Ralph Menikoff
Los Alamos National Lab.
Continuum mechanics typically treats materials as homogeneous. This is valid for gases and liquids but not for solids. A granular bed provides an extreme example of a heterogeneous material. Behind a moderate strength wave, the shock compression in a granular material is due to squeezing out pore space. The increase in the density of individual grains is negligible. This type of shock is known as a compaction wave. The key properties of compaction waves are displayed in meso-mechanics simulations (continuum mechanics calculations in which individual grains are resolved). Behind the wave front, fluctuations in hydrodynamic quantities arise from material heterogeneities. Nevertheless, average wave profiles have the appearance of a dispersed shock wave. Consequently, on a coarse grain scale heterogeneous materials can be described by the usual continuum mechanics models. However, the average constitutive properties of a granular material need to account for visco-elastic or visco-plastic response not present in the individual grains. Determining the effective constitutive properties of a composite from those of its components has important engineering applications. Numerical experiments can provide insight and guidance for developing an analytical theory for heterogeneous materials.
LA-UR-01-1274
Workshop: Dynamics of Phase Boundaries and Nonclassical Waves
Frieburg, Germany
May 7-9, 2001