Kinematic quantities of finite elastic and plastic deformation

Kinematic quantities for finite elastic and plastic deformations are defined via an approach that does not rely on auxiliary elements like reference frame and reference configuration, and that gives account of the inertial-noninertial aspects explicitly. These features are achieved by working on Galilean spacetime directly. The quantity expressing elastic deformations is introduced according to its expected role: to measure how different the current metric is from the relaxed/stressless metric. Further, the plastic kinematic quantity is the change rate of the stressless metric. The properties of both are analyzed, and their relationship to frequently used elastic and plastic kinematic quantities is discussed. One important result is that no objective elastic or plastic quantities can be defined from deformation gradient.Comment: v5: minor changes, one section moved to an Appendix, 26 pages, 2 figure

Fractional Calculus for Continuum Mechanics - anisotropic non-locality

In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in literature. The overall concept bases on the fractional deformation gradient which is non-local, as a consequence of fractional derivative definition. The main advantage of the proposed formulation is its analogical structure to the general framework of classical continuum mechanics. In this sense, it allows, to give similar physical and geometrical meaning of introduced objects

The origins of length contraction: I. The FitzGerald-Lorentz deformation hypothesis

One of the widespread confusions concerning the history of the 1887 Michelson-Morley experiment has to do with the initial explanation of this celebrated null result due independently to FitzGerald and Lorentz. In neither case was a strict, longitudinal length contraction hypothesis invoked, as is commonly supposed. Lorentz postulated, particularly in 1895, any one of a certain family of possible deformation effects for rigid bodies in motion, including purely transverse alteration, and expansion as well as contraction; FitzGerald may well have had the same family in mind. A careful analysis of the Michelson-Morley experiment (which reveals a number of serious inadequacies in many text-book treatments) indeed shows that strict contraction is not required.Comment: 29 pages; accepted April 2001 for publication in American Journal of Physic

The effects of shoe temperature on the kinetics and kinematics of running

The aim of the current investigation was to examine the effects of cooled footwear on the kinetics and kinematics of running in comparison to footwear at normal temperature. Twelve participants ran at 4.0 m/s ± 5% in both cooled and normal temperature footwear conditions over a force platform. Two identical footwear were worn, one of which was cooled for 30 min. Lower extremity kinematics were obtained using a motion capture system and tibial accelerations were measured using a triaxial accelerometer. Differences between cooled and normal footwear temperatures were contrasted using paired samples t-tests. The results showed that midsole temperature (cooled = 4.21 °C and normal = 23.25 °C) and maximal midsole deformation during stance (cooled = 12.85 mm and normal = 14.52 mm) were significantly reduced in the cooled footwear. In addition, instantaneous loading rate (cooled = 186.21 B.W/s and normal = 167.08 B W/s), peak tibial acceleration (cooled = 12.75 g and normal = 10.70 g) and tibial acceleration slope (cooled = 478.69 g/s and normal = 327.48 g/s) were significantly greater in the cooled footwear. Finally, peak eversion (cooled = −10.57 ° and normal = −7.83°) and tibial internal rotation (cooled = 10.67 ° and normal = 7.77°) were also shown to be significantly larger in the cooled footwear condition. This study indicates that running in cooled footwear may place runners at increased risk from the biomechanical parameters linked to the aetiology of injuries

Biomechanics

Biomechanics is a vast discipline within the field of Biomedical Engineering. It explores the underlying mechanics of how biological and physiological systems move. It encompasses important clinical applications to address questions related to medicine using engineering mechanics principles. Biomechanics includes interdisciplinary concepts from engineers, physicians, therapists, biologists, physicists, and mathematicians. Through their collaborative efforts, biomechanics research is ever changing and expanding, explaining new mechanisms and principles for dynamic human systems. Biomechanics is used to describe how the human body moves, walks, and breathes, in addition to how it responds to injury and rehabilitation. Advanced biomechanical modeling methods, such as inverse dynamics, finite element analysis, and musculoskeletal modeling are used to simulate and investigate human situations in regard to movement and injury. Biomechanical technologies are progressing to answer contemporary medical questions. The future of biomechanics is dependent on interdisciplinary research efforts and the education of tomorrow’s scientists

An overview of a Lagrangian method for analysis of animal wake dynamics

The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a Lagrangian approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the Eulerian perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available

Shape of optimal active flagella

Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molecular motors forcing the flagellum, only a portion of which ending up dissipated in the fluid. This optimisation approach allows us to derive a family of shapes depending on a single dimensionless number quantifying the relative importance of elastic to viscous effects: the Sperm number. The computed optimal shapes are found to agree with the waveforms observed on spermatozoon of marine organisms, thus suggesting that these eukaryotic flagella might have evolved to be mechanically optimal.Comment: 10 pages, 5 figure