This book includes a numerical investigation of shear localization in granular materials within micro-polar hypoplasticity, which was carried out during my long research stay at the Institute of Soil and Rock Mechanics at Karlsruhe University from 1985 to 1996. I dedicate my book to Prof. Gerd Gudehus from Germany, the former head of the Institute of Rock and Soil Mechanics at Karlsruhe University and the supervisor of my scientific research during my stay in Karlsruhe, who encouraged me to deal with shear localization in granular bodies within micro-polar hypoplasticity.

The simplest way to formulate the basic equations of continuum mech- ics and the constitutive or evolutional equations of various materials is to restrict ourselves to rectangular cartesian coordinates. However, solving p- ticular problems, for instance in Chapter 5, it may be preferable to work in terms of more suitable coordinate systems and their associated bases. The- fore, Chapter 2 is also concerned with the standard techniques of tensor an- ysis in general coordinate systems. Creep mechanics is a part of continuum mechanics, like elasticity or pl- ticity. Therefore, some basic equations of continuum mechanics are put - gether in Chapter 3. These equations can apply equally to all materials and they are insuf?cient to describe the mechanical behavior of any particular material. Thus, we need additional equations characterizing the individual material and its reaction under creep condition according to Chapter 4, which is subdivided into three parts: the primary, the secondary, and the tertiary creep behavior of isotropic and anisotropic materials. The creep behavior of a thick-walled tube subjected to internal pressure is discussed in Chapter 5. The tube is partly plastic and partly elastic at time zero. The investigation is based upon the usual assumptions of incompre- ibility and zero axial creep. The creep deformations are considered to be of such magnitude that the use of ?nite-strain theory is necessary. The inner and outer radius, the stress distributions as functions of time, and the cre- failure time are calculated.

Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!

For the last decade, the author has been working to extend continuum mechanics to treat moving boundaries in materials focusing, in particular, on problems of metallurgy. This monograph presents a rational treatment of the notion of configurational forces; it is an effort to promote a new viewpoint. Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture. The work should be of interest to materials scientists, mechanicians, and mathematicians.

I was delighted when I learned in the fall of 2005 that Steve Cowin was working on a textbook in biomechanics. Steve and I were in the same department at Tulane University in the 1970s, and under his influence I learned the beauty and power of continuum mechanics as a means to better understand the musculoskeletal system. When I began teaching courses in biomechanics during that decade, it was natural to teach the material from a continuum mechanics persp- tive. Over the years I have used a variety of continuum mechanics texts, but, for the most part, I have had to find the biomedical examples I used directly from the research literature. I have now had a chance to review a draft of Tissue Mechanics by Cowin and Doty, and it exceeds my high expectations. The material includes a rigorous and comprehensive introd- tion to continuum mechanics oriented toward biomechanics. Indeed, all of the foundation t- ics for continuum models of biological materials are covered. This material is illustrated through applications to the hard and soft tissues of the human body. Steve Cowin is now one of the leading researchers in the mechanics of bone, so one would expect the chapters on bone tissue and bone tissue adaptation to be of a very high order. But the presentation on collagen and cartilage mechanics is also excellent. Their presentation of finite deformation mechanics and its application to tendons and ligaments is one of the most accessible in the literature.

This textbook provides a mathematical introduction to the theory of large-scale ocean circulation and is accessible for readers with an elementary knowledge of mathematics and physics, including continuum mechanics and solution methods for ordinary differential equations. The book consists of four parts. Part I (chapters 1 - 4) is a very brief introduction to ocean circulation and the mathematical formulation of the governing equations of ocean flows. In addition, concepts are introduced that are necessary to describe and understand large-scale ocean currents. In part II (chapters 5 - 10), the theory of mid-latitude wind-driven ocean circulation is presented. The consideration of model development includes a top-down approach and reduced equations are derived using asymptotics and scaling. Part III (chapters 11 - 12) focuses on the understanding of equatorial currents and El Nino. In the last part IV, chapters 13 - 16, the theory of planetary scale flows is presented, covering topics such as the thermocline problem, the Antarctic Circumpolar Current, the stability of the thermohaline circulation and the Arctic Ocean circulation. At the end of each chapter several exercises are formulated. Many of these are aimed to further develop methodological skills and to get familiar with the physical concepts. New material is introduced in only a few of these exercises. Fully worked out answers to all exercises can be downloaded from the book web site.