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Local and nonlocal material models, spatial randomness, and impact loading

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Abstract

In many material systems, both man-made and natural, we have an incomplete knowledge of geometric or material properties, which leads to uncertainty in predicting their performance under dynamic loading. Given the uncertainty and a high degree of spatial variability in properties of geological formations subjected to impact, a stochastic theory of continuum mechanics would be useful for modeling dynamic response of such systems. In this paper, we examine spatial randomness in local and nonlocal material-mechanics models. We begin with classical linear elasticity. Then, we consider nonlocal elasticity and, finally, peridynamic theory. We discuss a formulation of stochastic peridynamic theory and illustrate this formulation with examples of impact loading of geological materials with uncorrelated versus correlated properties, sampled in a Monte Carlo sense. We examine wave propagation and damage to the material. The most salient feature is the absence of spallation, referred to as disorder toughness, which, in fact, generalizes similar results from earlier quasi-static damage mechanics.

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Notes

  1. In (29) and elsewhere, bold quantities are vectors unless stated otherwise.

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Acknowledgments

This research was made possible by the support from DTRA Grant HDTRA1-08-10-BRCWM and, in part, by the NSF under Grants CMMI-1462749 and IP-1362146 (I/UCRC on Novel High Voltage/Temperature Materials and Structures).

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Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, 87185, USA

    P. N. Demmie

  2. Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    M. Ostoja-Starzewski

  3. Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    M. Ostoja-Starzewski

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  1. P. N. Demmie
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  2. M. Ostoja-Starzewski
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Correspondence to M. Ostoja-Starzewski.

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Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Demmie, P.N., Ostoja-Starzewski, M. Local and nonlocal material models, spatial randomness, and impact loading. Arch Appl Mech 86, 39–58 (2016). https://doi.org/10.1007/s00419-015-1095-3

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