Sia Nemat-Nasser

Bio: Sia Nemat-Nasser is an academic researcher from University of California, San Diego. The author has contributed to research in topics: Strain rate & Deformation (engineering). The author has an hindex of 72, co-authored 463 publications receiving 20783 citations. Previous affiliations of Sia Nemat-Nasser include University of California, Los Angeles & North Carolina State University.

Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure

Abstract: Micromechanisms of rock failure (axial splitting and shear failure) are examined in light of simple mathematical models motivated by microscopic observations. The elasticity boundary value problem associated with cracks growing from the tips of a model flaw is solved. It is shown that under axial compression, tension cracks nucleate at the tips of the preexisting model flaw, grow with increasing compression, and become parallel to the direction of the maximum far-field compression. When a lateral compression also exists, the crack growth is stable and stops at some finite crack length. With a small lateral tension, on the other hand, the crack growth becomes unstable after a certain crack length is attained. This is considered to be the fundamental mechanism of axial splitting observed in uniaxially compressed rock specimens. To model the mechanism of shear failure, a row of suitably oriented model flaws is considered and the elasticity boundary value problem associated with the out-of-plane crack growth from the tips of the flaws is solved. It is shown that for a certain overall orientation of the flaws the growth of the out-of-plane cracks may become unstable, leading to possible macroscopic faulting. On the basis of this model the variations of the “ultimate strength” and the orientation of the overall fault plane with confining pressure are estimated, and the results are compared with published experimental data. In addition, the results of a set of model experiments on plates of Columbia resin CR39 containing preexisting flaws are reported. These experiments are specifically designed in order to show the effect of confining pressure on the crack growth regime. The experiments seem to support qualitatively the analytical results.

Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst

Abstract: Uniaxial compression of plates of brittle materials containing pre-existing planar cracks oriented at certain angles with respect to the direction of overall compression has revealed that the relative frictional sliding of the faces of the pre-existing cracks may produce, at their tips, tension cracks which deviate at sharp angles from the sliding plane. These tension cracks then continue to grow in a stable manner with increasing axial compression, curving toward an orientation parallel to the direction of axial compression. Within the framework of linear fracture mechanics, the out-of-plane extension of a pre-existing straight crack, induced by overall far-field compression, is analyzed, and various parameters which characterize the growth process are quantified. It is shown analytically that, for a wide range of pre-existing crack orientations, the out-of-plane crack extension initiates at an angle close to 70° from the direction of the pre-existing crack; the exact value of this angle, of course, depends on the friction factor and the orientation of the pre-existing crack. It is found that the growth process is stable initially, but the rate of increase of the length of the extended portion with respect to the increasing axial compression dramatically increases after a certain extension length is attained, and in fact, this length becomes unbounded if a small lateral tension also exists. Various limiting cases are examined and the corresponding analytical estimates are compared with the numerical results, arriving at good correlations. A series of qualitative experiments is performed on thin plates of Columbia Resin CR 39, arriving at excellent agreement with the analytical results. In light of the analysis, the phenomena of axial splitting, exfoliation (or sheet fracture), and rockburst are examined, and it is suggested that they may all be the results of the out-of-plane (tensile) extension of pre-existing cracks, induced by large overall far-field compressions. This assertion is then supported by a series of experiments which show that the relative frictional sliding of the faces of one or even an array of pre-existing cracks does not result in coplanar (sliding mode) crack growth, but rather leads to the formation of tension cracks which grow in the direction of maximum compression. Moreover, a pre-existing crack close to a free boundary grows in a similar manner under compression parallel to the boundary, and shows no tendency to move toward the free surface. Possible lateral buckling which may result, and which may cause further unstable crack extension, is illustrated experimentally, and discussed in an effort to shed light on the phenomena of rockburst and surface spalling.

A Micromechanical Description of Granular Material Behavior

Abstract: Considered is a sample of cohesionless granular material, in which the individual granules are regarded rigid, and which is subjected to overall macroscopic average stresses. On the basis of the principle of virtual work, and by an examination of the manner by which adjacent granules transmit forces through their contacts, a general representation is established for the macroscopic stresses in terms of the volume average of the (tensorial) product of the contact forces and the vectors which connect the centroids of adjacent contacting granules. Then the corresponding kinematics is examined and the overall macroscopic deformation rate and spin tensors are developed in terms of the volume average of relevant microscopic kinematical variables. As an illustration of the application of the general expressions developed, two explicit macroscopic results are deduced: (1) a dilatancy equation which both qualitatively and quantitatively seems to be in accord with experimental observation, and (2) a noncoaxiality equation which seems to support the vertex plasticity model. Since the development is based on a microstructural consideration, all material coefficients entering the results have well-defined physical interpretations.

Brittle Failure in Compression: Splitting, Faulting and Brittle-Ductile Transition

Abstract: The micromechanics of brittle failure in compression and the transition from brittle to ductile failure, observed under increasing confining pressures, are eaxamined in the light of existing experimental results and model studies. First, the micromechanics of axial splitting and faulting is briefly reviewed, certain mathematical models recently developed for analysing these failure modes are outlined, and some new, simple closed-form analytic solutions of crack growth in compression and some new quantitative model experimental results are presented. Then, a simple two-dimensional mathematical model is proposed for the analysis of the brittle-ductile transition process, the corresponding elasticity boundary-value problem is formulated in terms of singular integral equations, the solution method is given, and numerical results are obtained and their physical implications are discussed. In addition, a simple closed-form analytic solution is presented and, by comparing its results with those of the exact formulation, it is shown that the analytic estimates are reasonably accurate in the range of the brittle response of the material. Finally, the results of some laboratory model experiments are reported in an effort to support the mathematical models.

Overall moduli of solids with microcracks: Load-induced anisotropy

Abstract: For a linearly elastic brittle solid containing microcracks that may be closed or may undergo frictional sliding, a general method is developed for estimating the overall instantaneous moduli which depend on the loading conditions. When the cracks are all open and when they are randomly distributed, then the overall response is isotropic. The moduli for this case have been obtained by B udiansky and O'C onnell (1976). On the other hand, when some cracks close, and when some closed cracks undergo frictional sliding, then the overall response becomes anisotropic and dependent on the loading conditions, as well as on the loading path. The self-consistent method is used to estimate the overall moduli. The effects of crack closure and loadinduced anisotropy are included. Several illustrative examples are worked out, showing the important influence of the load path on the overall response when crack closure and frictional sliding are involved.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Controlling Electromagnetic Fields

Abstract: Using the freedom of design that metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields-electric displacement field D, magnetic induction field B, and Poynting vector B-are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.

Metamaterial Electromagnetic Cloak at Microwave Frequencies

Abstract: A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was "hidden" inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.

Perfect metamaterial absorber.

Abstract: We present the design for an absorbing metamaterial (MM) with near unity absorbance A(omega). Our structure consists of two MM resonators that couple separately to electric and magnetic fields so as to absorb all incident radiation within a single unit cell layer. We fabricate, characterize, and analyze a MM absorber with a slightly lower predicted A(omega) of 96%. Unlike conventional absorbers, our MM consists solely of metallic elements. The substrate can therefore be optimized for other parameters of interest. We experimentally demonstrate a peak A(omega) greater than 88% at 11.5 GHz.

Mixed mode cracking in layered materials

Abstract: Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.