TY  - BOOK
AU  - Ibrahimbegović,Adnan
TI  - Nonlinear solid mechanics: theoretical formulations and finite element solution methods 
T2  - Solid mechanics and its applications
SN  - 9048123305
AV  - QA808.2 
U1  - 510 
PY  - 2009///
CY  - Dordrecht, Netherlands
PB  - Springer
KW  - Nonlinear mechanics
KW  - Finite element method
KW  - Structural analysis (Engineering)
N1  - 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
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