Elastoplasticity Theory

This book was written to serve as the standard textbook for instruction of elastoplasticity theory. It opens with an explanation of the mathematics and continuum mechanics which are necessary as a foundation of elastoplasticity theory. Subsequently, conventional and unconventional elastoplasticity theories are explained comprehensively for description of general loading behavior covering monotonic, nonproportional, and cyclic loading processes. Fundamental notions such as continuity and smoothness conditions, decomposition of deformation into elastic and plastic parts, the associated flow rule, the loading criterion and the anisotropy are defined, and then presented with their mechanical interpretations. Explicit constitutive equations of metals and soils, which are useful in engineering practice for the mechanical design of machinery and structures, are also introduced. Moreover, constitutive equations of friction with transition from static to kinetic friction and vice versa, and rotational and orthotropic anisotropy are provided. They are indispensable for analyses of boundary-value problems.