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Eran Bouchbinder - One of the best experts on this subject based on the ideXlab platform.
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dynamic instabilities of frictional sliding at a bimaterial interface
Journal of The Mechanics and Physics of Solids, 2016Co-Authors: Efim A Brener, Marc Weikamp, Robert Spatschek, Yohai Barsinai, Eran BouchbinderAbstract:Abstract Understanding the dynamic stability of bodies in frictional contact steadily sliding one over the other is of basic interest in various disciplines such as physics, solid mechanics, materials science and geophysics. Here we report on a two-dimensional linear stability analysis of a deformable solid of a finite height H, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e. an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small Wave-number k limit and demonstrate that homogeneous sliding in this case is universally unstable, independent of the details of the friction law. This universal instability is mediated by propagating Waveguide-like modes, whose fastest growing mode is characterized by a Wave-number satisfying kH ∼ O ( 1 ) and by a growth rate that scales with H−1. We then consider the limit kH → ∞ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the Dilatational Wave-speed in the opposite direction to the sliding direction. In a certain parameter range this instability is manifested through unstable modes at all Wave-numbers, yet the frictional response is shown to be mathematically well-posed. Instability modes which travel at nearly the shear Wave-speed in the sliding direction also exist in some range of physical parameters. Previous results obtained in the quasi-static regime appear relevant only within a narrow region of the parameter space. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability. The relevance of our results to the rupture of bi-material interfaces is briefly discussed.
Robert Spatschek - One of the best experts on this subject based on the ideXlab platform.
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dynamic instabilities of frictional sliding at a bimaterial interface
Journal of The Mechanics and Physics of Solids, 2016Co-Authors: Efim A Brener, Marc Weikamp, Robert Spatschek, Yohai Barsinai, Eran BouchbinderAbstract:Abstract Understanding the dynamic stability of bodies in frictional contact steadily sliding one over the other is of basic interest in various disciplines such as physics, solid mechanics, materials science and geophysics. Here we report on a two-dimensional linear stability analysis of a deformable solid of a finite height H, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e. an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small Wave-number k limit and demonstrate that homogeneous sliding in this case is universally unstable, independent of the details of the friction law. This universal instability is mediated by propagating Waveguide-like modes, whose fastest growing mode is characterized by a Wave-number satisfying kH ∼ O ( 1 ) and by a growth rate that scales with H−1. We then consider the limit kH → ∞ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the Dilatational Wave-speed in the opposite direction to the sliding direction. In a certain parameter range this instability is manifested through unstable modes at all Wave-numbers, yet the frictional response is shown to be mathematically well-posed. Instability modes which travel at nearly the shear Wave-speed in the sliding direction also exist in some range of physical parameters. Previous results obtained in the quasi-static regime appear relevant only within a narrow region of the parameter space. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability. The relevance of our results to the rupture of bi-material interfaces is briefly discussed.
Efim A Brener - One of the best experts on this subject based on the ideXlab platform.
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dynamic instabilities of frictional sliding at a bimaterial interface
Journal of The Mechanics and Physics of Solids, 2016Co-Authors: Efim A Brener, Marc Weikamp, Robert Spatschek, Yohai Barsinai, Eran BouchbinderAbstract:Abstract Understanding the dynamic stability of bodies in frictional contact steadily sliding one over the other is of basic interest in various disciplines such as physics, solid mechanics, materials science and geophysics. Here we report on a two-dimensional linear stability analysis of a deformable solid of a finite height H, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e. an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small Wave-number k limit and demonstrate that homogeneous sliding in this case is universally unstable, independent of the details of the friction law. This universal instability is mediated by propagating Waveguide-like modes, whose fastest growing mode is characterized by a Wave-number satisfying kH ∼ O ( 1 ) and by a growth rate that scales with H−1. We then consider the limit kH → ∞ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the Dilatational Wave-speed in the opposite direction to the sliding direction. In a certain parameter range this instability is manifested through unstable modes at all Wave-numbers, yet the frictional response is shown to be mathematically well-posed. Instability modes which travel at nearly the shear Wave-speed in the sliding direction also exist in some range of physical parameters. Previous results obtained in the quasi-static regime appear relevant only within a narrow region of the parameter space. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability. The relevance of our results to the rupture of bi-material interfaces is briefly discussed.
M. Asce - One of the best experts on this subject based on the ideXlab platform.
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EFFECT OF THE SPATIAL VARIATION IN THE HYDROGEOTECHNICAL PROPERTIES ON THE DYNAMIC RESPONSE OF POROUS SOIL MEDIA
2015Co-Authors: K. Mitsuji, Y. Sugimura, M. Asce, Madan B. KarkeeAbstract:Dynamic response of porous soil is studied by considering the spatial variation of porosity, permeability coefficient and bulk modulus of pore water, referred to as the hydrogeotechnical properties in this paper. Numerical study of the propagation of Dilatational Wave (P-Wave) in porous soil is the focus of investigation. Dynamic behavior is described by Biot’s theory in which porosity, permeability coefficient and bulk modulus play important role. These properties, as well as other physical properties such as density and shear Wave velocity, are actually known to have spatial variation. The variation of the parameters is modeled by multivariate probability density function proposed by Freeze, and the dynamic response of porous soil is studied by Monte Carlo technique. The numerical scheme is utilized to show the effect of the spatial variation of the hydogeotechnical properties on the dynamic response of porous soil. Spatial variations in porosity and bulk modulus of pore water are particularly influential in causing attenuation due to scattering and clear lowering of the natural frequency indicating effective softening of the porous soil
Elijah E. W. Van Houten - One of the best experts on this subject based on the ideXlab platform.
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Parameter identification in a generalized time-harmonic Rayleigh damping model for elastography.
PloS one, 2014Co-Authors: Elijah E. W. Van HoutenAbstract:The identifiability of the two damping components of a Generalized Rayleigh Damping model is investigated through analysis of the continuum equilibrium equations as well as a simple spring-mass system. Generalized Rayleigh Damping provides a more diversified attenuation model than pure Viscoelasticity, with two parameters to describe attenuation effects and account for the complex damping behavior found in biological tissue. For heterogeneous Rayleigh Damped materials, there is no equivalent Viscoelastic system to describe the observed motions. For homogeneous systems, the inverse problem to determine the two Rayleigh Damping components is seen to be uniquely posed, in the sense that the inverse matrix for parameter identification is full rank, with certain conditions: when either multi-frequency data is available or when both shear and Dilatational Wave propagation is taken into account. For the multi-frequency case, the frequency dependency of the elastic parameters adds a level of complexity to the reconstruction problem that must be addressed for reasonable solutions. For the Dilatational Wave case, the accuracy of compressional Wave measurement in fluid saturated soft tissues becomes an issue for qualitative parameter identification. These issues can be addressed with reasonable assumptions on the negligible damping levels of Dilatational Waves in soft tissue. In general, the parameters of a Generalized Rayleigh Damping model are identifiable for the elastography inverse problem, although with more complex conditions than the simpler Viscoelastic damping model. The value of this approach is the additional structural information provided by the Generalized Rayleigh Damping model, which can be linked to tissue composition as well as rheological interpretations.