The elasticity and failure of fluid-filled cellular solids: Theory and experiment

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.