Coherent stress relaxation in a half space: Modulated layers, inclusions, steps, and a general solution

1991 ◽  
Vol 70 (7) ◽  
pp. 3556-3571 ◽  
Author(s):  
Frank Glas
Keyword(s):  
Stress Relaxation ◽  
General Solution ◽  
Half Space

Stress relaxation in a semi-infinite viscoelastic earth model

1973 ◽  
Vol 63 (6-1) ◽  
pp. 2145-2154
Author(s):  
Martin Rosenman ◽  
Sarva Jit Singh
Keyword(s):  
Free Surface ◽  
Stress Relaxation ◽  
Half Space ◽  
Epicentral Distance ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Earth Model ◽  
Contour Maps ◽  
Surface Stresses ◽  
Stress Components

Abstract Expressions for quasi-static surface stresses resulting from a finite, rectangular, vertical, strike-slip fault in a Maxwellian viscoelastic half-space are derived. Variation of the stresses with time and epicentral distance is studied. Contour maps are obtained in some representative cases. It is found that all nonvanishing stress components at the free surface die exponentially with time. This is in contrast to the behavior of the displacements and strains which, in general, do not vanish for large times.

scholarly journals Plane waves in thermoelasticity with one relaxation time

2001 ◽  
Vol 26 (4) ◽  
pp. 225-232
Author(s):  
Jun Wang ◽  
Wen Dong Chang
Keyword(s):  
Relaxation Time ◽  
General Solution ◽  
Laplace Transform ◽  
Half Space ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Second Sound ◽  
Boundary Temperature ◽  
Explicit Expressions

We apply the thermoelastic equations with one relaxation time developed by Lord and Shulman (1967) to solve some elastic half-space problems. Laplace transform is used to find the general solution. Problems concerning the ramp-type increase in boundary temperature and stress are studied in detail. Explicit expressions for temperature and stress are obtained for small values of time, where second sound phenomena are of relevance. Numerical values of stress and temperature are calculated and displayed graphically.

scholarly journals PSEUDO-DIFFERENTIAL OPERATORS AND EQUATIONS IN A DISCRETE HALF-SPACE

2018 ◽  
Vol 23 (3) ◽  
pp. 492-506 ◽  
Author(s):  
Vladimir B. Vasilyev ◽  
Alexander V. Vasilyev
Keyword(s):  
Differential Operator ◽  
General Solution ◽  
Differential Equations ◽  
Half Space ◽  
Differential Operators ◽  
Pseudo Differential Operator ◽  
Pseudo Differential Operators ◽  
Special Case

We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space. The theorem on a general solution of such equations is proved for a special case.

Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity

1965 ◽  
Vol 287 (1411) ◽  
pp. 549-567 ◽  
Keyword(s):  
General Solution ◽  
Point Source ◽  
Half Space ◽  
Dynamic Problem ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Time Dependent ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Limit Case

The dynamic problem of the deformation of a homogeneous, perfectly elastic and isotropic half space due to harmonically time-dependent tractions over the boundary of an embedded spherical cavity is discussed. The solution is developed completely and rigorously by a method of successive approximations. Lamb’s solution for a point source in a half-space is derived as a limit case of the general solution. The problem is suggested by its applications in the theory of underground explosions and in seismology.

Axisymmetric Inclusion in a Half Space

1990 ◽  
Vol 57 (1) ◽  
pp. 74-77 ◽  
Author(s):  
H. Y. Yu ◽  
S. C. Sanday
Keyword(s):  
General Solution ◽  
Half Space ◽  
Transformation Method ◽  
Dislocation Loops ◽  
Hankel Transformation ◽  
New Approach ◽  
Elastic Fields ◽  
Special Cases

An alternate method of approach for solving the axisymmetric elastic fields in the half space with an isotropic spheriodal inclusion is proposed. This new approach involves the application of the Hankel transformation method for the solution of prismatic dislocation loops and Eshelby’s solution for ellipsoidal inclusions. Existing solutions by other methods for the inclusion with pure dilatational misfit in a half space are shown to be special cases of the present, more general solution.

The Propagation of an Impulse Into a Viscous-Locking Medium

1961 ◽  
Vol 28 (1) ◽  
pp. 21-24 ◽  
Author(s):  
J. W. Miles
Keyword(s):  
Shock Wave ◽  
General Solution ◽  
Compressive Stress ◽  
Half Space ◽  
Similarity Solution ◽  
Peak Pressure ◽  
Compressive Strain ◽  
Depth Of Penetration ◽  
Stress Strain Relation ◽  
Peak Value

A viscous-locking medium is defined by the compressive stress-strain relation p = f(ε) + μεt, where f(ε) = 0 for ε < εc and f′(εc) = ∞; it behaves as a viscous liquid until the compressive strain attains the value εc, after which it behaves as a rigid solid. A general solution is given for the disturbance produced by a pressure p0(t) acting on an inviscid (μ = 0) half space, in which case the transition from viscous to rigid phases occurs through a shock wave. It is found that the stress falls off inversely as the square of the depth of penetration and that it may be approximated (asymptotically) by the disturbance produced by a concentrated impulse. A similarity solution then is given for a concentrated impulse acting on a viscous half space. It is concluded that viscosity reduces the peak pressure at all depths, even though the disturbance is diffused into the viscous phase and may achieve its peak value in that phase.

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