This book provides readers with a deep understanding of the use of objective algorithms for
integration of constitutive relations (CRs) for Hooke-like hypoelasticity based on the use of
corotational stress rates. The purpose of objective algorithms is to perform the step-by-step
integration of CRs using fairly large time steps that provide high accuracy of this integration
in combination with the exact reproduction of superimposed rigid body motions. Since Hooke-like
hypoelasticity is included as a component in CRs for elastic-inelastic materials (e.g. in CRs
for elastic-plastic materials) the scope of these algorithms is not limited to hypoelastic
materials but extends to many other materials subjected to large deformations. The authors
performed a comparative analysis of the performance of most currently available objective
algorithms provided some recommendations for improving the existing formulations of these
algorithms and presented new formulations of the so-called absolutely objective algorithms.
The proposed book will be useful for beginner researchers in the development of economical
methods for integrating elastic-inelastic CRs as well as for experienced researchers by
providing a compact overview of existing objective algorithms and new formulations of these
algorithms. The book will also be useful for developers of computer codes for implementing
objective algorithms in FE systems. In addition this book will also be useful for users of
commercial FE codes since often these codes are so-called black boxes and this book shows how
to test accuracy of the algorithms of these codes for integrating elastic-inelastic CRs in
modeling large rotations superimposed on the uniform deformation of any sample.
