Can a curved beam bistable mechanism have a secondary equilibrium that is more stable than its stress-free configuration?

A new concept for the geometry of a curved beam bistable micromechanical mechanism is proposed aiming at producing a secondary equilibrium state that is more stable (in terms of transformation force) than the primary, stress-free, configuration. The proposed geometry is simple and compatible with common MEMS mass-production processes. A parametric study is performed by means of a non-linear finite-elements analysis in order to study the post-buckling behavior and performance of the mechanism. Based on this analysis, we show that it is theoretically possible to have a mechanism that exhibits a secondary equilibrium state that is more stable than the stress-free configuration. We also find that the post-buckling response of the proposed design is very sensitive to a particular geometrical feature. Besides this particular weakness, the mechanism is rather robust with respect to geometrical inaccuracies. We report our findings with the hope of inspiring others to propose new ideas for overcoming this geometrical sensitivity.     

Improved functional perturbation method for reliability analysis of randomly heterogeneous beams

The strength reliability of randomly heterogeneous beams is studied. The beams are considered as brittle, and failure by the weakest link criterion is assumed. The structure is statically indeterminate, thus the stress field is a function of the random morphology. The probabilistic beam strength is a coupled functional of morphology and stresses. Correlation between local strength and local modulus is also considered, and its effect on reliability is investigated. Heterogeneity is confined to the longitudinal direction only. An improved analytical solution is found by a new, optimized functional perturbation method (FPM). The improvement is achieved by two operations: generalizing the previously used FPM to account for multifunctional dependency, and choosing the perturbation to be around the proper homogeneous case for each type of morphology. It is shown that the improvement of the optimized method for reliability analysis is significant, and depends on the type of local strength-modulus statistical correlation. In addition, analytical results for very large and very small correlation lengths are obtained, and their validity range is examined by numerical solutions.     

A theoretical study of biological membrane response to temperature gradients at the single-cell level

Recent experimental studies provide evidence for the existence of a spatially non-uniform temperature field in living cells and in particular in their plasma membrane. These findings have led to the development of a new and exciting field: thermal biology at the single-cell level. Here, we examine theoretically a specific aspect of this field, i.e. how temperature gradients at the single-cell level affect the phase behaviour and geometry of heterogeneous membranes. We address this issue by using the Onsager reciprocal relations combined with a simple model for a binary lipid mixture. We demonstrate that even small temperature variations along the membrane may introduce intriguing phenomena, such as phase separation above the critical temperature and unusual shape response. These results also suggest that the shape of a membrane can be manipulated by dynamically controlling the temperature field in its vicinity. The effects of intramembranous temperature gradients have never been studied experimentally. Thus, the predictions of the current contribution are of a somewhat speculative nature. Experimental verification of these results could mark the beginning of a new line of research in the field of biological membranes. We report our findings with the hope of inspiring others to perform such experiments.     

Fracture mechanics of a randomly heterogeneous double cantilever beam

A Heterogeneous Double Cantilever Beam, commonly used for fracture energy measurements, is analyzed by the Functional Perturbation Method (FPM). External force and displacement are considered as functionals of materials morphology. Both stiffness and fracture energies are random fields, from which the average and variance of the external loading and displacement at the onset of crack growth are found explicitly. The inverse problem, in which the stochastic properties of the fracture energy (average and variance) are found from the load-displacement-crack length data, is also solved. The solution is given in terms of intrinsic correlation length, which is equivalent to `grain size' in polycrystals. It is shown that a different characteristic length for the fracture energy and for moduli may exist. Special attention is given to very small or very large `grains', for which an analytical approximation is permitted. It is shown that the `classical' design loads for a common, fracture related reliability level, may be non-conservative and deviate significantly from the accurate value.