Computational Inelasticity This book describes the theoretical foundations of inelasticity its numerical formulation and implementation. The subject matter described herein constitutes a representative sample of state of the art methodology currently used in inelastic calculations. Among the numerous topics covered are small deformation plasticity and viscoplasticity convex optimization theory integration algorithms for the constitutive equation of plasticity and viscoplasticity the variational setting of boundary value problems and discretization by finite element methods. Also addressed are the generalization of the theory to non smooth yield surface mathematical numerical analysis issues of general return mapping algorithms the generalization to finite strain inelasticity theory objective integration algorithms for rate constitutive equations the theory of hyperelastic based plasticity models and small and large deformation viscoelasticity. Computational Inelasticity will be of great interest to researchers and graduate students in various branches of engineering especially civil aeronautical and mechanical and applied mathematics. Motivation. One Dimensional Plasticity and Viscoplasticity Classical Rate Independent Plasticity and Viscoplasticity Integration Algorithms for Plasticity and Viscoplasticity Discrete Variational Formulation and Finite Element Implementation Nonsmooth Multisurface Plasticity and Viscoplasticity Numerical Analysis of General Return Mapping Algorithms Nonlinear Continuum Mechanics and Phenomenological Plasticity Models Objective Integration Algorithms for Rate Formulations of Elastoplasticity Phenomenological Plasticity Models Based on the Notion of an Intermediate Stress Free Configuration Viscoelasticity.