Image from Coce

Nonlinear solid mechanics : theoretical formulations and finite element solution methods / Adnan Ibrahimbegovic.

By: Material type: TextTextLanguage: English Original language: French Series: Solid mechanics and its applications ; v. 160.Publisher: Dordrecht, Netherlands : Springer, 2009Description: xx, 574 pages : illustrations ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9048123305
  • 9789048123308
Uniform titles:
  • Mécanique non linéaire des solides déformables English.
Subject(s): DDC classification:
  • 510
LOC classification:
  • QA808.2
Contents:
1. Introduction -- 1.1. Motivation and objectives -- 1.2. Outline of the main topics -- 1.3. Further studies recommendations -- 1.4. Summary of main notations -- 2. Boundary value problem in linear and nonlinear elasticity -- 2.1. Boundary value problem in elasticity with small displacement gradients -- 2.1.1. Domain and boundary conditions -- 2.1.2. Strong form of boundary value problem in 1D elasticity -- 2.1.3. Weak from of boundary value problem in 1D elasticity and the principle of virtual work -- 2.1.4. Variational formulation of boundary value problem in 1D elasticity and principle of minimum potential energy -- 2.2. Finite element solution of boundary value problems in 1D linear and nonlinear elasticity -- 2.2.1. Qualitative methods of functional analysis for solution existence and uniqueness -- 2.2.2. Approximate solution construction by Galerkin, Ritz and finite element methods -- 2.2.3. Approximation error and convergence of finite element method -- 2.2.4. Solving a system of linear algebraic equations by Gauss elimination method -- 2.2.5. Solving a system of nonlinear algebraic equations by incremental analysis -- 2.2.6. Solving a system of nonlinear algebraic equations by Newton's iterative method -- 2.3. Implementation of finite element method in 1D boundary value problems -- 2.3.1. Local or elementary description -- 2.3.2. Consistence of finite element approximation -- 2.3.3. Equivalent nodal external load vector -- 2.3.4. Higher order finite elements -- 2.3.5. Role of numerical integration -- 2.3.6. Finite element assembly procedure -- 2.4. Boundary value problems in 2D and 3D elasticity -- 2.4. 1Tensor, index and matrix notations -- 2.4.2. Strong from of a boundary value problem in 2D and 3D elasticity -- 2.4.3. Weak form of boundary value problem in 2D and 3D elasticity -- 2.5. Detailed aspects of the finite element method -- 2.5.1. Isoparametric finite elements -- 2.5.2. Order of numerical integration -- 2.5.3. The patch test -- 2.5.4. Hu-Washizu (mixed) variational principle and method of incompatible modes -- 2.5.5. Hu-Washizu (mixed) variational principle and assumed strain method for quasi-incompressible behavior -- 3. Inelastic behavior at small strains -- 3.1. Boundary value problem in thermomechanics -- 3.1.1. Rigid conductor and heat equation -- 3.1.2. Numerical solution by time-integration scheme for heat transfer problem -- 3.1.3. Thermomechanical coupling in elasticity -- 3.1.4. Thermodynamics potentials in elasticity -- 3.1.5. Thermodynamics of inelastic behavior: constitutive models with internal variables -- 3.1.6. Internal variables in viscoelasticity -- 3.1.7. Internal variables in viscoelasticity -- 3.2. 1D models of perfect plasticity and plasticity with hardening -- 3.2.1. 1D perfect plasticity -- 3.2.2. 1D plasticity with isotropic hardening -- 3.2.3. Boundary value problem for 1D plasticity -- 3.3. 3D plasticity -- 3.3.1. Standard format of 3D plasticity model: Prandtl-Reuss equations -- 3.3.2. J2 plasticity model with von Mises plasticity criterion -- 3.3.3. Implicit backward Euler scheme and operator split for von Mises plasticity -- 3.3.4. Finite element numerical implementation in 3D plasticity -- 3.4. Refined models of 3D plasticity -- 3.4.1. Nonlinear isotropic hardening -- 3.4.2. Kinematic hardening -- 3.4.3. Plasticity model dependent on rate of deformation or viscoplasticity -- 3.4.4. Multi-surface plasticity criterion -- 3.4.5. Plasticity model with nonlinear elastic response -- 3.5. Damage models -- 3.5.1. 1D damage model -- 3.5.2. 3D damage model -- 3.5.3. Refinements of 3D damage model -- 3.5.4. Isotropic damage model of Kachanov -- 3.5.5. Numerical examples: damage model combining isotropic and multisurface criteria -- 3.6. Coupled plasticity-damage model -- 3.6.1. Theoretical formulation of 3D coupled model -- 3.6.2. Time integration of stress for coupled plasticity-damage model -- 3.6.3. Direct stress interpolation for coupled plasticity-damage model -- 4. Large displacements and deformations -- 4.1. Kinematics of large displacements -- 4.1.1. Motion in large displacements -- 4.1.2. Deformation gradient -- 4.1.3. Large deformation measures -- 4.2. Equilibrium equations in large displacements -- 4.2.1. Strong form of equilibrium equations -- 4.2.2. Weak form of equilibrium equations -- 4.3. Linear elastic behavior in large displacements: Saint-Venant-Kirchhoff material model -- 4.3.1. Weak form of Saint-Venant-Kirchhoff 3D elasticity model and its consistent linearization -- 4.4. Numerical implementation of finite element method in large displacements elasticity -- 4.4.1. 1D boundary value problem: elastic bar in large displacements -- 4.4.2. 2D plane elastic membrane in large displacements -- 4.5. Spatial description of elasticity in large displacements -- 4.5.1. Finite element approximation of spatial description of elasticity in large displacements -- 4.6. Mixed variational formulation in large displacements and discrete approximations -- 4.6.1. Mixed Hu-Washizu variational principle in large displacements and method of incompatible modes -- 4.6.2. Mixed Hu-Washizu variational principle in large displacements and assumed strain methods for quasi-incompressible behavior -- 4.7. Constitutive models for large strains -- 4.7.1. Invariance restrictions on elastic response -- 4.7.2. Constitutive laws for large deformations in terms of principal stretches -- 4.8. Plasticity and viscoplasticity for large deformations -- 4.8.1. Multiplicative decomposition of deformation gradient -- 4.8.2. Perfect plasticity for large deformations -- 4.8.3. Isotropic and kinematic hardening in large deformation plasticity -- 4.8.4. Spatial description of large deformation plasticity -- 4.8.5. Numerical implementation of large deformation plasticity --
5. Changing boundary conditions: contact problems -- 5.1. Unilateral 1D contact problem -- 5.1.1. Strong form of 1D elasticity in presence of unilateral contact constraint -- 5.1.2. Weak form of unilateral 1D contact problem and its finite element solution -- 5.2. Contact problems in 2D and 3D -- 5.2.1. Contact between two deformable bodies in 2D case -- 5.2.2. Mortar element method for contact -- 5.2.3. Numerical examples of contact problems -- 5.2.4. Refinement of contact model -- 6. Dynamics and time-integration schemes -- 6.1. Initial boundary value problem -- 6.1.1. Strong form of elastodynamics -- 6.1.2. Weak form of equations of motion -- 6.1.3. Finite element approximation for mass matrix -- 6.2. Time-integration schemes -- 6.2.1. Central difference (explicit) scheme -- 6.2.2. Trapezoidal rule or average acceleration (implicit) scheme -- 6.2.3. Mid-point (implicit) scheme and its modifications for energy conservation and energy dissipation -- 6.3. Mid-point (implicit) scheme for finite deformation plasticity -- 6.4. Contact problem and time-integration schemes -- 6.4.1. Mid-point (implicit) scheme for contact problem in dynamics -- 6.4.2. Central difference (explicit) scheme and impact problem -- 7. Thermodynamics and solution methods for coupled problems -- 7.1. Thermodynamics of reversible processes -- 7.1.1. Thermodynamical coupling in 1D elasticity -- 7.1.2. Thermodynamics coupling in 3D elasticity and constitutive relations -- 7.2. Initial-boundary value problem in thermoelasticity and operator split solution method -- 7.2.1. Weak form of initial-boundary value problem in 3D elasticity and its discrete approximation -- 7.2.2. Operator split solution method for 3D thermoelasticity -- 7.2.3. Numerical examples in thermoelasticity -- 7.3. Thermodynamics of irreversible processes -- 7.3.1. Thermodynamics coupling for 1D plasticity -- 7.3.2. Thermodynamics coupling in 3D plasticity -- 7.3.3. Operator split solution method for 3D thermoplasticity -- 7.3.4. Numerical example: thermodynamics coupling in 3D plasticity -- 7.4. Thermomechanical coupling in contact -- 8. Geometric and material instabilities -- 8.1. Geometric instabilities -- 8.1.1. Buckling, nonlinear instability and detection criteria -- 8.1.2. Solution methods for boundary value problem in presence of instabilities -- 8.2. Material instabilities -- 8.2.1. Detection criteria for material instabilities -- 8.2.2. Illustration of finite element mesh lack of objectivity for localization problems -- 8.3. Localization limiters -- 8.3.1. List of localization limiters -- 8.3.2. Localization limiter based on mesh-dependent softening modulus - 1D case -- 8.3.3. Localization limiter based on viscoplastic regularization - 1D case -- 8.3.4. Localization limiter based on displacement or deformation discontinuity - 1D case -- 8.4. Localization limiter in plasticity for massive structure -- 8.4.1. Theoretical formulation of limiter with displacement discontinuity - 2D /3D case -- 8.4.2. Numerical implementation within framework of incompatible mode method -- 8.4.3. Numerical examples for localization problems -- 8.5. Localization problem in large strain plasticity -- 9. Multi-scale modelling of inelastic behavior -- 9.1. Scale coupling for inelastic behavior in quasi-static problems -- 9.1.1. Weak coupling: nonlinear homogenization -- 9.1.2. Strong coupling micro-macro -- 9.2. Microstructure representation -- 9.2.1. Microstructure representation by structured mesh with isoparametric finite elements -- 9.2.2. Microstructure representation by structured mesh with incompatible mode elements -- 9.2.3. Microstructure representation with uncertain geometry and probabilistic interpretation of size effect for dominant failure mechanism -- 9.3. Conclusions and remarks on current research works.
Tags from this library: No tags from this library for this title. Log in to add tags.

Includes bibliographical references (pages 557-569) and index.

1. Introduction -- 1.1. Motivation and objectives -- 1.2. Outline of the main topics -- 1.3. Further studies recommendations -- 1.4. Summary of main notations -- 2. Boundary value problem in linear and nonlinear elasticity -- 2.1. Boundary value problem in elasticity with small displacement gradients -- 2.1.1. Domain and boundary conditions -- 2.1.2. Strong form of boundary value problem in 1D elasticity -- 2.1.3. Weak from of boundary value problem in 1D elasticity and the principle of virtual work -- 2.1.4. Variational formulation of boundary value problem in 1D elasticity and principle of minimum potential energy -- 2.2. Finite element solution of boundary value problems in 1D linear and nonlinear elasticity -- 2.2.1. Qualitative methods of functional analysis for solution existence and uniqueness -- 2.2.2. Approximate solution construction by Galerkin, Ritz and finite element methods -- 2.2.3. Approximation error and convergence of finite element method -- 2.2.4. Solving a system of linear algebraic equations by Gauss elimination method -- 2.2.5. Solving a system of nonlinear algebraic equations by incremental analysis -- 2.2.6. Solving a system of nonlinear algebraic equations by Newton's iterative method -- 2.3. Implementation of finite element method in 1D boundary value problems -- 2.3.1. Local or elementary description -- 2.3.2. Consistence of finite element approximation -- 2.3.3. Equivalent nodal external load vector -- 2.3.4. Higher order finite elements -- 2.3.5. Role of numerical integration -- 2.3.6. Finite element assembly procedure -- 2.4. Boundary value problems in 2D and 3D elasticity -- 2.4. 1Tensor, index and matrix notations -- 2.4.2. Strong from of a boundary value problem in 2D and 3D elasticity -- 2.4.3. Weak form of boundary value problem in 2D and 3D elasticity -- 2.5. Detailed aspects of the finite element method -- 2.5.1. Isoparametric finite elements -- 2.5.2. Order of numerical integration -- 2.5.3. The patch test -- 2.5.4. Hu-Washizu (mixed) variational principle and method of incompatible modes -- 2.5.5. Hu-Washizu (mixed) variational principle and assumed strain method for quasi-incompressible behavior -- 3. Inelastic behavior at small strains -- 3.1. Boundary value problem in thermomechanics -- 3.1.1. Rigid conductor and heat equation -- 3.1.2. Numerical solution by time-integration scheme for heat transfer problem -- 3.1.3. Thermomechanical coupling in elasticity -- 3.1.4. Thermodynamics potentials in elasticity -- 3.1.5. Thermodynamics of inelastic behavior: constitutive models with internal variables -- 3.1.6. Internal variables in viscoelasticity -- 3.1.7. Internal variables in viscoelasticity -- 3.2. 1D models of perfect plasticity and plasticity with hardening -- 3.2.1. 1D perfect plasticity -- 3.2.2. 1D plasticity with isotropic hardening -- 3.2.3. Boundary value problem for 1D plasticity -- 3.3. 3D plasticity -- 3.3.1. Standard format of 3D plasticity model: Prandtl-Reuss equations -- 3.3.2. J2 plasticity model with von Mises plasticity criterion -- 3.3.3. Implicit backward Euler scheme and operator split for von Mises plasticity -- 3.3.4. Finite element numerical implementation in 3D plasticity -- 3.4. Refined models of 3D plasticity -- 3.4.1. Nonlinear isotropic hardening -- 3.4.2. Kinematic hardening -- 3.4.3. Plasticity model dependent on rate of deformation or viscoplasticity -- 3.4.4. Multi-surface plasticity criterion -- 3.4.5. Plasticity model with nonlinear elastic response -- 3.5. Damage models -- 3.5.1. 1D damage model -- 3.5.2. 3D damage model -- 3.5.3. Refinements of 3D damage model -- 3.5.4. Isotropic damage model of Kachanov -- 3.5.5. Numerical examples: damage model combining isotropic and multisurface criteria -- 3.6. Coupled plasticity-damage model -- 3.6.1. Theoretical formulation of 3D coupled model -- 3.6.2. Time integration of stress for coupled plasticity-damage model -- 3.6.3. Direct stress interpolation for coupled plasticity-damage model -- 4. Large displacements and deformations -- 4.1. Kinematics of large displacements -- 4.1.1. Motion in large displacements -- 4.1.2. Deformation gradient -- 4.1.3. Large deformation measures -- 4.2. Equilibrium equations in large displacements -- 4.2.1. Strong form of equilibrium equations -- 4.2.2. Weak form of equilibrium equations -- 4.3. Linear elastic behavior in large displacements: Saint-Venant-Kirchhoff material model -- 4.3.1. Weak form of Saint-Venant-Kirchhoff 3D elasticity model and its consistent linearization -- 4.4. Numerical implementation of finite element method in large displacements elasticity -- 4.4.1. 1D boundary value problem: elastic bar in large displacements -- 4.4.2. 2D plane elastic membrane in large displacements -- 4.5. Spatial description of elasticity in large displacements -- 4.5.1. Finite element approximation of spatial description of elasticity in large displacements -- 4.6. Mixed variational formulation in large displacements and discrete approximations -- 4.6.1. Mixed Hu-Washizu variational principle in large displacements and method of incompatible modes -- 4.6.2. Mixed Hu-Washizu variational principle in large displacements and assumed strain methods for quasi-incompressible behavior -- 4.7. Constitutive models for large strains -- 4.7.1. Invariance restrictions on elastic response -- 4.7.2. Constitutive laws for large deformations in terms of principal stretches -- 4.8. Plasticity and viscoplasticity for large deformations -- 4.8.1. Multiplicative decomposition of deformation gradient -- 4.8.2. Perfect plasticity for large deformations -- 4.8.3. Isotropic and kinematic hardening in large deformation plasticity -- 4.8.4. Spatial description of large deformation plasticity -- 4.8.5. Numerical implementation of large deformation plasticity --

5. Changing boundary conditions: contact problems -- 5.1. Unilateral 1D contact problem -- 5.1.1. Strong form of 1D elasticity in presence of unilateral contact constraint -- 5.1.2. Weak form of unilateral 1D contact problem and its finite element solution -- 5.2. Contact problems in 2D and 3D -- 5.2.1. Contact between two deformable bodies in 2D case -- 5.2.2. Mortar element method for contact -- 5.2.3. Numerical examples of contact problems -- 5.2.4. Refinement of contact model -- 6. Dynamics and time-integration schemes -- 6.1. Initial boundary value problem -- 6.1.1. Strong form of elastodynamics -- 6.1.2. Weak form of equations of motion -- 6.1.3. Finite element approximation for mass matrix -- 6.2. Time-integration schemes -- 6.2.1. Central difference (explicit) scheme -- 6.2.2. Trapezoidal rule or average acceleration (implicit) scheme -- 6.2.3. Mid-point (implicit) scheme and its modifications for energy conservation and energy dissipation -- 6.3. Mid-point (implicit) scheme for finite deformation plasticity -- 6.4. Contact problem and time-integration schemes -- 6.4.1. Mid-point (implicit) scheme for contact problem in dynamics -- 6.4.2. Central difference (explicit) scheme and impact problem -- 7. Thermodynamics and solution methods for coupled problems -- 7.1. Thermodynamics of reversible processes -- 7.1.1. Thermodynamical coupling in 1D elasticity -- 7.1.2. Thermodynamics coupling in 3D elasticity and constitutive relations -- 7.2. Initial-boundary value problem in thermoelasticity and operator split solution method -- 7.2.1. Weak form of initial-boundary value problem in 3D elasticity and its discrete approximation -- 7.2.2. Operator split solution method for 3D thermoelasticity -- 7.2.3. Numerical examples in thermoelasticity -- 7.3. Thermodynamics of irreversible processes -- 7.3.1. Thermodynamics coupling for 1D plasticity -- 7.3.2. Thermodynamics coupling in 3D plasticity -- 7.3.3. Operator split solution method for 3D thermoplasticity -- 7.3.4. Numerical example: thermodynamics coupling in 3D plasticity -- 7.4. Thermomechanical coupling in contact -- 8. Geometric and material instabilities -- 8.1. Geometric instabilities -- 8.1.1. Buckling, nonlinear instability and detection criteria -- 8.1.2. Solution methods for boundary value problem in presence of instabilities -- 8.2. Material instabilities -- 8.2.1. Detection criteria for material instabilities -- 8.2.2. Illustration of finite element mesh lack of objectivity for localization problems -- 8.3. Localization limiters -- 8.3.1. List of localization limiters -- 8.3.2. Localization limiter based on mesh-dependent softening modulus - 1D case -- 8.3.3. Localization limiter based on viscoplastic regularization - 1D case -- 8.3.4. Localization limiter based on displacement or deformation discontinuity - 1D case -- 8.4. Localization limiter in plasticity for massive structure -- 8.4.1. Theoretical formulation of limiter with displacement discontinuity - 2D /3D case -- 8.4.2. Numerical implementation within framework of incompatible mode method -- 8.4.3. Numerical examples for localization problems -- 8.5. Localization problem in large strain plasticity -- 9. Multi-scale modelling of inelastic behavior -- 9.1. Scale coupling for inelastic behavior in quasi-static problems -- 9.1.1. Weak coupling: nonlinear homogenization -- 9.1.2. Strong coupling micro-macro -- 9.2. Microstructure representation -- 9.2.1. Microstructure representation by structured mesh with isoparametric finite elements -- 9.2.2. Microstructure representation by structured mesh with incompatible mode elements -- 9.2.3. Microstructure representation with uncertain geometry and probabilistic interpretation of size effect for dominant failure mechanism -- 9.3. Conclusions and remarks on current research works.

Machine converted from AACR2 source record.

There are no comments on this title.

to post a comment.

Powered by Koha