## Abstract

Determining the effects of material spatial randomness on the distance to form shocks from acceleration waves, x_{∞}, in random media is the objective of the present study. A very general class of random media is modeled by two random fields-the dissipation (μ) and elastic nonlinearity (β). The reason for considering the randomness of said material coefficients is the fact that a wavefront's length scale is not necessarily greater than the representative volume element-a condition tacitly assumed in deterministic continuum mechanics. There are two entirely new aspects considered in the present study. One is the explicit consideration of μ and β as functions of four more fundamental material properties, and themselves random fields: the instantaneous modulus (G_{0}), the dissipation coefficient ( G_{0}^{′} ), the instantaneous second-order tangent modulus ( over(E, ∼)_{0} ), the mass density in the reference state (ρ_{R}). The second new facet is the coupling of the four-component random field [ G_{0}, G_{0}^{′}, over(E, ∼)_{0}, ρ_{R} ]_{x} to the wavefront amplitude α, because as the amplitude grows, the wavefront gets thinner tending to a shock, and thus the material random heterogeneity shows up as a random field with ever stronger fluctuations. In effect, the wavefront is an object which is more appropriately analyzed as a statistical volume element, and therefore to be treated via a stochastic rather than a deterministic dynamical system.

Original language | English (US) |
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Pages (from-to) | 840-848 |

Number of pages | 9 |

Journal | Mechanics of Materials |

Volume | 38 |

Issue number | 8-10 |

DOIs | |

State | Published - Aug 2006 |

Externally published | Yes |

## Keywords

- Random media
- Stochastic mechanics
- Waves in random media

## ASJC Scopus subject areas

- Materials Science(all)
- Instrumentation
- Mechanics of Materials