The Physics and Mathematics of Adiabatic Shear Bands [Hardcover]

Establishes the mathematical setting within which shear bands may be studied.This book is a research monograph on the material instability known as adiabatic shear banding. The phenomenon is important as a damage mechanism in rapidly deforming materials. Examples where shear bands are to be expected are ballistic impact, studies of crashworthiness, or rapid manufacturing processes. Depending on the application, shear bands may be harmful or beneficial, but to be controlled, they must first be understood. This book establishes the mathematical setting within which shear bands may be studied and uses well established asymptotic techniques to obtain scaling laws that describe major aspects of the formation and morphology of shear bands. This book should help shear mechanics to become a major companion to fracture mechanics.This book is a research monograph on the material instability known as adiabatic shear banding. The phenomenon is important as a damage mechanism in rapidly deforming materials. Examples where shear bands are to be expected are ballistic impact, studies of crashworthiness, or rapid manufacturing processes. Depending on the application, shear bands may be harmful or beneficial, but to be controlled, they must first be understood. This book establishes the mathematical setting within which shear bands may be studied and uses well established asymptotic techniques to obtain scaling laws that describe major aspects of the formation and morphology of shear bands. This book should help shear mechanics to become a major companion to fracture mechanics.This monograph covers the material instability known as adiabatic shear banding which often occurs in a plastically deforming material as it undergoes rapid shearing. This book surveys these exciting developments at the frontier of mathematics and presents many new results. materials with continued straining, a process which is usually unstable. In this case the instability results in thin regions of highly lC=