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.
Holdings
Item type Current library Call number Copy number Status Date due Barcode
Book City Campus City Campus Main Collection 510 IBR (Browse shelf(Opens below)) 1 Available A457019B

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