Frictional Heterogeneity Research Articles

Dynamics in miscible blends of polyisoprene and poly(p-tert-butyl styrene): thermo–rheological behavior of components

Viscoelastic and dielectric properties were examined for miscible blends of moderately entangled cis-polyisoprene (PI) and poly(p-tert-butyl styrene) (PtBS). The dielectric response exclusively detected the global motion of PI chains having type-A dipoles. In most of the blends, PI and PtBS were the fast and much slower components, respectively. In those blends, the dielectric response of PI was thermo–rheologically complex because the slow PtBS chains quenched the dynamic frictional heterogeneity in the time scale of the PI relaxation. In contrast, the viscoelastic response of PtBS was thermo–rheologically simple because the fast PI chains smeared the heterogeneity. Nevertheless, PtBS exhibited no ordinary entanglement relaxation but retarded Rouse-like relaxation attributable to pseudo-constraint release activated by the PI motion. A simple model based on this molecular picture well described the viscoelastic data of the blends.

Dynamics of Polyisoprene-Poly(p-tert-butylstyrene) Diblock Copolymer in Disordered State

Linear viscoelastic and dielectric behavior was examined for a diblock copoly-mer composed of cis-polyisoprene (PI) and poly(p-tert-butylstyrene) (PtBS) blocks of the molecular weights MPI = 52.6 × 103 and MPtBS = 41.8 × 103 (PI weight fraction wPI = 55.7 wt %). These blocks were miscible and the copolymer was in the disordered state at temperatures examined, 20 ≤ T/°C ≤ 120. PI has the type-A dipole parallel along the chain backbone while PtBS does not. Thus, the dielectric response at low frequencies exclusively detected the global motion (end-to-end vector fluctuation) of the PI block, while the viscoelastic response reflected the motion of the copolymer chain as a whole. The dielectric data of the PI block exhibited prominent thermo-rheological complexity. Since the PI and PtBS blocks behaved as the fast and slow blocks at low T and this difference of their relaxation rates decreased at high T, the complexity was related partly to the dynamic frictional heterogeneity for the PI block resulting from th...

Spatial heterogeneity of tectonic stress and friction in the crust: new evidence from earthquake focal mechanisms in Taiwan

We performed inversions of earthquake focal mechanisms in central Taiwan to investigate the heterogeneity of the stress field and fault strength, and temporal variations of stress parameters, friction and pore pressure associated with the 1999 Chi-Chi earthquake. We divided the focal mechanism data into two groups: before and after the Chi-Chi earthquake, and analysed them separately. With the assumption of a uniform stress field, the friction coefficient is mostly within a range of 0.2–0.4 in central Taiwan, which is lower than the commonly quoted laboratory result, 0.6–0.85. The low friction coefficient is also inferred by the rotation of principal stress axes after the Chi-Chi earthquake. By contrast, if we assume that the friction is constant and failures occur on optimally oriented planes, we find that the resulting stress orientations must be spatially variable. However, a large dispersion of stress orientations is not seen in borehole breakouts and fault slip data, implying a constant friction model might be ruled out. Our analysis suggests that either the distribution of the coefficient of friction or pore pressure changed during the 1999 Chi-Chi earthquake. We infer that the pore pressure probably rose in the Chi-Chi rupture area and northern Longitudinal Valley and dropped in the areas south of the coseismic rupture area after the main shock.

Solvent Friction Changes the Folding Pathway of the Tryptophan Zipper TZ2

Because the rate of a diffusional process such as protein folding is controlled by friction encountered along the reaction pathway, the speed of folding is readily tunable through adjustment of solvent viscosity. The precise relationship between solvent viscosity and the rate of diffusion is complex and even conformation-dependent, however, because both solvent friction and protein internal friction contribute to the total reaction friction. The heterogeneity of the reaction friction along the folding pathway may have subtle consequences. For proteins that fold on a multidimensional free-energy surface, an increase in solvent friction may drive a qualitative change in folding trajectory. Our time-resolved experiments on the rapidly and heterogeneously folding β-hairpin TZ2 show a shift in the folding pathway as viscosity increases, even though the energetics of folding is unaltered. We also observe a nonlinear or saturating behavior of the folding relaxation time with rising solvent viscosity, potentially an experimental signature of the shifting pathway for unfolding. Our results show that manipulations of solvent viscosity in folding experiments and simulations may have subtle and unexpected consequences on the folding dynamics being studied.

Evidence from coseismic slip gradients for dynamic control on rupture propagation and arrest through stepovers

Analysis of historic slip distributions from large‐magnitude continental strike‐slip earthquake ruptures reveals a pronounced correlation between the distance over which slip decreases as a rupture approaches a structural “step” in the fault and the ability of the rupture to propagate through the step. Our analysis of coseismic slip gradients near these stepovers indicates that in earthquakes in which slip decreases gradually toward a step, rupture will not continue on the next segment. Conversely, in earthquakes in which slip decreases abruptly, rupture commonly renucleates on the next segment. The fact that ruptures that stopped had low slip gradients near stepovers, relative to those that continued, indicates that rupture dynamics control the propagation of rupture through stepovers. These results corroborate dynamic rupture models that show that ruptures in which slip decreases abruptly at a step generate strong seismic waves that serve to renucleate rupture on the opposite side of the structural step. There are several potential causes for gradual decrease of displacement as rupture approaches a stepover, including transference of deformation onto subsidiary structures, rheological contrasts that could dictate favored rupture propagation directions, the existence of stress shadows from previous earthquakes within the system, or other material or frictional heterogeneities. All of these are potentially observable, and, if mapped systematically, could provide the basis for a strong constraint on the likely end points of future earthquakes. Inasmuch as earthquake magnitude is strongly dependent on the size of the rupture, such predictions would be of great utility as a basic component of scenario‐based earthquake rupture forecasts.

Earthquake nucleation on dip‐slip faults with depth‐dependent frictional properties

Previous research has indicated that for dip‐slip faults embedded in a half‐space, the nonvertical, asymmetric fault geometry can have a significant effect on the seismic nucleation process. Using quasi‐static simulation methods and a slip‐weakening friction law, we investigate the coupled effects of asymmetric fault geometry and depth‐dependent frictional properties on seismic nucleation on dip‐slip faults. As a first‐order approximation to the depth‐dependent parameters in the Earth, we assume that the normal stress tapers to a small value near the free surface, and we assume that the drop in frictional coefficient decreases with depth. We find that these depth‐dependent properties have an important effect on the nucleation process of these faults: Compared to models with homogeneous frictional properties, the nucleation point moves down dip, the time to unstable slip nucleation decreases, and the amount of preseismic surface slip increases significantly. However, these effects do not dominate the effects of the asymmetric dipping geometry of these faults on the nucleation process: thrust faults nucleate farther up dip than normal faults and nucleate earlier as well. Normal faults have a larger amount of preseismic surface slip than thrust faults. The results indicate that both geometrical and frictional heterogeneity can have important effects on nucleation and that both sources of complexity must be taken into account to produce accurate models of the seismic nucleation process.

Models of kinematics dependent anisotropic and heterogeneous friction

Anisotropy and heterogeneity of friction and wear can result from anisotropic roughness of engineering surfaces and from anisotropic and heterogeneous microstructures present in many materials (wood, single crystals, ceramics, composites, layer-lattice materials, polymers, biomaterials, monomolecular layers). In sliding surfaces of some materials, kinematics of sliding initiates microstructural and frictional changes. This research deals with advanced constitutive models, which describe evolutions of frictional anisotropy and heterogeneity induced by the sliding kinematics. First-, second- and higher-order constitutive equations of friction are developed with respect to powers of a sliding path curvature. The first-order equation of the friction force has two independent variables: sliding velocity unit vector and its derivative. The second- and higher-order equations are polynomials with respect to odd order tensors composed by the sliding velocity unit vector and the derivative. In the equations, friction tensors of even orders describe anisotropy and inhomogeneity of friction and effects associated with the sliding kinematics. The sliding path curvature generates: (a) an additional resistance to sliding, (b) a constraint force normal to the sliding trajectory. The friction constitutive equations satisfy the axiom of objectivity. A condition of dissipated energy restricts the friction tensors and the radius of curvature. Examples illustrate friction descriptions.

SLIP-WEAKENING FRICTION INSTABILITIES: EIGENVALUE ANALYSIS

We consider the evolution problem for the wave equation with nonlinear boundary conditions, modeling the anti-plane shearing on a system of finite faults under a slip-dependent friction in a linear elastic continuum. The associated eigenvalue problem is studied for bounded and unbounded domains. Recent studies showed that this eigenvalue problem plays a key role in earthquake nucleation modeling. We investigate the structure of the positive eigenvalues set and prove the monotone dependence of the first eigenvalue on the friction parameter. For the elastic plane with a collinear system of faults, the eigenvalue problem is reduced to a hyper-singular integral equation. This equation is solved through a semi-analytical technique. Numerical results show a sensible dependence of the first eigenfunction on the geometry and friction heterogeneity.

A numerical method of viscoelastic finite element coupled with spring-block model to simulate the interaction of faults and crustal blocks

A numerical method of viscoelastic finite element coupled with spring-block model is developed to study temporal processes from the slow tectonic motion of large-scale crust to the rapid failure of small-scale faults. Our modeling demonstrates that the motion of crustal blocks is driven by forces from tectonic plate boundaries, and the deformation is distributed on faults for the stress accumulating. The coupling model generates earthquake sequences that display a magnitude-frequency scaling consistent with Gutenberg-Richter law. The frictional heterogeneities affeci earthquakes occurrence and stresses distribution of crustal blocks. Rupture of earthquakes starts at the nucleation node, and propagates bilaterally along faults with the stress triggering, release and redistribution. The failure of faults releases part of crustal stresses, the stress state of crustal blocks near fault is affected by the rupture of local segments on the fault, and the stress state of crustal blocks far away from the fault is controlled by the seismic activity of the whole fault.

Spatial heterogeneity of tectonic stress and friction in the crust

The complex geometry of faults, seismicity, and diversity of earthquake mechanisms suggest that the stress and strength in Earth's crust are spatially heterogeneous. We investigated the degree of heterogeneity using the following two end‐member models. In one end‐member model, we assumed that the orientation of stress is uniform in the crust as is assumed in many stress inversion studies. In this model, the variability of earthquake mechanisms means that friction during faulting must vary for each event. We computed friction μ from the ratio of the resolved shear stress to the effective normal stress on the fault plane with the assumption of hydrostatic pore pressure. The values of μ vary over a large range from 0 to 1.5. In the other extreme model we assumed optimally oriented slip and a constant μ = 0.6, as is suggested by Byerlee's law, for all the earthquakes, and determined the local stress orientation for each earthquake. The orientation of the stress changes drastically from one earthquake to another, and the assumption of uniform stress field commonly used in stress inversion is not warranted. An important conclusion is that a regionally uniform stress field and constant friction on optimally oriented faults are mutually exclusive. The actual situation in the crust is most likely to be intermediate between these two end‐member models. From the existing data alone, we cannot determine the degree of heterogeneity uniquely, but both μ and the local stress field near earthquake faults are likely to vary substantially, and studies on earthquake rupture dynamics must take these heterogeneities into consideration.