A Course on Plasticity Theory

Plasticity Theory is characterized by many competing and often incompatible points of view. This book seeks to strengthen the foundations of continuum plasticity theory,emphasizing a unifying perspective grounded in the fundamental notion of material symmetry. Steigmann's book offers a systematic framework for the proper understanding of established models of plasticity and for their modern extensions and generalizations. Particular emphasis is placed on the differential-geometric aspects of the subject and their role in illuminating the conceptual foundations of plasticity theory.

Format: Hardback
Length: 208 pages
Publication date: 20 January 2023
Publisher: Oxford University Press

Plasticity Theory is a complex and multifaceted concept that encompasses a wide range of competing and often contradictory viewpoints. This book aims to provide a solid foundation for continuum plasticity theory, emphasizing a unified perspective rooted in the fundamental concept of material symmetry. Steigmann's comprehensive work offers a systematic framework for comprehending established models of plasticity and their modern extensions and generalizations. Special attention is given to the differential-geometric aspects of the subject, which play a crucial role in illuminating the conceptual underpinnings of plasticity theory. Classical models, along with several topics of current interest in continuum mechanics, are presented in a unified and coherent manner. This book is intended for graduate students and scholars engaged in the field of continuum mechanics.

Introduction:
Plasticity theory is a fundamental concept in continuum mechanics that describes the deformation and flow of materials under applied stresses and strains. It encompasses a wide range of phenomena, including plastic deformation, creep, stress relaxation, and fracture. The theory has played a crucial role in the development of engineering materials, structures, and devices.

Plasticity Theory: A Complex and Multifaceted Concept:
Plasticity theory is characterized by a multitude of competing and often incompatible points of view. Different researchers and scholars have proposed different models, assumptions, and mathematical formulations to explain the behavior of materials under plastic deformation. This diversity of perspectives has led to a rich and complex body of knowledge, but it has also created challenges in terms of consolidating and integrating different theories.

The Need for a Unifying Perspective:
One of the main goals of this book is to strengthen the foundations of continuum plasticity theory by emphasizing a unifying perspective grounded in the fundamental notion of material symmetry. Material symmetry refers to the inherent property of a material to maintain its shape and properties under certain conditions, regardless of the direction or magnitude of the applied stresses and strains. By focusing on material symmetry, this book seeks to provide a coherent framework for understanding the behavior of materials under plastic deformation.

Steigmann's Contributions:
Professor Steigmann is a renowned expert in continuum mechanics and plasticity theory. His book offers a systematic framework for the proper understanding of established models of plasticity and for their modern extensions and generalizations. Particular emphasis is placed on the differential-geometric aspects of the subject and their role in illuminating the conceptual foundations of plasticity theory.

Differential-Geometric Aspects of Plasticity:
Differential geometry is a branch of mathematics that deals with the study of curves, surfaces, and manifolds. It provides a powerful set of tools for analyzing the behavior of materials under plastic deformation. In this book, Professor Steigmann discusses the differential-geometric aspects of plasticity theory in detail. He explains how the geometry of curves, surfaces, and manifolds can be used to describe the deformation and flow of materials under applied stresses and strains.

Classical Models of Plasticity:
Professor Steigmann develops classical models of plasticity, such as the yield criterion, the plastic potential, and the flow rule. He explains these models in a unified and coherent manner, providing a clear understanding of their underlying principles and assumptions. He also discusses the limitations and assumptions of these models and highlights the areas where they can be extended and generalized.

Contemporary Research Topics:
In addition to classical models, Professor Steigmann discusses several topics of current interest in continuum mechanics. These topics include the study of viscous flow, the behavior of materials under high-temperature conditions, and the development of new models for brittle materials. He provides a comprehensive overview of these topics, highlighting the recent advances and challenges in the field.

Conclusion:
Plasticity theory is a complex and multifaceted concept that requires a solid foundation to be understood and applied effectively. This book provides a comprehensive and systematic framework for comprehending established models of plasticity and their modern extensions and generalizations. By emphasizing a unifying perspective grounded in the fundamental notion of material symmetry, Professor Steigmann's work offers a valuable resource for graduate students and academics working in the field of continuum mechanics.

Weight: 578g
Dimension: 176 x 255 x 17 (mm)
ISBN-13: 9780192883155