Nonequilibrium and Nonlinear Dynamics in Geomaterials I : The Low Strain Regime

Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10^{-7}. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10^{-9}. Our study establishes the existence of two strain thresholds, the first, epsilon_L, below which the material is essentially linear, and the second, epsilon_M, below which the material is nonlinear but where quasiequilibrium thermodynamics still applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above epsilon_M the behavior becomes truly nonequilibrium -- as demonstrated by the existence of material conditioning -- and Landau theory no longer applies. The main focus of this paper is the study of the region below the second threshold, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.Comment: 14 pages, 15 figure

A novel protamine variant reversal of heparin anticoagulation in human blood in vitro

AbstractPurpose: Protamine reversal of heparin anticoagulation during cardiovascular surgery may cause severe hypotension and pulmonary hypertension. A novel protamine variant, [+18RGD], has been developed that effectively reverses heparin anticoagulation without toxicity in canine experiments. Heretofore, human studies have not been undertaken. This investigation hypothesized that [+18RGD] would effectively reverse heparin anticoagulation of human blood in vitro. Methods: Fifty patients who underwent anticoagulation therapy during vascular surgery had blood sampled at baseline and 30 minutes after receiving heparin (150 IU/kg). Activated clotting times were used to define specific quantities of [+18RGD] or protamine necessary to completely reverse heparin anticoagulation in the blood sample of each patient. These defined amounts of [+18RGD] or protamine were then administered to the heparinized blood samples, and percent reversals of activated partial thromboplastin time, thrombin clotting time, and antifactor Xa/IIa levels were determined. In addition, platelet aggregation assays, as well as platelet and white blood cell counts were performed. Results: [+18RGD] and protamine were equivalent in reversing heparin as assessed by thrombin clotting time, antifactor Xa, antifactor IIa levels, and white blood cell changes. [+18RGD], when compared with protamine, was superior in this regard, as assessed by activated partial thromboplastin time (94.5 ± 1.0 vs 86.5 ± 1.3%δ, respectively; p < 0.001) and platelet declines (–3.9 ± 2.9 vs –12.8 ± 3.4 per mm3, respectively; p = 0.048). Platelet aggregation was also decreased for [+18RGD] compared with protamine (23.6 ± 1.5 vs 28.5 ± 1.9%, respectively; p = 0.048). Conclusions: [+18RGD] was as effective as protamine for in vitro reversal of heparin anticoagulation by most coagulation assays, was statistically more effective at reversal than protamine by aPTT assay, and was associated with lesser platelet reductions than protamine. [+18RGD], if less toxic than protamine in human beings, would allow for effective clinical reversal of heparin anticoagulation. (J Vasc Surg 1997;26:1043-8.

LA4R-00-4691 NEW NONLINEAR ACOUSTIC TECHNIQUES FOR NDE

Abstract. Acoustic nonlinearity in a medium may occur as a result of a variety of mechanisms. Some of the more common nonlinear effects may come from: (1) one or several cracks, volumetrically distributed due to age or fatigue or single disbonds or delamination; (2) imperfect grain-to-grain contacts, e.g., materials like concretes that are &quot;cemented&quot; together and have less than perfect bonds; (3) hard parts in a &quot;soft&quot; matrix, e.g., extreme duty materials like tungsten/copper alloys; or (4) atomic-scale nonlinearities. Nonlinear effects that arise from the first two mechanisms are considerably larger than the last two; thus, we have focused considerable attention on these. The most pervasive nonlinear measure of damage today is a second harmonic measurement. We show that for many cases of interest to NDE, a second harmonic measurement may not be the best choice. We examine the manifestations of nonlinearity in (nonlinear) materials with cracks and/or imperfect bonds and illustrate their applicability to NDE. For example, nonlinear resonance frequency shifts measured at increasing drive levels correlate strongly with the amount of ASR (alkali-silica reaction) damage of concrete cores. Memory effects (slow dynamics) also seem to correlate with the amount of damage

Electric field effects in RUS measurements

Much of the power of the Resonant Ultrasound Spectroscopy (RUS) technique is the ability to make mechanical resonance measurements while the environment of the sample is changed. Temperature and magnetic field are important examples. Due to the common use of piezoelectric transducers near the sample, applied electric fields introduce complications, but many materials have technologically interesting responses to applied static and RF electric fields. Non-contact optical, buffered, or shielded transducers permit the application of charge and externally applied electric fields while making RUS measurements. For conducting samples, in vacuum, charging produces a small negative pressure in the volume of the material - a state rarely explored. At very high charges we influence the electron density near the surface so the propagation of surface waves and their resonances may give us a handle on the relationship of electron density to bond strength and elasticity. Our preliminary results indicate a charge sign dependent effect, but we are studying a number of possible other effects induced by charging. In dielectric materials, external electric fields influence the strain response, particularly in ferroelectrics. Experiments to study this connection at phase transformations are planned. The fact that many geological samples contain single crystal quartz suggests a possible use of the piezoelectric response to drive vibrations using applied RF fields. In polycrystals, averaging of strains in randomly oriented crystals implies using the "statistical residual" strain as the drive. The ability to excite vibrations in quartzite polycrystals and arenites is explored. We present results of experimental and theoretical approaches to electric field effects using RUS methods

TenCate, “Soft-ratchet modeling of slow dynamics in the nonlinear resonant response of sedimentary rocks”, in this Proceedings. Downloaded 02 Oct 2006 to 128.165.206.18. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/pr

Abstract. We propose a closed-form scheme that reproduces a wide class of nonlinear and hysteretic effects exhibited by sedimentary rocks in longitudinal bar resonance. In particular, we correctly describe: hysteretic behavior of a resonance curve on both its upward and downward slopes; linear softening of resonant frequency with increase of driving level; gradual (almost logarithmic) recovery (increase) of resonance frequency after large dynamical strains; and temporal relaxation of response amplitude at fixed frequency. Further, we are able to describe how water saturation enhances hysteresis and simultaneously decreases quality factor. The basic ingredients of the original bar system are assumed to be two coupled subsystems, namely, an elastic subsystem sensitive to the concentration of intergrain defects, and a kinetic subsystem of intergrain defects supporting an asymmetric response to an alternating internal stress

Dynamic and quasi-static measurements of PBXN-5 and comp-B explosives

We have measured dynamic and quasi-static mechanical properties of PBXN-5 and Comp-B explosive materials to provide input data for modeling efforts. Dynamic measurements included acoustic and split-Hopkinson pressure bar tests. Quasi-static testing was done in compression on a load frame. Hopkinson bar and quasistatic testing was done at five temperatures from -50{sup o}C to 50{sup o}C. Our results were dominated by the low density of the samples and showed up as low acoustic velocities and lower strengths, as compared to other materials of the same or similar formulations. The effects seem to be consistent with the high porosity of the materials. The data do provide useful input to models that include density as a parameter and suggest caution when using measurements of ideal materials to predict behavior of damaged materials

Low temperature elastic constants and nonlinear acoustic response in rocks and complex materials

The 'P-M Space' model of Guyer and McCall has some success in describing the large nonlinear effects ('slow dynamics') observed by Johnson et al. in rocks. The model uses elements which couple classical nonlinear elasticity with hysteretic components. The actual processes and scales corresponding to the model elements are not yet defined, however it is reasonable to seek energy scales by studying the low-temperature dependence of the elastic constants. We have measured qualitative elastic properties of basalt and Berea sandstone from room temperature down to 4 K using Resonant Ultrasound Spectroscopy (RUS). A simple elastic solid should show a monotonic increase in the elastic constants as temperature decreases. The basalt samples show this gross behavior but the sandstone shows a very unexpected anomalous regime between 40 K and 200 K where the elastic constants decrease with decreasing temperature. Both rocks show temperature-dependent structure in both the modulus and internal friction, and also significant hysteresis, indicating history and rate-dependent properties. This data provides insight into the time and energy scales of dynamical effects observed in sandstones