A recursive-faulting model of distributed damage in confined brittle materials
We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement.
© 2006 Elsevier Ltd. Received 17 August 2005; received in revised form 9 February 2006; accepted 11 February 2006. M.O. and A.P. gratefully acknowledge the support of the Department of Energy through Caltech's ASCI ASAP Center for the Simulation of the Dynamic Response of Materials. A.P. additionally acknowledges the support of the Italian MIUR through the Cofin2003 program ''Interfacial damage failure in structural systems: applications to civil engineering and emerging research fields''. The work of S.C. was supported by the Deutsche Forschungsgemeinschaft through the Schwerpunktprogramm 1095 Analysis, Modeling and Simulation of Multiscale Problems. This work was partially carried during M.O.'s stay at the Max Planck Institute for Mathematics in the Sciences of Leipzig, Germany, under the auspices of the Humboldt Foundation. M.O.'s gratefully acknowledges the financial support provided by the Foundation and the hospitality extended by the Institute.
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