arXiv subjects

Wayne M. Falk

Publications and source records attributed to Wayne M. Falk.

2 recordsLinked to original sources

arXiv2022

Modern Statistical Models and Methods for Estimating Fatigue-Life and Fatigue-Strength Distributions from Experimental Data

Engineers and scientists have been collecting and analyzing fatigue data since the 1800s to ensure the reliability of life-critical structures. Applications include (but are not limited to) bridges, building structures, aircraft and spacecraft components, ships, ground-based vehicles, and medical devices. Engineers need to estimate S-N relationships (Stress or Strain versus Number of cycles to failure), typically with a focus on estimating small quantiles of the fatigue-life distribution. Estimates from this kind of model are used as input to models (e.g., cumulative damage models) that predict failure-time distributions under varying stress patterns. Also, design engineers need to estimate lower-tail quantiles of the closely related fatigue-strength distribution. The history of applying incorrect statistical methods is nearly as long and such practices continue to the present. Examples include treating the applied stress (or strain) as the response and the number of cycles to failure as the explanatory variable in regression analyses (because of the need to estimate strength distributions) and ignoring or otherwise mishandling censored observations (known as runouts in the fatigue literature). The first part of the paper reviews the traditional modeling approach where a fatigue-life model is specified. We then show how this specification induces a corresponding fatigue-strength model. The second part of the paper presents a novel alternative modeling approach where a fatigue-strength model is specified and a corresponding fatigue-life model is induced. We explain and illustrate the important advantages of this new modeling approach.

stat.ME↗

arXiv2005

An elasticity theory for self-assembled protein lattices with application to the martensitic phase transition in bacteriophage T4 tail sheath

We propose an elasticity theory for one and two dimensional arrays of globular proteins for which the free energy is affected by relative position and relative rotation between neighboring molecules. The kinematics of such assemblies is described, the conditions of compatibility are found, a form of the free energy is given, and formulas for applied forces and moments are developed. It is shown that fully relaxed states of sheets consist of helically deformed sheets which themselves are composed of helical chains of molecules in rational directions. We apply the theory to the fascinating contractile deformation that occurs in the tail sheath of the virus bacteriophage T4, which aids its invasion of its bacterial host. Using electron density maps of extended and contracted sheath, we approximate the domains of each molecule by ellipsoids and then evaluate our formulas for the position and orientation of each molecule. We show that, with the resulting kinematic description, the configurations of extended and contracted tail sheath are generated by a simple formula. We proposed a constrained version of the theory based on measurements on extended and contracted sheath. Following a suggestion of Pauling [{\em Discussions of the Faraday Society} {\bf 13}, 170-6 (1953)], we develop a simple model of the molecular interaction. The resulting free energy is found to have a double-well structure. Certain simple deformations are studied (tension, torsion inflation); the theory predicts a first-order Poynting effect and some unexpected relations among moduli. Finally, the force of penetration is given, and a possibly interesting program of epitaxial growth and patterning of such sheets is suggested.

physics.bio-ph↗