Preface |
Principle of Mathematical Notations |
Elements of Continuum Mechanics and Thermodynamics / Chapter 1: |
Elements of kinematics and dynamics of materially simple continua / 1.1: |
Homogeneous transformation and gradient of transformation / 1.1.1: |
Homogeneous transformation / 1.1.1.1: |
Gradient of transformation and its inverse / 1.1.1.2: |
Polar decomposition of the transformation gradient / 1.1.1.3: |
Transformation of elementary vectors, surfaces and volumes / 1.1.2: |
Transformation of an elementary vector / 1.1.2.1: |
Transformation of an elementary volume: the volume dilatation / 1.1.2.2: |
Transformation of an oriented elementary surface / 1.1.2.3: |
Various definitions of stretch, strain and strain rates / 1.1.3: |
On some definitions of stretches / 1.1.3.1: |
On some definitions of the strain tensors / 1.1.3.2: |
Strain rates and rotation rates (spin) tensors / 1.1.3.3: |
Volumic dilatation rate, relative extension rate and angular sliding rate / 1.1.3.4: |
Various stress measures / 1.1.4: |
Conjugate strain and stress measures / 1.1.5: |
Change of referential or configuration and the concept of objectivity / 1.1.6: |
Impact on strain and strain rates / 1.1.6.1: |
Impact on stress and stress rates / 1.1.6.2: |
Impact on the constitutive equations / 1.1.6.3: |
Strain decomposition into reversible and irreversible parts / 1.1.7: |
On the conservation laws for the materially simple continua / 1.2: |
Conservation of mass: continuity equation / 1.2.1: |
Principle of virtual power: balance equations / 1.2.2: |
Energy conservation. First law of thermodynamics / 1.2.3: |
Inequality of the entropy. Second law of thermodynamics / 1.2.4: |
Fundamental inequalities of thermodynamics / 1.2.5: |
Heat equation deducted from energy balance / 1.2.6: |
Materially simple continuum thermodynamics and the necessity of constitutive equations / 1.3: |
Necessity of constitutive equations / 1.3.1: |
Some fundamental properties of constitutive equations / 1.3.2: |
Principle of determinism or causality axiom / 1.3.2.1: |
Principle of local action / 1.3.2.2: |
Principle of objectivity or material indifference / 1.3.2.3: |
Principle of material symmetry / 1.3.2.4: |
Principle of consistency / 1.3.2.5: |
Thermodynamic admissibility / 1.3.2.6: |
Thermodynamics of irreversible processes. The local state method / 1.3.3: |
A presentation of the local state method / 1.3.3.1: |
Internal constraints / 1.3.3.2: |
Mechanics of generalized continua. Micromorphic theory / 1.4: |
Principle of virtual power for micromorphic continua / 1.4.1: |
Thermodynamics of micromorphic continua / 1.4.2: |
Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage / Chapter 2: |
On the main schemes for modeling the behavior of materially simple continuous media / 2.1: |
Behavior and fracture of metals and alloys: some physical and phenomenological aspects / 2.2: |
On the microstructure of metals and alloys / 2.2.1: |
Phenomenology of the thermomechanical behavior of polycrystals / 2.2.2: |
Linear elastic behavior / 2.2.2.1: |
Inelastic behavior / 2.2.2.2: |
Inelastic behavior sensitive to the loading rate / 2.2.2.3: |
Initial and induced anisotropies / 2.2.2.4: |
Other phenomena linked to the shape of the loading paths / 2.2.2.5: |
Phenomenology of the inelastic fracture of metals and alloys / 2.2.3: |
Micro-defects nucleation / 2.2.3.1: |
Micro-defects growth / 2.2.3.2: |
Micro-defects coalescence and final fracture of the RVE / 2.2.3.3: |
A first definition of the damage variable / 2.2.3.4: |
From ductile damage at a material point to the total fracture of a structure by propagation of macroscopic cracks / 2.2.3.5: |
Summary of the principal phenomena to be modeled / 2.2.4: |
Theoretical framework of modeling and main hypotheses / 2.3: |
The main kinematic hypotheses / 2.3.1: |
Choice of kinematics and compliance with the principle of objectivity / 2.3.1.1: |
Decomposition of strain rates / 2.3.1.2: |
On some rotating frame choices / 2.3.1.3: |
Implementation of the local state method and main mechanical hypotheses / 2.3.2: |
Choice of state variables associated with phenomena being modeled / 2.3.2.1: |
Definition of effective variables: damage effect functions / 2.3.2.2: |
State potential: state relations / 2.4: |
State potential in case of damage anisotropy / 2.4.1: |
Formulation in strain space: Helmholtz free energy / 2.4.1.1: |
Formulation in stress space: Gibbs free enthalpy / 2.4.1.2: |
State potential in the case of damage isotropy / 2.4.2: |
Microcracks closure: quasi-unilateral effect / 2.4.2.1: |
Concept of micro-defect closure: deactivation of damage effects / 2.4.3.1: |
State potential with quasi-unilateral effect / 2.4.3.2: |
Dissipation analysis: evolution equations / 2.5: |
Thermal dissipation analysis: generalized heat equation / 2.5.1: |
Heat flux vector: Fourier linear conduction model / 2.5.1.1: |
Generalized heat equation / 2.5.1.2: |
Intrinsic dissipation analysis: case of time-independent plasticity / 2.5.2: |
Damageable plastic dissipation: anisotropic damage with two yield surfaces / 2.5.2.1: |
Damageable plastic dissipation: anisotropic damage with a single yield surface / 2.5.2.2: |
Incompressible and damageable plastic dissipation: isotropic damage with two yield surfaces / 2.5.2.3: |
Incompressible and damageable plastic dissipation: single yield surface / 2.5.2.4: |
Intrinsic dissipation analysis: time-dependent plasticity or viscoplasticity / 2.5.3: |
Damageable viscoplastic dissipation without restoration: anisotropic damage with two viscoplastic potentials / 2.5.3.1: |
Viscoplastic dissipation with damage: isotropic damage with a single viscoplastic potential and restoration / 2.5.3.2: |
Some remarks on the choice of rotating frames / 2.5.4: |
Modeling some specific effects linked to metallic material behavior / 2.5.5: |
Effects on non-proportional loading paths on strain hardening evolution / 2.5.5.1: |
Strain hardening memory effects / 2.5.5.2: |
Cumulative strains or ratchet effect / 2.5.5.3: |
Yield surface and/or inelastic potential distortion / 2.5.5.4: |
Viscosity-hardening coupling: the Piobert-Lüders peak / 2.5.5.5: |
Accounting for the material microstructure / 2.5.5.6: |
Some specific effects on ductile fracture / 2.5.5.7: |
Modeling of the damage-induced volume variation / 2.6: |
On the compressibility induced by isotropic ductile damage / 2.6.1: |
Concept of volume damage / 2.6.1.1: |
State coupling and state relations / 2.6.1.2: |
Dissipation coupling and evolution equations / 2.6.1.3: |
Modeling of the contact and friction between deformable solids / 2.7: |
Kinematics and contact conditions between solids / 2.7.1: |
Impenetrability condition / 2.7.1.1: |
Equilibrium condition of contact interface / 2.7.1.2: |
Contact surface non-adhesion condition / 2.7.1.3: |
Contact unilaterality condition / 2.7.1.4: |
On the modeling of friction between solids in contact / 2.7.2: |
Time-independent friction model / 2.7.2.1: |
Nonlocal modeling of damageable behavior of micromorphic continua / 2.8: |
Principle of virtual power for a micromorphic medium: balance equations / 2.8.1: |
State potential and state relations for a micromorphic solid / 2.8.2: |
Dissipation analysis: evolution equations for a micromorphic solid / 2.8.3: |
Continuous tangent operators and thermodynamic admissibility for a micromorphic solid / 2.8.4: |
Transformation of micromorphic balance equations / 2.8.5: |
On the micro-macro modeling of inelastic flow with ductile damage / 2.9: |
Principle of the proposed meso-macro modeling scheme / 2.9.1: |
Definition of the initial RVE / 2.9.2: |
Localization stages / 2.9.3: |
Constitutive equations at different scales / 2.9.4: |
State potential and state relations / 2.9.4.1: |
Intrinsic dissipation analysis: evolution equations / 2.9.4.2: |
Homogenization and the mean values of fields at the aggregate scale / 2.9.5: |
Summary of the meso-macro polycrystalline model / 2.9.6: |
Numerical Methods for Solving Metal Forming Problems / Chapter 3: |
Initial and boundary value problem associated with virtual metal forming processes / 3.1: |
Strong forms of the initial and boundary value problem / 3.1.1: |
Posting a fully coupled problem / 3.1.1.1: |
Some remarks on thermal conditions at contact interfaces / 3.1.1.2: |
Weak forms of the initial and boundary value problem / 3.1.2: |
On the various weak forms of the IBVP / 3.1.2.1: |
Weak form associated with equilibrium equations / 3.1.2.2: |
Weak form associated with heat equation / 3.1.2.3: |
Weak form associated with micromorphic damage balance equation / 3.1.2.4: |
Summary of the fully coupled evolution problem / 3.1.2.5: |
Temporal and spatial discretization of the IBVP / 3.2: |
Time discretization of the IBVP / 3.2.1: |
Spatial discretization of the IBVP by finite elements / 3.2.2: |
Spatial semi-discretization of the weak forms of the IBVP / 3.2.2.1: |
Examples of isoparametric finite elements / 3.2.2.2: |
On some global resolution scheme of the IBVP / 3.3: |
Implicit static global resolution scheme / 3.3.1: |
Newton-Raphson scheme for the solution of the fully coupled IBVP / 3.3.1.1: |
On some convergence criteria / 3.3.1.2: |
Calculation of the various terms of the tangent matrix / 3.3.1.3: |
The purely mechanical consistent Jacobian matrix / 3.3.1.4: |
Implicit global resolution scheme of the coupled IBVP / 3.3.1.5: |
Dynamic explicit global resolution scheme / 3.3.2: |
Solution of the mechanical problem / 3.3.2.1: |
Solution of thermal (parabolic) problem / 3.3.2.2: |
Solution of micromorphic damage problem / 3.3.2.3: |
Sequential scheme of explicit global resolution of the IBVP / 3.3.2.4: |
Numerical handling of contact-friction conditions / 3.3.3: |
Lagrange multiplier method / 3.3.3.1: |
Penalty method / 3.3.3.2: |
On the search for contact nodes / 3.3.3.3: |
On the numerical handling of the incompressibility condition / 3.3.3.4: |
Local integration scheme: state variables computation / 3.4: |
On numerical integration using the Gauss method / 3.4.1: |
Local integration of constitutive equations: computation of the stress tensor and the state variables / 3.4.2: |
On the numerical integration of first-order ODEs / 3.4.2.1: |
Choice of constitutive equations to integrate / 3.4.2.2: |
Integration of time-independent plastic constitutive equations: the case of a von Mises isotropic yield criterion / 3.4.2.3: |
Integration of time-independent plastic constitutive equations: the case of a Hill quadratic anisotropic yield criterion / 3.4.2.4: |
Integration of the constitutive equation in the case of viscoplastic flow / 3.4.2.5: |
Calculation of the rotation tensor: incremental objectivity / 3.4.2.6: |
Remarks on the integration of the micromorphic damage equation / 3.4.2.7: |
On the local integration of friction equations / 3.4.3: |
Adaptive analysis of damageable elasto-inelastic structures / 3.5: |
Adaptation of time steps / 3.5.1: |
Adaptation of spatial discretization or mesh adaptation / 3.5.2: |
On other spatial discretization methods / 3.6: |
An outline of non-mesh methods / 3.6.1: |
On the FEM-meshless methods coupling / 3.6.2: |
Application to Virtual Metal Forming / Chapter 4: |
Why use virtual metal forming? / 4.1: |
Model identification methodology / 4.2: |
Parametrical study of specific models / 4.2.1: |
Choosing typical constitutive equations / 4.2.1.1: |
Isothermal uniaxial tension (compression) load without damage / 4.2.1.2: |
Accounting for ductile damage effect / 4.2.1.3: |
Accounting for initial anisotropy in inelastic flow / 4.2.1.4: |
Identification methodologies / 4.2.2: |
Some general remarks on the issue of identification / 4.2.2.1: |
Recommended identification methodology / 4.2.2.2: |
Illustration of the identification methodology / 4.2.2.3: |
Using a nonlocal model / 4.2.2.4: |
Some applications / 4.3: |
Sheet metal forming / 4.3.1: |
Some deep drawing processes of thin sheets / 4.3.1.1: |
Some hydro-bulging test of thin sheets and tubes / 4.3.1.2: |
Cutting processes of thin sheets / 4.3.1.3: |
Bulk metal forming processes / 4.3.2: |
Classical bulk metal forming processes / 4.3.2.1: |
Bulk metal forming processes under severe conditions / 4.3.2.2: |
Toward the optimization of forming and machining processes / 4.4: |
Appendix: Legendre-Fenchel Transformation |
Bibliography |
Index |