Effect of inclusions and holes on the stiffness and strength of honeycombs

A finite element study has been performed on the effects of holes and rigid inclusions on the elastic modulus and yield strength of regular honeycombs under biaxial loading. The focus is on honeycombs that have already been weakened by a small degree of geometrical imperfection, such as a random distribution of fractured cell walls, as these imperfect honeycombs resemble commercially available metallic foams. Hashin-Shtrikman lower and upper bounds and self-consistent estimates of elastic moduli are derived to provide reference solutions to the finite element calculations. It is found that the strength of an imperfect honeycomb is relatively insensitive to the presence of holes and inclusions, consistent with recent experimental observations on commercial aluminum alloy foams.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.