Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories

Abstract

This book is the third in a series of volumes by Y. C. Fung on biomechanics. The first two were Biomechanics: Mechanical Properties of Living Tissues (1981) and Biodynamics: Circulation (1984). In these books the author describes the constitutive behavior of biological tissues, the functional mechanics of the body's organs, and related engineering problems. The present volume, like the previous two, summarizes the application of an enormously wide spectrum of mechanics and thermodynamics to physiology and the engineering of biologically related problems. The mechanics applied includes rigid-body mechanics, mechanical vibration theory, viscous and perfect fluid theory, linear and nonlinear elasticity, wave propagation in fluid and solid media, multiphase mixture theory, chemical thermodynamics, and numerous subtopics of mechanics. The problems addressed cover the spectrum from birds flying and fish swimming to oxygen transport, human impact tolerance, and the engineering of activities at the cellular level. The introductory chapter describes the principles of mechanics, the modeling of phenomena, and the nature of the practical problems to be dealt with, e.g., basic physiology, prostheses, sports techniques, etc. Chapter 2 discusses the mechanics and modeling of whole bodies or whole body segments. Chapter 3 reviews the mechanics of the fluid dynamic forces that act on bodies moving through the fluid and Chapter 4 applies these results of classical mechanics to the mechanics of flying and swimming. The flight of birds and insects is compared with the flight of aircraft. The mechanics of hovering as well as the swimming of very small flagella are described. The circulatory system is considered in Chapters 5 and 6. Chapter 5 describes blood flow in the heart, lung, arteries, and veins while Chapter 6 addresses the microcirculation, blood rheology and blood flow in the lung. Respiratory gas flow, convection, diffusion, gas exchange, and pulmonary function tests are the topics of Chapter 7. Chapters 8 and 9 concern molecular diffusion and mass transport, fluid movement in interstitial space and across capillary blood vessel walls, filtration and transport across cell membranes. Chapter 10 is a presentation of nonlinear elasticity including the first report I have seen of an additive decomposition of the deformation gradient into a symmetric and an orthogonal matrix of tensor components. This additive decomposition is an analog of the multiplicative polar decomposition theorem used in continuum mechanics to separate the rotational and deformational components of a motion. Chapter 11 concerns residual strains in 'Professor, City College, New York, NY 10024.

Control of folding by gravity and matrix thickness: Implications for large‐scale folding

“…This discrepancy occurs because they employed the so-called equilibrium analysis [e.g., Bazant and Cedolin, 1991], which requires anapproximation of the inherently time-dependent viscous formulationby an effective quasi-static (e.g., elastic) model involving only stationary parameters (e.g., background strain rate _ e B ). To achieve this reduction, the kinematic equation (8) was approximated as…”

Experimental and Numerical Study of the Buckling of Composite Profiles with Open Cross Section under Axial Compression

“…In short thin-walled plate structures, the lowest critical load corresponds to local buckling which does not cause damage to these structures. This being the case, when the critical load is exceeded, the element can still operate because the post-critical equilibrium path is stable and symmetric [1][2][3][4]. This means that the increase in wall deflection involves an increase in compressive load both for the positive and negative total deflection (Fig.…”

Experimental and theoretical fracture mechanics applied to fracture of the crust of Venus

“…Although there is no exact solution for the horizontal stress distribution at the surface of a half plane due to an edge crack, this stress shadow can be estimated. The simplest approximation is that the stress increases linearly from zero at the edge of the fracture with a gradient of 1/p [Bazant and Cedolin, 1991].…”