Elastic Block Research Articles

Variational formulation of rate‐ and state‐dependent friction problems

We propose a variational formulation of rate‐ and state‐dependent models for the dynamic sliding of a linearly elastic block on a rigid surface in terms of two coupled variational inequalities. Classical Dieterich–Ruina models are covered as special cases. We show existence and uniqueness of solutions for the two spatial subproblems arising from time discretisation. Existence of solutions to the coupled spatial problems is established for Dieterich's state equation through a fixed point argument. We conclude with some numerical experiments that suggest mesh independent convergence of the underlying fixed point iteration, and illustrate quasiperiodic occurrence of stick/slip events.

The Model for Calculating Elastic Modulus and Poisson's Ratio of Coal Body

Coal body is a type of fractured rock mass in which lots of cleat fractures developed. Its mechanical properties vary with the parametric variation of coal rock block, face cleat and butt cleat. Based on the linear elastic theory and displacement equivalent principle and simplifying the face cleat and butt cleat as multi-bank penetrating and intermittent cracks, the model was established to calculate the elastic modulus and Poisson's ratio of coal body combined with cleat. By analyzing the model, it also obtained the influence of the parameter variation of coal rock block, face cleat and butt cleat on the elastic modulus and Poisson's ratio of the coal body. Study results showed that the connectivity rate of butt cleat and the distance between face cleats had a weak influence on elastic modulus of coal body. When the inclination of face cleat was 90°, the elastic modulus of coal body reached the maximal value and it equaled to the elastic modulus of coal rock block. When the inclination of face cleat was 0°, the elastic modulus of coal body was exclusively dependent on the elastic modulus of coal rock block, the normal stiffness of face cleat and the distance between them. When the distance between butt cleats or the connectivity rate of butt cleat was fixed, the Poisson's ratio of the coal body initially increased and then decreased with increasing of the face cleat inclination.

Slip rates and off‐fault deformation in Southern California inferred from GPS data and models

In Southern California, fault slip rate estimates along the San Andreas fault (SAF) and Garlock fault from geodetically constrained kinematic models are systematically at the low end or lower than geologic slip rate estimates. The sum of geodetic model slip rates across the eastern California shear zone is higher than the geologic sum. However, the ranges of reported model and geologic slip rate estimates in the literature are sufficiently large that it remains unclear whether these apparent discrepancies are real or attributable to epistemic uncertainties in the two types of estimates. We further examine uncertainties in geodetically derived slip rate estimates on major faults in Southern California by conducting a suite of inversions with four kinematic models. Long‐term rigid elastic block models constrained by the geologic slip rates cannot fit the present‐day GPS‐derived velocity field. Deforming (permanent off‐fault strain) elastic block models and viscoelastic earthquake cycle block models constrained by geologic slip rates can fit the present‐day GPS‐derived velocity field with 28–33% of the total geodetic moment rate occurring as distributed deformation off of the major faults. Models incorporating viscoelastic mantle flow predict systematically higher slip rates than purely elastic models on many of the major Southern California faults with ranges of (elastic/viscoelastic) 29–34/30–37 mm/yr for the Carrizo SAF segment, 20–24/20–32 mm/yr for the Mojave SAF segment, 14–17/18–22 mm/yr for the Coachella SAF segment, 13–19/14–22 mm/yr for the San Jacinto fault, and 5–11/5–11 mm/yr for the western Garlock fault.

High-sensitivity triaxial tactile sensor with elastic microstructures pressing on piezoresistive cantilevers

In this paper, we proposed a design to increase the sensitivity of a piezoresistive-type triaxial tactile sensor. Using conventional piezoresistive tactile sensors, in which the piezoresistive elements were completely embedded inside an elastic block, our proposed tactile sensor design features an air cavity underneath the piezoresistive elements. The cavity was created by pressing an elastic cap with microstructures onto the piezoresistive cantilevers of a sensor chip. We confirmed that the proposed design increased the sensitivity of the tactile sensor by approximately 150 times and 100 times in response to normal and lateral forces, respectively.

Geodetic investigation into the deformation of the Salton Trough

AbstractThe Salton Trough represents a complex transition between the spreading center in Baja California and the strike‐slip San Andreas fault system and is one of the most active zones of deformation and seismicity in California. We present a high‐resolution interseismic velocity field for the Salton Trough derived from 74 continuous GPS sites and 109 benchmarks surveyed in three GPS campaigns during 2008–2009 and previous surveys between 2000 and 2005. We also investigate small‐scale deformation by removing the regional velocity field predicted by an elastic block model for Southern California from the observed velocities. We find a total extension rate of 11 mm/yr from the Mesquite Basin to the southern edge of the San Andreas Fault, coupled with 15 mm/yr of left‐lateral shear, the majority of which is concentrated in the southern Salton Sea and Obsidian Buttes and is equivalent to 17 mm/yr oriented in the direction of the San Andreas Fault. Differential shear strain is exclusively localized in the Brawley Seismic Zone, and dilatation rate indicates widespread extension throughout the zone. In addition, we infer clockwise rotation of 10°/Ma, consistent with northwestward propagation of the Brawley Seismic Zone over geologic time.

SU-E-T-521: Monte Carlo Dose Calculation for TomoTherapy Using Cloud Computing

Purpose: Monte Carlo (MC) dose calculation has been regarded as the gold standard for accuracy, especially in the presence of patient in‐homogeneities. However, the calculation can be very time consuming as a large number of particle histories are needed to reduce the statistical noise to a level acceptable for clinical use. The purpose of this work is to explore the option of cloud computing to achieve ultra‐fast MC calculation. Methods: A MC package developed for TomoTherapy, TomoPen, was ported to run on Amazon Elastic Cloud (EC2). The executable as well as the phase space file for the MC program was packaged into an Amazon machine image (AMI), which was loaded from Amazon Elastic Block Store (EBS) to each cloud node during initialization process. Message‐Passing‐Interface (MPI) was used to distribute computing tasks to different nodes. Statistics independence of each node was achieved by reading from different location of the phase‐space files. Fifty clinical plans were used to benchmark the cloud computing performance. Results: Benchmarking cases were tested on EC2 with different type and number of computing instances. It was found that the program run time scaled inversely with the number of computing instances. The most cost‐effective EC2 instance was found to be the extra‐large high‐CPU instance. An EC2 cloud with 32 extra‐large high‐CPU computing instance was used to compute MC dose for 50 patient plans. On average, it took 22 seconds total to transfer CT to/dose from cloud and 117 seconds calculation time to get a MC dose with statistical uncertainty of less than 2%. The total cost was less than $3 for one hour when spot instance is used. Conclusion: Cloud computing provides a promising platform to regroup computing resources on‐demand to improve the speed of MC calculation at very little cost. This study is supported in part by UVa George Amorino Pilot Grant.

How do “ghost transients” from past earthquakes affect GPS slip rate estimates on southern California faults?

In this study, we investigate the extent to which viscoelastic velocity perturbations (or “ghost transients”) from individual fault segments can affect elastic block model‐based inferences of fault slip rates from GPS velocity fields. We focus on the southern California GPS velocity field, exploring the effects of known, large earthquakes for two end‐member rheological structures. Our approach is to compute, at each GPS site, the velocity perturbation relative to a cycle average for earthquake cycles on particular fault segments. We then correct the SCEC CMM4.0 velocity field for this perturbation and invert the corrected field for fault slip rates. We find that if asthenosphere viscosities are low (3 × 1018 Pa s), the current GPS velocity field is significantly perturbed by viscoelastic earthquake cycle effects associated with the San Andreas Fault segment that last ruptured in 1857 (Mw = 7.9). Correcting the GPS velocity field for this perturbation (or “ghost transient”) adds about 5 mm/a to the SAF slip rate along the Mojave and San Bernardino segments. The GPS velocity perturbations due to large earthquakes on the Garlock Fault (most recently, events in the early 1600s) and the White Wolf Fault (most recently, the Mw = 7.3 1952 Kern County earthquake) are smaller and do not influence block‐model inverted fault slip rates. This suggests that either the large discrepancy between geodetic and geologic slip rates for the Garlock Fault is not due to a ghost transient or that un‐modeled transients from recent Mojave earthquakes may influence the GPS velocity field.

G051043 衝撃波によって固体内に生じる応力波の可視化に関する研究([G051-04]流体工学部門,一般セッション : 乱流・超音速・制御)

Interaction phenomena of compressible flow and solid object have been attracted interest from a point of view of numerical analysis and experimental investigation. In addition, in the medical field, the development of the technology of the extracorporeal shock wave lithotripsy which employs a high temperature and a high pressure condition caused by a shock wave is remarkable. To prevent the glass of house from being damaged by a sonic boom, to prevent the structure from being destructed by the explosion, and etc., the interaction problem between shock wave and the solid object has been studied. In this study the flow field, in which a shock wave issuing from a diaphragmless shock tube impacts on an elastic block made by acrylic or polycarbonate, is visualized experimentally using Schlieren method. The shock Mach number is about 1.37. As a result, a stress wave is induced by a collision of shock wave and it is found that the characteristics of the stress wave depend on the material and the strength of shock wave.

Latest Pleistocene and Holocene slip rate for the San Bernardino strand of the San Andreas fault, Plunge Creek, Southern California: Implications for strain partitioning within the southern San Andreas fault system for the last ∼35 k.y.

An alluvial succession on the northeast side of the San Bernardino strand of the San Andreas fault includes distinctive aggradational and degradational features that can be matched with correlative features on the southwest side of the fault. Key among these are (1) a terrace riser on the northeast side of the fault that correlates with an offset channel wall on the southwest side of the fault and forms a basis for slip estimates for the period ca. 35 ka to the present, and (2) a small alluvial fan on the southwest side of the fault that has been matched with its most likely source gullies on the northeast side of the fault and forms a basis for slip estimates for the last 10.5 k.y. Slip-rate estimates for these two separate intervals are nearly identical. The rate for the older feature is most likely between 8.3 and 14.5 mm/yr, with a 95% confidence interval of 7.0–15.7 mm/yr. The rate for the younger feature is most likely between 6.8 and 16.3 mm/yr, with a 95% confidence interval of 6.3–18.5 mm/yr. These rates are only half the previously published slip rate for the San Andreas fault 35 km to the northwest in Cajon Pass, a rate that traditionally is extrapolated southeastward along the San Bernardino section of the fault. Results from Plunge Creek suggest that about half of the 25 mm/yr rate at Cajon Pass transfers southeastward to the San Jacinto fault, as proposed by other workers on the basis of regional geologic relations. These results indicate that the discrepancy between latest Quaternary slip rates and present-day rates of strain accumulation across the San Bernardino section of the San Andreas fault from geodesy can be largely explained by slip transfer between faults, leading to spatial variation in rate along the San Andreas fault. Nonetheless, the latest Pleistocene and Holocene slip rate at Plunge Creek is still somewhat faster than rates inferred for the San Bernardino section of the San Andreas fault based on elastic block modeling of geodetic data and may be more appropriate than those rates for hazard estimation.

GPS estimates of microplate motions, northern Caribbean: evidence for a Hispaniola microplate and implications for earthquake hazard

SUMMARY We use elastic block modelling of 126 GPS site velocities from Jamaica, Hispaniola, Puerto Rico and other islands in the northern Caribbean to test for the existence of a Hispaniola microplate and estimate angular velocities for the Gonave, Hispaniola, Puerto Rico-Virgin Islands and two smaller microplates relative to each other and the Caribbean and North America plates. A model in which the Gonave microplate spans the whole plate boundary between the Cayman spreading centre and Mona Passage west of Puerto Rico is rejected at a high confidence level. The data instead require an independently moving Hispaniola microplate between the Mona Passage and a likely diffuse boundary within or offshore from western Hispaniola. Our updated angular velocities predict 6.8 ± 1.0 mm yr−1 of left-lateral slip along the seismically hazardous Enriquillo-Plantain Garden fault zone of southwest Hispaniola, 9.8 ± 2.0 mm yr−1 of slip along the Septentrional fault of northern Hispaniola and ∼14–15 mm yr−1 of left-lateral slip along the Oriente fault south of Cuba. They also predict 5.7 ± 1 mm yr−1 of fault-normal motion in the vicinity of the Enriquillo-Plantain Garden fault zone, faster than previously estimated and possibly accommodated by folds and faults in the Enriquillo-Plantain Garden fault zone borderlands. Our new and a previous estimate of Gonave-Caribbean plate motion suggest that enough elastic strain accumulates to generate one to two Mw∼ 7 earthquakes per century along the Enriquillo-Plantain Garden and nearby faults of southwest Hispaniola. That the 2010 M= 7.0 Haiti earthquake ended a 240-yr-long period of seismic quiescence in this region raises concerns that it could mark the onset of a new earthquake sequence that will relieve elastic strain that has accumulated since the late 18th century.

Another approach of WKB method for the stability analysis of the bending of an elastic rubber block

Our concern in this paper is to study the bifurcation of the pure bending of a rubber block made of elastic Varga material which has a ratio of thickness A to length L. The governing equations are reduced to an eigenvalue system.We then apply the WKB method with repeated roots for describing the angle of bending and also the azimuthal shear. In this process, very interesting solvability conditions are derived and solved. We obtained sufficient conditions for different kinds of L/A. Our findings shows that by increasing the value of L/A the bending angle also increases.

Trapping of a crack advancing through an elastic lattice

The paper presents the model of trapping of a crack within an elastic lattice in two loading configurations, which correspond to different types of engineering applications. First, the model of thermal striping of a continuum slab, containing a Mode I edge crack, under temporally sinusoidal thermal loading is extended to the situation when the continuum is replaced with a uniform triangular lattice. It is shown that in quasi-static growth, the crack advance is influenced by the micro-structure. In the homogenisation approximation, the stress intensity factor in the continuum elastic block is greater than the analogous value for the crack in the lattice. Furthermore, dynamic effects are investigated for the configuration when the size of the lattice cell is comparable with the wavelength of elastic waves generated by an external load. A nonlinear model of dynamic fracture is analysed for a crack advancing in a non-uniform triangular lattice. A comparison is made with a solution of the linearised problem to assess the average speed of the propagating crack.

Numerical analysis of quasistatic frictional contact of an elastic block under combined normal and tangential cyclic loading

Contact between solid bodies has become important in manufacturing in recent years as joining processes involving frictional contact such as friction stir welding and ultrasonic welding have shown significant promise in a number of applications, including the automotive industry. In this study, contact between an elastic block and a rigid surface under normal and/or tangential cyclic loading with mean normal loading is investigated using a commercial FEM package, ABAQUS. The slip/stick status and frictional energy dissipation per cycle are investigated for select combined loading conditions, as well as for different block heights, and cyclic loading frequencies. The results indicate that the combined cyclic loading has the potential to improve ultrasonic weld quality.

Lubrication Simulation of Main Bearing about a Marine Diesel Engine Based on Multi-Body Dynamics and Elastohydrodynamic

The purpose of this paper is to find a method to study the lubrication character of the main bearings and load condition of the crankshaft about the marine two-stroke diesel engine. Based on the finite element method, multi-body dynamics, elastohydrodynamic and Green-Tripp theory about contact, the simulation of coupling between the elastic crankshaft and engine block is carried out. The load of main bearings, the minimum of oil film thick, orbital path of journal, average of asperity contact pressure are explored. The results indicate that the lubrication is good except No.2 main bearing. Parts of main bearings appear three peaks in a working cycle, which shows that above theory and elastic crankshaft and engine block is obligatory to simulate the lubrication and load condition accurately.

Analysis of Present Tectonic Stress and Regional Ground Fissure Formation Mechanism of the Weihe Basin

In this paper, the crustal horizontal velocity fields of the Weihe Basin and the Xi'an area are determined using high-precision GPS campaign measurements, which in turn provide constraints to calculate tectonic stress fields. A finite element dynamic model is employed for the Weihe Basin and an elastic block model for the Xi'an area. It is suggested that the ground fissures in the Weihe Basin are shaped by active faults under the effect of a NW-SE regional tension stress field. Fault motion is the fundamental factor influencing the ground fissures and controls their directions and distribution, though the excessive extraction of underground water might be another major factor that accelerates the development of ground fissures. It is believed the results obtained in this study can provide important information for the prevention of basin ground fissure disasters and aid urban construction.

Long wavelength bifurcations and multiple neutral axes of elastic layered structures subject to finite bending

Geometries and rigidities involving the presence of more than one neutral axis during finite (plane-strain) bending of a multilayered elastic (incompressible) block make numerically stiff the differential equations governing the incremental problem necessary to investigate diffuse-mode instabilities. We have developed a compound matrix method to solve these cases, so that we have shown that the presence of two neutral axes occurs within sets of parameters where the elastic system may display long-wavelength bifurcation modes. Following the predictions of the theory, we have designed and realized qualitative experiments in which these modes become visible.

Slip rates and seismic moment deficits on major active faults in mainland China

[1] The Chinese mainland features widespread active faults and intensive seismic activity; both can be described in terms of slip rates on these faults. Previous studies of fault slip rates in mainland China have focused on individual faults or fault segments, and large discrepancies exist among results derived from different methods. Here we derive a self-consistent estimate of the slip rates on all major faults in mainland China using the recently updated GPS data and an elastic block model. The predicted slip rates are high in western and low in eastern China, ranging from 25.1 ± 2.0 mm/yr in the Himalayan Thrust System to less than 1.0 mm/yr in north China. Using these slip rates, we estimated the rates of moment accumulation on the major fault zones and compared them with the seismic moment released on each fault zone using the Chinese historical earthquake catalog that extends for more than 2000 years in many regions. The results show nine seismic zones with large moment deficits (unreleased moment). Future refinement of GPS measurements and earthquake history will allow better estimates of slip rates on individual faults and better assessment of earthquake hazard on these faults in mainland China.

Elastic block copolymer nanocomposites with controlled interfacial interactions for artificial muscles with direct voltage control

Soft, physically crosslinking, block copolymer elastomers were filled with surface-treated nanoparticles, in order to evaluate the possibility for improvement of their properties when used as soft dielectric actuators. The nanoparticles led to improvements in dielectric properties, however they also reinforced the elastomer matrix. Comparing dielectric spectra of composites with untreated and surface-treated particles showed a measurable influence of the surface on the dielectric loss behaviour for high filler amounts, strongly indicating an improved host–guest interaction for the surface-treated particles. Breakdown strength was measured using a test bench and was found to be in good agreement with the results from the actuation measurements. Actuation responses predicted by a model for prestrained actuators agreed well with measurements up to a filler amount of 20%vol. Strong improvements in actuation behaviour were observed, with an optimum near 15%volnanoparticles, corresponding to a reduction in electrical field of 27% for identical actuation strains. The use of physically crosslinking elastomer ensured the mechanical properties of the matrix elastomer were unchanged by nanoparticles effecting the crosslinking reaction, contrary to similar experiments performed with chemically crosslinking elastomers. This allows for a firm conclusion about the positive effects of surface-treated nanoparticles on actuation behavior.

Present‐day strain accumulation and slip rates associated with southern San Andreas and eastern California shear zone faults

We present the first results from a dense network of 36 campaign and 46 continuous GPS stations located in the Eastern Transverse Ranges Province (ETR), a transition zone between the southernmost San Andreas fault (SSAF) and eastern California shear zone (ECSZ). We analyzed the campaign data together with available data from continuous GPS stations for the period 1994–2009. We used the GPS velocity estimates to constrain elastic block models to investigate fault‐loading rates representing four hypotheses characterized by different fault‐block geometries. Fault‐block scenarios include blocks bounded by the east‐striking left‐lateral Pinto Mountain, Blue Cut, and Chiriaco faults of the ETR; blocks bounded by a right‐lateral north‐northwest striking structure (the “Landers‐Mojave earthquake line”) that cuts obliquely across the ETR and mapped Mojave Desert faults; and combinations of these end‐member hypotheses. Each model implies significantly different active fault geometries, block rotation rates, and slip rates for ETR and ECSZ structures. All models suggest that SSAF slip rate varies appreciably along strike, generally consistent with rates derived from tectonic geomorphology and paleoseismology, with a maximum of ∼23 mm/yr right‐lateral along the southernmost Coachella Valley strand, decreasing systematically to <10 mm/yr right‐lateral through the San Gorgonio Pass region. Slip rate estimates for the San Jacinto fault are ∼12 mm/yr for all models tested. All four models fit the data equally well in a statistical sense. Qualitative comparison among models and consideration of geologic slip rates and other independent data reveals strengths and weaknesses of each model.

Strain accumulation across the Messina Straits and kinematics of Sicily and Calabria from GPS data and dislocation modeling

We use Global Positioning System (GPS) velocities and dislocation modeling to investigate the rate and nature of interseismic strain accumulation in the area affected by the 1908 Mw 7.1 Messina earthquake (southern Italy) within the framework of the complex central Mediterranean microplate kinematics. Our data confirm a change in the velocity trends between Sicily and Calabria, moving from NNW-ward to NE-ward with respect to Eurasia, and detail a fan-like pattern across the Messina Straits where maximum extensional strain rates are ~ 65 nanostrains/yr. Extension normal to the coast of northern Sicily is consistent with the presence of SW–NE trending normal faults. Half-space dislocation models of the GPS velocities are used to infer the slip-rates and geometric fault parameters of the fault zone that ruptured in the Messina earthquake. The inversion, and the bootstrap analysis of model uncertainties, finds optimal values of 3. 5 + 2.0 − 1.3 and 1.6 + 0.3 − 0.2 mm/yr for the dip–slip and strike–slip components, respectively, along a 30 + 1.1 − 0.7 ° SE-ward dipping normal fault, locked above 7.6 + 4.6 − 2.9 km depth. By developing a regional elastic block model that accounts for both crustal block rotations and strain loading at block-bounding faults, and adopting two different competing models for the Ionian–Calabria convergence rates, we show that the measured velocity gradient across the Messina Straits may be significantly affected by the elastic strain contribution from other nearby faults. In particular, when considering the contribution of the possibly locked Calabrian subduction interface onto the observed velocity gradients in NE-Sicily and western Calabria, we find that this longer wavelength signal can be presently super-imposed on the observed velocity gradients in NE-Sicily and Calabria. The inferred slip-rate on the Messina Fault is significantly impacted by elastic strain from the subduction thrust. By varying the locking of the subduction thrust fault, in fact, the Messina Fault slip-rate varies from 0 to 9 mm/yr.