Validating Theories for Brittle Damage
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ODELING damage and the eventual failure of brittle materials continues to be a ‘‘grand challenge’’ in the theoretical and computational physics community. Often, the physical and mathematical underpinnings are more complicated for brittle materials than for other engineering materials, and damage diagnostic data have not, until recently, been detailed enough to discriminate between competing models. Fundamentally different models, for example, are capable of reproducing plate slap or penetration data.[1] Higher fidelity, more detailed, experimental data, such as time-resolved measurements of penetration[2] and images of crack network morphology,[3] seem essential to deciding whether one model is better than another. Regarding the usefulness of existing models for brittle failure, an Army experimentalist and modeler commented:[2] ‘‘In the hands of an experienced user with a good understanding of computational mechanics and ballistics, current computational tools can be effectively used to gain insight into the effects of specific design variables on various indicators of performance including overall performance. However, our understanding of the fundamental phenomena (such as contact, penetration, fragmentation, inelastic behavior, and failure) that are encountered in a ballistic event is still limited. This has been due in part to our failure or inability to accurately or directly study these complex phenomena under relevant REBECCA M. BRANNON, Associate Professor, is with the Materials Engineering Department, University of Utah, Salt Lake City, UT 84112, USA. JOSEPH M. WELLS, Consultant, is with the JMW Associates, Mashpee, MA 02649, USA. Contact e-mail: brannon@ mech.utah.edu O. ERIK STRACK, Senior Member of Technical Staff, is with the Sandia National Laboratories, Albuquerque, NM 87185, USA. This article is based on a presentation made in the symposium entitled ‘‘Dynamic Behavior of Materials,’’ which occurred during the TMS Annual Meeting and Exhibition, February 25–March 1, 2007 in Orlando, Florida, under the auspices of The Minerals, Metals and Materials Society, TMS Structural Materials Division, and TMS/ASM Mechanical Behavior of Materials Committee. Article published online September 28, 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A
conditions and at the length-scales required. Consequently, accurate prediction of the performance of ceramic armors is still a challenge.’’
Perhaps the greatest impediment to testing the merits of brittle failure models is that none of them (including ours) is convincingly verified, much less validated. Although scholarly definitions are available (cf. Reference 4), the distinction between verification and validation is frequently explained as follows: verification ensures that we are solving the equations right, whereas validation ensures that we are solving the right equations. Verification is a purely mathematical and comprehensive demonstration of the well-posedness of the equations and of the accuracy of their numerical implementation (preferably relative to simplified analyti
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