Charles G. Sammis

The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ∼10− 6to 103s− 1. Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.

This report results from a contract tasking University of Birmingham as follows: The Grantee will investigate data collected on coronal mass ejections (CME), and attempt to construct images of CMEs as they move towards the earth and predict their arrival. The objective of this research is to create a mathematical model for predicting the arrival and severity of geomagnetic storms resulting from CMEs.

Recent observations of nanometer‐scale particles in the cores of exhumed fault zones raise questions about how such small particles are formed and how they survive, especially if significant shear heating is produced during an earthquake. Commercial crushing and grinding operations encounter a grind limit near 1 μm below which particles deform plastically rather than fracturing. A fragmentation model and low‐temperature plasticity mechanics indicate that it is not possible to produce under compressive loading and short timescale significantly smaller particles at any strain rate. However, shock loading and subcritical crack growth can produce nanometer‐scale fragments in compression. Under tensile loading the fragment size is determined by a competition between the nucleation of cracks and stress relaxation in their neighborhoods. Therefore higher tensile strain rates produce smaller fragments. The ultimate limit is determined by the availability of elastic strain energy, which does not place a significant constraint on the minimum grain size. Grain growth kinetics suggests that survivability of grains is very temperature sensitive. A 10 nm quartz fragment will double its size in 0.1 s at 1000°C, in 20 s at 800°C, in 14 h at 600°C, and in 10 years at 400°C. The observation of grains smaller than 10 nm places meaningful constraints on the dynamic fields and permeability of the fault zone during a large earthquake. Microstructural analysis of the grains and rock damage may be used to infer whether fragmentation occurred under macroscopic tension or compression.

A nearest neighbor fragmentation model, previously developed to explain observations of power law particle distributions in 3D with mass dimension D₃ ≈ 2.6 (D₂ ≈ 2.6 in 2D section) in low‐strain fault gouge and breccia, is extended to the case of large strains to explain recent observations of D₃ ≈ 3.0 (D₂ ≈ 2.0 in 2D section) in the highly strained cores of many exhumed fault zones. At low strains, the elimination of same‐sized nearest neighbors has been shown to produce a power law distribution which is characterized by a mass dimension near D₃ ≈ 2.6. With increasing shear strain these isolated same‐size neighbors can collide, in which case one of them fractures. The probability of two same size neighbors colliding and fragmenting in a simple shear flow is a function of the size and density of the two particles. Only for a power law distribution with D₃ = 3.0 is this collision probability independent of the size of the particles.

We review the “critical point” concept for large earthquakes and enlarge it in the framework of so-called “finite-time singularities.” The singular behavior associated with accelerated seismic release is shown to result from a positive feedback of the seismic activity on its release rate. The most important mechanisms for such positive feedback are presented. We solve analytically a simple model of geometrical positive feedback in which the stress shadow cast by the last large earthquake is progressively fragmented by the increasing tectonic stress.