Means W.D. Stress and Strain. Basic Concepts of Continuum Mechanics for Geologists

New York: Springer-Verlag, 1976. — 339 p.This is an elementary book on stress and strain theory for geologists. It is written in the belief that a sound introduction to the mechanics of continuous bodies is essential for students of structural geology and tectonics, just as a sound introduction to physical chemistry is necessary for students of petrology. This view is shared by most specialists in structural geology, but it is not yet reflected in typical geology curricula. Undergraduates are still traditionally given just a few lectures on mechanical fundamentals, and there is rarely any systematic lecturing on this subject at the graduate level. The result is that many students interested in structure and tectonics finish their formal train­ ing without being able to understand or contribute to modem literature on rocks as mechanical systems. The long-term remedy for this is to introduce courses in continuum mechanics and material behavior as routine parts of the undergraduate curriculum. These subjects are difficult, but no more so than optical mineralogy or thermo­ dynamics or other rigorous subjects customarily studied by undergraduates. The short-term remedy is to provide books suitable for independ­ ent study by those students and working geologists alike who wish to improve their understanding of mechanical topics relevant to geology. This book is intended to meet the short-term need with respect to stress and strain, two elementary yet challenging concepts of continuum mechanics.
This text provides an extensive introduction to the theories of stress and strain. The first section introduces fundamental ideas such as the distinction between instantaneous quantities like stress and two-state quantities like finite strain. Part two discusses stress in detail. Part three treats deformation and strain, introduces infinitesimal and finite strain tensors and discusses strain history.Material Constitution of Rocks
Mechanical State
Change in Mechanical State
Mechanical Significance of Structure
Classes of Forces
Stress on a Plane
The Stress Ellipsoid
Mohr Circle for Stress
Tensor Components of Stress
Cauchy’s Formula, Transformation of Tensor Components
Stress Fields
Stress History
Distortion and Deformation, Measures of Distortion
The Strain Ellipsoid
Mohr Circle for Infinitesimal Strain
Mohr Circle for Finite Strain
Displacement and Deformation Gradients
Tensor Components of Infinitesimal Strain
Tensor Components of Finite Strain
Strain Fields
Strain History
Hookean Behavior