Constitutive Law for Earthquake Production Based on Rate‐and‐State Friction: Theory and Application of Interacting Sources

2019 ◽  
Vol 124 (2) ◽  
pp. 1802-1821 ◽  
Author(s):  
Elías R. Heimisson
Keyword(s):  
Constitutive Law ◽  
Friction Theory ◽  
Rate And State Friction

Dynamic Instability of Two Elastic Half-Spaces Sliding With a Rate-and-State Friction Constitutive Law

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Jérôme Colin
Keyword(s):  
Dynamic Instability ◽  
Constitutive Law ◽  
Steady State Regime ◽  
Stick Slip ◽  
Slip Regime ◽  
Rate And State Friction ◽  
Modulus Difference ◽  
State Regime ◽  
Loss Of Contact ◽  
Elastic Coefficients

The destabilization of the steady-state regime of two semi-infinite half-spaces of different elastic coefficients sliding upon each other has been theoretically investigated when a rate-and-state friction constitutive law controls the sliding. In the framework of linear and isotropic elastodynamics, the effect of the frictional constitutive law has been investigated onto the development of self-excited oscillations as well as the influence of the shear modulus difference between the two materials. The possibility of existence of a stick–slip regime and the conditions for the loss-of-contact are finally discussed.

Mathematical model to predict the characteristics of polarization in dielectric materials: The concept of piezoelectrcity and electrostriction

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Mathematical Model ◽  
Electric Field ◽  
Lead Zirconate Titanate ◽  
Dielectric Material ◽  
Strain Curve ◽  
Dielectric Materials ◽  
Lead Zirconate ◽  
Simulation Software ◽  
Constitutive Law ◽  
Basic Material

Model was developed for the prediction of polarization characteristics in a dielectric material exhibiting piezoelectricity and electrostriction based on mathematical equations and MATLAB computer simulation software. The model was developed based on equations of polarization and piezoelectric constitutive law and the functional coefficient of Lead Zirconate Titanate (PZT) crystal material used was 2.3×10-6 m (thickness), the model further allows the input of basic material and calculation of parameters of applied voltage levels, applied stress, pressure, dielectric material properties and so on, to generate the polarization curve, strain curve and the expected deformation change in the material length charts. The mathematical model revealed that an application of 5 volts across the terminals of a 2.3×10-6 m thick dielectric material (PZT) predicted a 1.95×10-9 m change in length of the material, which indicates piezoelectric properties. Both polarization and electric field curve as well as strain and voltage curve were also generated and the result revealed a linear proportionality of the compared parameters, indicating a resultant increase in the electric field yields higher polarization of the dielectric materials atmosphere.

scholarly journals Validation of a one-dimensional model of the systemic arterial tree

2009 ◽  
Vol 297 (1) ◽  
pp. H208-H222 ◽  
Author(s):  
Philippe Reymond ◽  
Fabrice Merenda ◽  
Fabienne Perren ◽  
Daniel Rüfenacht ◽  
Nikos Stergiopulos
Keyword(s):  
Constitutive Law ◽  
Distributed Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Continuity Equations ◽  
Nonlinear Viscoelastic ◽  
Model Predictions ◽  
The One ◽  
D Model ◽  
Systemic Arterial Tree

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the “generic 1-D model” and the “average subject” of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

Numerical Modeling and Experimental Characterization of the Pyroplasticity in Ceramic Materials during Sintering

2010 ◽  
Vol 62 ◽  
pp. 203-208 ◽  
Author(s):  
Pasquale Bene ◽  
Danilo Bardaro ◽  
Daniela Bello ◽  
Orazio Manni
Keyword(s):  
Ceramic Material ◽  
Ceramic Materials ◽  
Constitutive Law ◽  
Beam Deflection ◽  
Firing Cycle ◽  
Experimental Characterization ◽  
Viscosity Increase ◽  
Ceramic Components ◽  
Deflection Theory ◽  
Sintering Shrinkage

The aim of the work is the study of the pyroplasticity in ceramic materials in order to simulate the deformations of complex ceramic component during sintering. A ceramic material undergoing densification can be treated as a linear viscous material. Generally, the viscosity decreases as the temperature increases, however the densification and the consequent grain growth, result in a viscosity increase. A bending creep test is proposed for measuring the change in viscosity of the ceramic material during densification. Equations, based on beam deflection theory, are derived to determine the viscosity during the whole firing cycle by measuring the deflection in the centre of specimens. In addition, dilatometric analyses are performed to measure the sintering shrinkage and the specimen density, which continuously changes during the sintering process. On the basis of an accurate experimental characterization the parameters of Maxwell viscoelastic constitutive law are derived. A numerical-experimental procedure has been adopted in order to calibrate the numerical model that, finally, has been used to predict the pyroplastic deformations of complex ceramic components.

Application of generalized Fourier heat conduction law on MHD viscoinelastic fluid flow over stretching surface

2019 ◽  
Vol 30 (6) ◽  
pp. 3481-3496 ◽  
Author(s):  
Arif Hussain ◽  
Muhammad Yousaf Malik ◽  
Mair Khan ◽  
Taimoor Salahuddin
Keyword(s):  
Heat Flux ◽  
Fluid Flow ◽  
Friction Factor ◽  
Numerical Technique ◽  
Wall Heat Flux ◽  
Constitutive Law ◽  
Wall Friction ◽  
Theoretical Physics ◽  
Stretching Surface ◽  
Content Type

Purpose The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface. Design/methodology/approach The fluid momentum problem is mathematically formulated by using the Prandtl–Eyring constitutive law. Also, the non-Fourier heat flux model is considered to disclose the heat transfer characteristics. The governing problem contains the nonlinear partial differential equations with appropriate boundary conditions. To facilitate the computation process, the governing problem is transmuted into dimensionless form via appropriate group of scaling transforms. The numerical technique shooting method is used to solve dimensionless boundary value problem. Findings The expressions for dimensionless velocity and temperature are found and investigated under different parametric conditions. The important features of fluid flow near the wall, i.e. wall friction factor and wall heat flux, are deliberated by altering the pertinent parameters. The impacts of governing parameters are highlighted in graphical as well as tabular manner against focused physical quantities (velocity, temperature, wall friction factor and wall heat flux). A comparison is presented to justify the computed results, it can be noticed that present results have quite resemblance with previous literature which led to confidence on the present computations. Originality/value The computed results are quite useful for researchers working in theoretical physics. Additionally, computed results are very useful in industry and daily-use processes.

scholarly journals Micromechanically Derived Constitutive Law for Granular Materials

1998 ◽  
Vol 1 ◽  
pp. 469-480
Author(s):  
Kenji KANEKO ◽  
Yuji KISHINO ◽  
Takashi KYOYA
Keyword(s):  
Granular Materials ◽  
Constitutive Law
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