This book collects recent theoretical developments in the area of material instability in elastic and plastic solids along with related analytical and numerical methods and applications. The existing different approaches to instability phenomena in metal single crystals, polycristals and in geomaterials are presented with the emphasis laid on mutual relations and on unifying concepts, including elliptictly loss and the energy criterion. Quasi-static bifurcation, initiation of single or multiple shear bands and post-critical strain localization are examined along with dynamic phenomena as wave propagation, moving shocks, internal snap-through and instability of flutter type. This gives an overview of a variety of material instability problems, methods and applications.
Fracture in structural materials remains a vital consideration in engineering systems, affecting the reliability of machines throughout their lives. Impressive advances in both the theoretical understanding of fracture mechanisms and practical developments that offer possibilities of control have re-shaped the subject over the past four decades. The contributors to this volume, including some of the most prominent researchers in the field, give their long-range perspectives of the research on the fracture of solids and its achievements. The subjects covered in this volume include: statistics of brittle fracture, transition of fracture from brittle to ductile, mechanics and mechanisms of ductile separation of heterogenous solids, the crack tip environment in ductile fracture, and mechanisms and mechanics of fatigue. Materials considered range from the usual structural solids to composites. The chapters include both theoretical points of view and discussions of key experiments. Contributors include: from MIT, A.S. Argon, D.M. Parks; from Cambridge, M.F. Ashby; from U.C. Santa Barbara, A.G. Evans, R. McMeeking; from Glasgow, J. Hancock; from Harvard, J.W. Hutchinson, J.R. Rice; from Sheffield, K.J. Miller; from Brown, A. Needleman; from the Ecole des Mines, A. Pineau; from U.C. Berkeley, R. O. Ritchie; and from Copenhagen, V. Tvergaard.
Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based.Develop Intuitive Ability to Identify and Avoid Physically Meaningless PredictionsApplied Mechanics o
Instabilities Modeling in Geomechanics describes complex mechanisms which are frequently met in earthquake nucleation, geothermal energy production, nuclear waste disposal and CO2 sequestration. These mechanisms involve systems of non-linear differential equations that express the evolution of the geosystem (e.g. strain localization, temperature runaway, pore pressure build-up, etc.) at different length and time scales. In order to study the evolution of a system and possible instabilities, it is essential to know the mathematical properties of the governing equations. Therefore, questions of the existence, uniqueness and stability of solutions naturally arise. This book particularly explores bifurcation theory and stability analysis, which are robust and rigorous mathematical tools that allow us to study the behavior of complex geosystems, without even explicitly solving the governing equations. The contents are organized into 10 chapters which illustrate the application of these methods in various fields of geomechanics.
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
The book is written by leading experts in the field presenting an up-to-date view of the subject matter in a didactically sound manner. It presents a review of the current knowledge of the behaviour of soft tissues in the cardiovascular system under mechanical loads, and the importance of constitutive laws in understanding the underlying mechanics is highlighted. Cells are also described together with arteries, tendons and ligaments, heart, and other biological tissues of current research interest in biomechanics. This includes experimental, continuum mechanical and computational perspectives, with the emphasis on nonlinear behaviour, and the simulation of mechanical procedures such as balloon angioplasty.
The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.
