Front Cover -- Gradient-Enhanced Continuum Plasticity -- Copyright Page -- Dedication -- Contents -- About the authors -- Preface -- 1 Introduction -- References -- 2 Review of experimental observations on the gradient-enhanced continuum plasticity -- 2.1 Uniaxial tests -- 2.2 Bending tests -- 2.3 Torsion tests -- 2.4 Indentation tests -- 2.5 Bulge tests of thin film -- 2.6 Shear tests -- References -- 3 Review of theoretical developments on the gradient-enhanced continuum plasticity -- 3.1 Aifantis theory -- 3.2 Fleck and Hutchinson theory

3.2.1 Strain gradient plasticity version of J2 deformation theory -- 3.2.2 Strain gradient plasticity version of the J2 flow theory -- 3.3 Gudmundson, Gurtin and Anand theory -- 3.3.1 Irrotational plastic flow -- 3.3.2 Rotational plastic flow -- 3.4 Implicit gradient plasticity theory -- 3.5 Micromorphic approach -- 3.6 Mechanism-based strain gradient plasticity theory -- 3.7 Voyiadjis theory -- 3.8 Other types of theories -- References -- 4 Review of numerical approaches using the gradient-enhanced continuum plasticity -- 4.1 Aifantis theory -- 4.2 Fleck and Hutchinson theory

4.3 Gudmundson, Gurtin, and Anand theory -- 4.3.1 Irrotational plastic flow -- 4.3.2 Rotational plastic flow -- 4.4 Implicit gradient plasticity theory -- 4.5 Micromorphic approach -- 4.6 Mechanism-based strain gradient plasticity theory -- 4.7 Voyiadjis theory -- 4.8 Other types of theories -- References -- 5 Lower-order strain gradient plasticity theory with variable length scales -- 5.1 Gradient plasticity theories -- 5.2 Physical bases -- 5.3 Applications -- 5.3.1 Microbending of thin films -- 5.3.2 Microtorsion of thin wires -- 5.4 Comparing with experiments

5.5 A nonfixed material length scale -- References -- 6 Gradient-enhanced continuum plasticity for small deformations -- 6.1 Background -- 6.2 Kinematics -- 6.3 Grain interior -- 6.3.1 Principle of virtual power -- 6.3.2 Laws of thermodynamics -- 6.3.3 Energetic and dissipative constitutive equations -- 6.3.4 Free energy and energetic thermodynamic microforces -- 6.3.5 Dissipation potential and dissipative thermodynamic microforces -- 6.3.6 Flow rule -- 6.3.7 Thermodynamic derivations of the heat evolution equation -- 6.4 Grain boundary -- 6.4.1 Principle of virtual power

6.4.2 Energetic and dissipative constitutive equations -- 6.4.3 Free energy and energetic thermodynamic microforces -- 6.4.4 Dissipation potential and dissipative thermodynamic microforce -- 6.4.5 Flow rule -- 6.5 Finite element formulation for the proposed model -- 6.6 Validation of the proposed model -- 6.6.1 Uniaxial tensile test with aluminum thin films -- 6.6.2 Biaxial bulge test with copper thin films -- 6.6.3 Microtensile test with nickel thin films -- 6.7 Simple shear problem -- 6.7.1 Energetic gradient hardening -- 6.7.2 Dissipative gradient strengthening