Elastoplasticity TheoryContents Recent advancements in the performance of industrial products and structures are quite intense. Consequently, mechanical design of high accuracy is necessary to enhance their mechanical performance, strength and durability. The basis for their mechanical design can be provided through elastoplastic deformation analyses. For that reason, industrial engineers in the fields of mechanical, civil, architec- ral, aerospace engineering, etc. must learn pertinent knowledge relevant to elas- plasticity. Numerous books about elastoplasticity have been published since “Mathema- cal Theory of Plasticity”, the notable book of R. Hill (1950), was written in the middle of the last century. That and similar books mainly address conventional plasticity models on the premise that the interior of a yield surface is an elastic domain. However, conventional plasticity models are applicable to the prediction of monotonic loading behavior, but are inapplicable to prediction of deformation behavior of machinery subjected to cyclic loading and civil or architectural str- tures subjected to earthquakes. Elastoplasticity has developed to predict defor- tion behavior under cyclic loading and non-proportional loading and to describe nonlocal, finite and rate-dependent deformation behavior. |
Contents
1 | |
Motion and Strain Rate | 57 |
Conservation Laws and Stress Tensors | 101 |
Objectivity and Corotational Rate Tensor | 110 |
Elastic Constitutive Equations | 127 |
Basic Formulations for Elastoplastic Constitutive Equations | 134 |
Subloading Surface Model | 171 |
Extended Subloading Surface Model | 191 |
Constitutive Equations of Soils | 249 |
Corotational Rate Tensor | 309 |
Localization of Deformation | 326 |
Numerical Calculation | 337 |
Constitutive Equation for Friction | 349 |
Appendixes | 386 |
References | 395 |
407 | |
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Common terms and phrases
addition adopted analysis anisotropy assumed behavior calculated called Chapter components condition consider constitutive equation conventional curve cyclic loading defined deformation denoting derivative described deviatoric direction Drucker-Prager elastic element evolution rule Experiment expressed extended following equation formulation friction function Further given gradient hand hardening Hashiguchi holds homogeneous function incorporated independent induced infinitesimal initial isotropic hardening leads loading loading process material constant mechanical modulus normal normal-yield surface noting numerical obtained plane plastic strain rate positive predicted present principal quantity ratio relation respectively rotation rule scalar shear shown in Fig sliding sliding-yield soils stress rate subloading surface model Substituting Eq tangential tensor term test data theory traction transformation variables various vector yield surface σ σ σ