Spatial and Material Forces in Nonlinear Continuum Mechanics: A Dissipation-Consistent Approach

This monograph explores non-linear continuum mechanics through a dissipation-consistent approach, focusing on spatial and material vistas. It introduces the concept of configurational forces, which are power conjugate to changes in the material configuration of a continuum body. Configurational mechanics provides a unified framework for understanding the evolution of continuum bodies, including crack propagation, and offers a versatile computational approach. The author argues that configurational forces are dissipation-consistent with configurational changes, making it an ideal formulation for tackling sophisticated problems in continuum defect mechanics.

Format: Hardback
Length: 395 pages
Publication date: 29 March 2022
Publisher: Springer Nature Switzerland AG

This comprehensive monograph delves into the intricate realms of non-linear continuum mechanics, employing a dissipation-consistent approach to explore both spatial and material perspectives. The spatial vista sheds light on the conventional approach to nonlinear continuum mechanics, along with the associated spatial forces, while the material vista delves into the realm of configurational mechanics, focusing on the corresponding material or configurational forces. At the core of configurational mechanics lies the concept of force, a fundamental principle. In analytical mechanics, force emerges as a derived object, directly proportional to changes in generalized coordinates. For a continuum body, these generalized coordinates typically refer to the spatial positions of its continuum points. However, when in accordance with the second law, continuum points, such as those located at boundaries, may also undergo material position changes. Consequently, configurational forces emerge, directly proportional to these configurational alterations. A notable example is a crack tip, representing a singular portion of the boundary undergoing position changes during crack propagation. The associated configurational force, commonly known as the J-integral, drives the evolution of the crack tip, consuming power, often expressed as the energy release rate. When considered collectively, configurational mechanics emerges as an unconventional branch of continuum physics, aimed at rationalizing and unifying the inherent tendency of a continuum body to alter its material configuration. It serves as an ideal framework for addressing complex problems in continuum defect mechanics. Remarkably, configurational mechanics operates without any constraints regarding geometrical and constitutive nonlinearities, providing a versatile computational approach to continuum defect mechanics. In this monograph, I provide a detailed account of my approach to configurational mechanics, further substantiating my belief that configurational forces indeed exhibit dissipation-consistent behavior.

Weight: 799g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030890698
Edition number: 1st ed. 2022