Ferroelectric ceramics are susceptible to fracture under high magnitude cyclic electric field. Flaws concentrate the electric field, inducing a large incompatible strain, and thereby a large stress. Stable growth of cracks with either conducting or insulating interiors is observed in 8/65/35 lanthanum lead zirconate titanate samples. Indentations on the electroded surface are filled with distilled water or a water-salt solution. Under cyclic electric field, tree like damage grows from the indented electrode. Indentations on the surfaces 90" to the electrodes are filled with silicone oil. This results in stable crack growth perpendicular to the cyclic electric field. Nonlinear fracture models are presented for both conducting and insulating cracks. Tensile stress intensity factors are predicted for both cases.

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We analyse the response of osteoblasts on grooved substrates via a model that accounts for the cooperative feedback between intracellular signalling, focal adhesion development and stress fibre contractility. The grooved substrate is modelled as a pattern of alternating strips on which the cell can adhere and strips on which adhesion is inhibited. The coupled modelling scheme is shown to capture some key experimental observations including (i) the observation that osteoblasts orient themselves randomly on substrates with groove pitches less than about 150 nm but they align themselves with the direction of the grooves on substrates with larger pitches and (ii) actin fibres bridge over the grooves on substrates with groove pitches less than about 150 nm but form a network of fibres aligned with the ridges, with nearly no fibres across the grooves, for substrates with groove pitches greater than about 300 nm. Using the model, we demonstrate that the degree of bridging of the stress fibres across the grooves, and consequently the cell orientation, is governed by the diffusion of signalling proteins activated at the focal adhesion sites on the ridges. For large groove pitches, the signalling proteins are dephosphorylated before they can reach the regions of the cell above the grooves and hence stress fibres cannot form in those parts of the cell. On the other hand, the stress fibre activation signal diffuses to a reasonably spatially homogeneous level on substrates with small groove pitches and hence stable stress fibres develop across the grooves in these cases. The model thus rationalizes the responsiveness of osteoblasts to the topography of substrates based on the complex feedback involving focal adhesion formation on the ridges, the triggering of signalling pathways by these adhesions and the activation of stress fibre networks by these signals.

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An alternate method to those of Bueckner and Rice is presented for the derivation of the two-dimensional weight function for determining crack tip stress intensity factors. The weight function has r−1|2 type displacement singularity at the crack tip. It is shown that this singular field can be formulated using Westergaard stress functions in a manner similar to the method used for r1⊢2 type fields in crack tip displacements. A straight-forward approach for obtaining weight functions for cracked finite bodies is presented. This technique can be combined in a simple fashion with the finite element method. As an example, a weight function for the SEN strip is obtained in this manner. Moreover, closed form infinite body weight functions are also developed and used to derive some well-known stress intensity factor formulas.

Very detailed finite-strain/finite-element analyses of deeply cracked plane-strain center-notch panel and single-edge crack bend specimens were generated using nonhardening and power-law-hardening constitutive laws. The deformation was followed from small-scale yielding into the fully plastic range. The objective was to provide insight as to the minimum specimen size limitations, relative to the characteristic crack-tip opening dimension J/σo, necessary to assure a J-based dominance of the crack-tip region. The criterion used to judge the degree of dominance was the extent of agreement of the present stress and deformation fields at the blunted crack tips with those calculated by McMeeking for small-scale yielding. For deeply cracked bend specimens, we find very close agreement of the near-tip fields with those of small-scale yielding up to J values of σoL/25, where L represents the remaining uncracked ligament (and in the deeply cracked case, the only pertinent specimen dimension). This value is consistent with previously proposed J testing size limitations. However, we find that quite detectable deviation from the small-scale yielding fields occurs in both hardening and nonhardening center-crack specimens at considerably smaller J values relative to ligament dimension. This suggests that minimum specimen size requirements necessary to ensure a J-based characterization of the crack tip region may well be more stringent for center-crack or other low plastic constraint configurations than in bend-type specimens. A perhaps overly conservative value of 200 is proposed as the minimum ligament-to-J/σo ratio which ensures a sensible J-based characterization of the crack-tip region in center-crack specimens of materials exhibiting moderate to low strain hardening.

ABSTRACT. Observations of surging glaciers indicate that the flow regime is one dominated by extensional flow. The stress state has substantial longitudinal deviatoric stress. This regime is very different from the conventional model for glacier dynamics which is dominated by shearing flow. In addition, the initiation of surging often involves a compression front which travels down the glacier. The compression front seems to divide an up-stream region of high drag at the base of the glacier from one of low drag which allows the rapid sliding. We develop a framework for the mechanics of glaciers undergoing surging. Relevant issues are the extensional and compressional flows, high longitudinal deviatoric stress, and the stress state near the basal discontinuity. We find that some of the down-slope component of glacier weight is borne by longitudinal stress in the rapidly sliding region. This stress thrusts against the slowly moving parts of the glacier. We hypothesize that this effect causes the rapidly sliding part to spread and causes the compression front to travel down the glacier. A criterion for spreading of the rapidly sliding part is developed. The mechanics outlined above are used to develop a highly idealized model for glacier surging. We propose that regions of low drag are relatively common features of glaciers. The surge initiates when conditions are met which allow the surge nucleus to spread. The rapidly sliding region of low drag spreads to a large part of the glacier. Surging ends when the low-drag conditions terminate. Because of the changed state of the glacier, surge nuclei are now stable against spreading. Several years of rebuilding must occur before nuclei are once more unstable. Calculations are performed for the evolution of the shape of Medvezhy Glacier during the surge of 1963. We find a remarkable similarity between the data and our computations. RESUME. Sur le mecanisme des avances catastrophiques.