Nonlinear Theory Of Elasticity Applications In Biomechanics

Soft biological tissues often undergo large (nearly) elastic deformations that can be modeled using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate.This volume clarifies and unifies those treatments, illustrating the advantages and disadvantages of each through various examples in biomechanics. Applications include muscle, arteries, the heart, and embryonic tissues.The revised edition includes new end-of-chapter problems, including answers and detailed solutions to most. The useful reference can be a good textbook for self-study, as well as senior- and graduate-level courses in biomechanics and nonlinear elasticity.

Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues. Contents: Vectors, Dyadics, and Tensors; Analysis of Deformation; Analysis of Stress; Constitutive Relations; Biomechanics Applications. Readership: Graduate students and researchers interested in mechanics problems involving large elastic deformations, like those in soft tissue biomechanics.

Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.

Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.

This is an essential book for students and academicians alike. In addition to discussing theory, topics include the connection between stresses and strains in an isotropic elastic body, the geometry of strain, and much more. Deductions are explained in the simplest, most intuitive manner for wide accessibility. 1953 edition.

The Nonlinear Theory of Elastic Shells: One Spatial Dimension presents the foundation for the nonlinear theory of thermoelastic shells undergoing large strains and large rotations. This book discusses several relatively simple equations for practical application. Organized into six chapters, this book starts with an overview of the description of nonlinear elastic shell. This text then discusses the foundation of three-dimensional continuum mechanics that are relevant to the shell theory approach. Other chapters cover several topics, including birods, beamshells, and axishells that begins with a derivation of the equations of motion by a descent from the equations of balance of linear and rotational momentum of a three-dimensional material continuum. This book discusses as well the approach to deriving complete field equations for one- or two-dimensional continua from the integral equations of motion and thermodynamics of a three-dimensional continuum. The final chapter deals with the analysis of unishells. This book is a valuable resource for physicists, mathematicians, and scientists.

This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.