Monday, 11 October 2004 - 3:30 PM

This presentation is part of : Torquato Symposium

Cellular damageable structures: Waves of damage

Andrej Cherkaev1, Elena Cherkaev1, and Leonid I. Slepyan2. (1) University of Utah, Department of Mathematics, 155 S 1400 E, Salt Lake City, UT 84109, (2) Tel Aviv University, Department of Solid Mechanics, Materials and Structures,, Ramat Aviv, 69978, Israel

The design of a structure under collision can be viewed as a problem of moderate damage distribution throughout the structure.Any structure experiences some damage absorbing the kinetic energy of a projectile; the desired structures must evenly distribute a moderate damage throughout the volume, transform the energy into high-frequencies modes, and provide effective dissipation.We show that these goals are achieved by using structural elements with non-unimodal force-elongation dependence. Particularly, damageable bistable "waiting links" are used for the increase of the dynamic strength of structures. They dissipate and/or radiate the energy by originating the transitional waves of a partial damage.The "domino problem'' is addressed of propagating of the damage through the chains and lattices. We calculate the speed of the nonlinear transition wave and the conditions of the spreading of damage. The long-range ordering of a regular two-dimensional networks helps propagating the wave of damage.The robustness of the design is discussed. A numerical study demonstrates a possibility of the control of andoptimization against the damage process. The project is supported by ARO and by NSF.

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