be applied to simulate the failure behaviour of engineering constructions. In the constitutive equations of the material a damage parameter is incorporated. A damage criterion and a damage evolution law are postulated and quantified based on experimental data. The elaboration of the mathematical formulation is performed by common finite element techniques. Without special precautions the numerical results appear to be unacceptably dependent on the measure of the spatial discretization. It is shown that a simple but effective procedure leads to the conservation of objectivity.
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References
Kachanov, L. M.: Introduction to continuum damage mechanics. Dordrecht: Martinus Nijhoff 1986.
Lemaitre, J.: Local approach of fracture. Eng. Fract. Mech.25, 523–537 (1986).
Chaboche, J. L.: Continuum damage mechanics, parts 1 and 2. J. Appl. Mech.55, 59–72 (1988).
Bathe, K. J.: Finite element procedures in engineering analysis. Englewood Cliffs: Prentice-Hall 1982.
Pietruszczak, S. T., Mroz, Z.: Finite element analysis of the deformation of strain-softening materials. J. Num. Meth. Eng.17, 327–334 (1981).
Bazant, Z. P., Lin, F. B., Pijaudier-Cabot, G.: Yield limit degradation: nonlocal continuum model with local strain. Proc. Int. Conf. on Computational Plasticity; Barcelona (Onate, E., Owen, R., Hinton, E., eds.), pp. 1757–1779 (1987).
Needleman, A.: Material rate dependence and mesh sensitivity in localization problems. Comp. Meth. Appl. mech. Eng.67, 69–85 (1988).
Mazars, J., Ramtani, S., Berthaud, Y.: An experimental procedure to delocalize tensile failure and to identify the unilateral effect of distributed damage. Proc. France-US Workshop on Strain Localization and Size Effect due to Cracking and Damage; Cachan, France (Mazars, J., Bazant, Z. P., eds.), pp. 55–64 (1988).
Bazant, Z. P.: Mechanics of distributed cracking. Appl. Mech. Rev. (ASME)39, 675–705 (1986).
Bazant, Z. P.: Stable states and stable paths of propagation of damage zones and interactive fractures. Proc. France-US Workshop on Strain Localization and Size Effect due to Cracking and Damage; Cachan, France (Mazars, J., Bazant, Z. P., eds.), pp. 183–206 (1988).
Schreyer, H. L., Chen, Z.: One-dimensional softening with localization. J. Appl. Mech. (ASME)53, 791–797 (1986).
de Borst, R., Mühlhaus, H. B.: Continuum models for discontinuous media. Proc. Int. RILEM/ESIS Conf. on Fracture Processes in Concrete, Rock and Ceramics, Noordwijk, The Netherlands (van Mier, J. G. M., Rots, J. G., Bakker, A., eds.), pp. 601–618 (1991).
Simo, J. C.: Strain softening and dissipation: a unification of approaches. Proc. France-US Workshop on Strain Localization and Size Effect due to Cracking and Damage; Cachan, France (Mazars, J., Bazant, Z. P., eds.), pp. 440–461 (1988).
Saouridis, C., Mazars, J.: A multiscale approach to distributed damage and its usefulness for capturing structural size effect. Proc. France-US Workshop on Strain Localization and Size Effect due to Cracking and Damage; Cachan, France (Mazars, J., Bazant, Z. P., eds.), pp. 391–403 (1988).
Triantafyllidis, N., Aifantis, E. C.: A gradient approach to localization of deformation. I. Hyperelastic materials. J. Elasticity16, 225–237 (1986).
Kachanov, L. M.: Time of the rupture process under creep conditions. Tzv. Akad. Nauk. SSR. Otd. Tekh.8, 26–31 (1958).
Brekelmans, W. A. M., Schreurs, P. J. G., de Vree, J. H. P.: Continuum damage mechanics for softening of brittle materials. Acta Mech.93, 133–143 (1992).
van der Varst, P. G. T., Brekelmans, W. A. M., de Vree, J. H. P., de Groot, R.: Mechanical performance of a dental composite: probabilistic failure prediction. J. Dent. Res.72, 1249–1256 (1993).
Carmeliet, J.: The durability of fiber-reinforced renderings for outside insulation. Ph. D. Thesis, University of Leuven 1992.
Bazant, Z. P., Pijaudier-Cabot, G.: Measurement of characteristic length of nonlocal continuum. J. Eng. Mech. (ASCE)115, 755–767 (1989).
Rots, J. G.: Computational modeling of concrete fracture. Ph. D. Thesis, Delft University of Technology 1988.
Mazars, J.: Probabilistic aspects of mechanical damage in concrete structures. Proc. Int. Conf. on Fracture Mechanics Technology Applied to Material Evaluation and Structural Design, melbourne, Australia, pp. 657–666 (1982).
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Brekelmans, W.A.M., de Vree, J.H.P. Reduction of mesh sensitivity in continuum damage mechanics. Acta Mechanica 110, 49–56 (1995). https://doi.org/10.1007/BF01215415
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DOI: https://doi.org/10.1007/BF01215415