摘要:

The mantle of the earth is rheologically similar to an amorphous polymer. The short‐time‐scale behavior in shear is anelastic and rather well described by a constantQabsorption band. The long‐time‐scale behavior is essentially Newtonian viscous and this mode of deformation dominates the material behavior for times in excess of a Maxwell time which is on the order of 200 years. Most geophysical observations seem to be adequately reconciled by a simple linear viscoelastic rheology which is a generalization of the classical Burger's body and which is uniformly valid in time. This model is particularly useful because there exists a simple analytic expression for the shear modulus in the Laplace transform domain so that correspondence principle methods may be easily applied to solve dynamical problems. This article provides a simple derivation of this expression for the shear modulus and demonstrates the manner in which the unknown rheological parameters may be determined by fitting appropriate geophysical observations. Particular attention is devoted to discussion of the long‐time‐scale viscous response which is a crucial ingredient in the thermal convection hypothesis of continental drift.

ISSN:0148-6055    

DOI:10.1122/1.549765

出版商:The Society of Rheology    

年代:1984

数据来源: AIP

摘要:

Snow is a geologic material which intermittently covers a large portion of the earth's surface. Since it is a highly porous and thermodynamically active material, previous efforts at characterizing the thermomechanical behavior of the material have not been very successful. Low‐ to medium‐density snow (with void volume fraction in excess of 0.5) is shown to have a very complex set of deformation mechanisms. Such mechanisms as bond growth, intergranular slip, grain deformation, and flexural deformation of crystal chains all are seen to contribute to the total deformation process. When coupled with the nonlinear rheological properties of ice, snow becomes a difficult material to characterize. Special attention is given to the properties of snow when subjected to plastic shock waves. Current methods of analysis are considered and applicability of new continuum theories to this problem are discussed.

ISSN:0148-6055    

DOI:10.1122/1.549764

出版商:The Society of Rheology    

年代:1984

数据来源: AIP

摘要:

Discrete memory is a phenomenon observed in elastic‐plastic materials with a material memory of a restricted type. Instead of the entire stress path, only a discrete set of stress reversal points is memorized. For certain types of stress path, parts of the discrete memory can be completely erased. In a series of experiments in which brittle rock was stressed under triaxial conditions, I have found that rock exhibits discrete memory which is associated with the phenomenon of dilatancy. Dilatancy in rock is characterized by an inelastic increase in volume strain that occurs when the sample is subjected to differential compressive stresses. The microcracking responsible for the inelastic strain produces substantial changes in elastic wave velocities. To very high precision the strains and elastic waves velocities in dilatant rock show discrete memory. Memory of maxima and minima of the stress difference can be developed, with multiple points remembered simultaneously. Discrete memory provides a strong constraint on possible mechanisms of dilatancy and brittle failure. Two models have been proposed for the basic crack mechanism: a shear crack and a tensile crack. Analysis of the shear crack shows that qualitatively it is capable of generating the observed properties but there are important details of discrete memory that are difficult to explain using this model. An analysis of the response of a tensile crack to cyclic loading, together with the introduction of an energy‐dissipating function, shows that a stable population of such cracks can produce discrete memory. The origin of the energy dissipation is not clear.

ISSN:0148-6055    

DOI:10.1122/1.549772

出版商:The Society of Rheology    

年代:1984

数据来源: AIP

摘要:

The inelastic behavior of fissured rock masses is due primarily to microcracking from the tips of preexisting fissures and frictional sliding on fissure surfaces. Consequently, the macroscopic inelastic response is inhibited by an increase of hydrostatic compression and exhibits volume change and strain softening. By generalizing the type of laws often used in metal plasticity, Rudnicki and Rice introduced a class of simple constitutive laws that incorporate these features and is useful for studying the inception of rupture. An important aspect of this generalization is that normality of the inelastic strain increment vector to a yield surface in stress space, as assumed in classical metal plasticity, is not appropriate. More detailed consideration of the preferential activation of sliding on differently oriented fissure surfaces during a program of loading suggests that, although this class of laws will be suitable for describing loading in which stress components increase nearly in proportion to a single parameter, they will be inadequate for describing abrupt changes in the pattern of deformation. An approximate remedy for this inadequacy can be interpreted as deformation (or total strain) theory of plasticity. Mechanical coupling between diffusion of an infiltrating pore fluid, for example, ground water, and deformation can also be included by replacing the hydrostatic stress σ by the effective stressσ−ζp,wherepis the pore fluid pressure and ζ satisfies0<ζ⩽1for elastic deformation andζ=1for inelastic deformation typical of brittle rock. This coupling causes the response to be time dependent even when the response of the matrix material is time independent. Specifically, the response is stiffer for load alterations that are rapid by comparison to the diffusion time of pore fluid than for those that allow time for equilibration of pore fluid pressure among neighboring material elements.

ISSN:0148-6055    

DOI:10.1122/1.549766

出版商:The Society of Rheology    

年代:1984

数据来源: AIP

摘要:

Generally, continuum theories of materials with damage treat the damage as an internal state variable, a variable whose evolution is governed by a rate‐type law. There is quite ample precedent, however, to treat such a quantity as governed instead by an equation of balance in addition to the conventional ones for mass, momentum, energy, and entropy. Here, we present a theory of this type. As a first test of the theory, we solve the problem of one‐dimensional creep. We assume homogeneous motion and thus obtain an ordinary differential equation for the damage. This equation is complicated enough so that the exact solution is not directly useful. Of course, a numerical solution would be easy to carry out, but it would have to be done with extreme care so as to ensure that appropriate ranges of the variables are considered to include all possible types of behavior of the equation. We use the qualitative theory of ordinary differential equations to study exhaustively the evolution of the damage. This leads to precise and natural definitions of material stability and instability. After that, we present representative numerical solutions for evolution of damage and strain. An interesting outcome is that there are some solutions which are welll behaved for a finite length of time, then fail to exist. Such solutions clearly imply the onset of localization of deformation.

ISSN:0148-6055    

DOI:10.1122/1.549736

出版商:The Society of Rheology    

年代:1984

数据来源: AIP