Nonlinear computational solid mechanics

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Bibliographic Details
Main Authors	Ghaboussi, J. (Author), Pecknold, D. A. W. (Author), Wu, Xiping, 1962- (Author)
Format	Electronic eBook
Language	English
Published	Boca Raton, FL : CRC Press, Taylor & Francis Group, [2017]
Subjects	Mechanics, Applied > Mathematics. Nonlinear mechanics > Matematics. Solids > Mathematical models. Materials > Mathematical models. elektronické knihy electronic books
Online Access	Full text
ISBN	9781498746137 1498746136 9781351682633 1351682636 9781523114221 1523114223 9781498746120 1498746128 9781315167329 1315167328
Physical Description	1 online resource (xvi, 378 pages)

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Table of Contents:

1.1. Linear computational mechanics
1.2. Nonlinear computational mechanics
1.3. Nonlinear behavior of simple structures
2.1. Motion and deformation of line elements
2.2. Deformation of volume and area elements
2.2.1. Volume elements
2.2.2. Area elements
2.3. Strains
2.3.1. Lagrangian (Green) strain
2.3.1.1. Interpretation of Green strain components
2.3.1.2. Diagonal components of Green strain
2.3.1.3. Off-diagonal components of Green strain
2.3.1.4. Simple shear
2.3.2. Eulerian (Almansi) strain
2.3.2.1. Uniaxial stretching
2.3.2.2. Uniaxial stretching and rigid body rotation
2.3.2.3. Relation between Green strain and Almansi strain
2.4. Objectivity and frame indifference
2.4.1. Objectivity of some deformation measures
2.4.1.1. Deformation gradient
2.4.1.2. Metric tensor
2.4.1.3. Strain tensors
2.5. Rates of deformation
2.5.1. Velocity and velocity gradient
2.5.2. Deformation and spin tensors.
2.5.3. Deformation gradient rates
2.5.4. Rate of deformation of a line element
2.5.5. Interpretation of deformation and spin tensors
2.5.6. Rate of change of a volume element
2.5.7. Rate of change of an area element
2.6. Strain rates
2.6.1. Lagrangian (Green) strain rate
2.6.2. Eulerian (Almansi) strain rate
2.7. Decomposition of motion
2.7.1. Polar decomposition
2.7.2. Polar decomposition of deformation gradient
2.7.3.Computation of polar decomposition
2.7.3.1. Right stretch tensor
2.7.3.2. Left stretch tensor
2.7.4. Strains
2.7.5. Strain and deformation rates
2.7.5.1. Green strain rate
2.7.5.2. Material rotation rate
2.7.6. Simple examples
2.7.6.1. Plate stretched and rotated
2.7.6.2. Simple shear
3.1. Traction vector on a surface
3.2. Cauchy stress principle
3.3. Cauchy stress tensor
3.4. Piola-Kirchhoff stress tensors
3.5. Stress rates
3.5.1. Material rates of stress.
3.5.2. Jaumann rate of Cauchy stress
3.5.3. Truesdell rate of Cauchy stress
3.S.4. Unrotated Cauchy stress and the Green-Naghdi rate
3.5.4.1. Unrotated Cauchy stress
3.5.4.2. Green-Naghdi rate
3.6. Examples of stress rates for simple stress conditions
3.6.1. Uniaxial extension of an initially stressed body
3.6.2. Rigid body rotation of an initially stressed body
3.6.3. Simple shear of an initially stressed body
3.6.3.1. Jaumann stress rate
3.6.3.2. Truesdell stress rate
4.1. Divergence theorem
4.2. Stress power
4.2.1.2PK stress power
4.2.2. Unrotated Cauchy stress power
4.3. Virtual work
4.4. Principle of virtual work
4.4.1. Internal virtual work
4.4.2. Lagrangian form of internal virtual work
4.5. Vector forms of stress and strain
5.1. Introduction
5.2. Linear elastic material models
5.3. Cauchy elastic material models
5.3.1. Characteristic polynomial of a matrix
5.3.2. Cayley-Hamilton theorem.
5.3.3. General polynomial form for isotropic Cauchy elastic materials
5.4. Hyperelastic material models
5.4.1. Strain energy density potential
5.4.2. Deformation invariants
5.4.3. Rubber and rubberlike materials
5.4.3.1. Ogden hyperelastic model
5.4.3.2. Balloon problem
5.4.4. Soft biological tissue
5.4.4.1. Fung exponential hyperelastic model
5.5. Hypoelastic material models
5.5.1. Hypoelastic grade zero
5.5.2. Hypoelastic grade one
5.5.3. Lagrangian versus hypoelastic material tangent stiffness
5.5.3.1. Truesdell stress rate
5.5.3.2. Jaumann stress rate
5.5.4.Comparison of linear isotropic hypoelastic models in simple shear
5.5.4.1. Truesdell rate hypoelastic model
5.5.4.2. Jaumann rate hypoelastic model
5.5.4.3. Green-Naghdi rate hypoelastic model
5.6. Numerical evaluation of a linear isotropic hypoelastic model
5.6.1. Natural coordinate system for triangle
5.6.2. Kinematics.
5.6.3. Nodal displacement patterns
5.6.4. Strain cycles
5.6.5. Calculation procedure
5.6.6. Numerical results
6.1. Introduction
6.2. Volumetric and deviatoric stresses and strains
6.3. Principal stresses and stress invariants
6.4. Alternative forms of stress invariants
6.5. Octahedral stresses
6.6. Principal stress space
6.7. Standard material tests and stress paths
6.7.1. Representations of stress paths
6.7.2. Uniaxial tests
6.7.2.1. Uniaxial tension
6.7.2.2. Uniaxial compression
6.7.3. Biaxial tests
6.7.4. Isotropic compression tests
6.7.5. Triaxial tests
6.7.6. True triaxial tests
6.7.6.1. Pure shear test
7.1. Introduction
7.2. Behavior of metals under uniaxial stress
7.2.1. Fundamental assumptions of classical plasticity theory
7.3. Inelastic behavior under multiaxial states of stress
7.3.1. Yield surface
7.4. Work and stability constraints
7.4.1. Work and energy
7.4.2. Stability in the small.
7.4.3.Complementary work
7.4.4.Net work
7.5. Associated plasticity models
7.5.1. Drucker's postulate
7.5.2. Convexity and normality
7.5.2.1. Normality of the plastic strain increment
7.5.2.2. Convexity of the yield surface
7.6. Incremental stress-Strain relations
7.6.1. Equivalent uniaxial stress and plastic strain
7.6.2. Loading and unloading criteria
7.6.3. Continuum tangent stiffness
7.6.4. Elastic-perfectly plastic behavior
7.6.5. Interpretation of incremental stresses
7.6.5.1. Elastic-perfectly plastic
7.6.5.2. Hardening plasticity
7.7. Yield surfaces in principal stress space
7.7.1. Material isotropy and symmetry requirements
7.7.2.von Mises yield surface
7.7.2.1. Biaxial (plane) stress
7.7.2.2. Tension-torsion test
7.7.3. Tresca yield surface
7.8. Hardening plasticity models
7.8.1. Determination of hardening parameter from uniaxial test
7.8.2. Isotropic hardening.
7.8.3. Kinematic hardening and back stress
7.8.4.Combined isotropic and kinematic hardening
7.9. Stress update
7.9.1.von Mises plasticity in simple shear problem
7.9.2. Stress update algorithm
7.9.2.1. Calculation of updated stress
7.9.2.2. Elastic trial stress at step (n + 1)
7.9.2.3. Stress correction
7.9.2.4. Elastoplastic response
7.10. Plasticity models for frictional and pressure-Sensitive materials
7.10.1. Mohr-Coulomb yield surface
7.10.2. Drucker-Prager yield surface
7.10.3. Model refinements
7.10.3.1. Cap models
7.10.3.2. Refined (q, theta) shape in octahedral plane
8.1. Introduction
8.2. Finite element discretization
8.2.1. Shape functions
8.2.1.1. Serendipity elements
8.2.1.2. Simplex elements
8.2.2. Isoparametric mapping
8.2.2.1. Numerical (Gaussian) quadrature
8.2.2.2. Shape function derivatives
8.3. Total Lagrangian formulation
8.3.1. Geometric nonlinearity
8.3.1.1. Green strain.
8.3.1.2. Green strain rate
8.3.1.3. Tangent stiffness matrix
8.3.2. Nonlinear material behavior
8.3.2.1. Elastoplastic material behavior
8.3.2.2. Consistent tangent stiffness
8.3.2.3.von Mises yield criterion
8.3.2.4. Discussion
8.3.2.5.2PK stress rate versus Green strain rate for TL formulation
8.3.3. Plane stress
8.3.3.1. Partial inversion and condensation of material stiffness
8.3.3.2. Nonlinear material properties
8.3.3.3. Expansion of strain increment and stress update
8.3.3.4. Condensed tangent stiffness and internal resisting force vector
8.3.4. Pressure loading
8.3.4.1. Load stiffness for 2D simplex element
8.3.4.2. Secant load stiffness
8.3.4.3. Tangent load stiffness
8.4. Updated Lagrangian methods
8.4.1. Basic UDL formulation
8.4.1.1. Virtual work in deformed configuration
8.4.1.2. Coordinate systems
8.4.1.3. Hughes-Winget incremental update
8.4.1.4. Element geometry updating
9.1. Introduction.
9.2. Finite rotations in three dimensions
9.2.1. Rotation matrix R
9.2.1.1. Euler's theorem
9.2.1.2. Rodrigues's formula
9.2.1.3. Extraction of the axial vector from R
9.2.1.4. Eigenstructure of the spin matrix
9.2.1.5. Matrix exponential
9.2.1.6. Exponential map
9.2.2. Cayley transform
9.2.3.Composition of finite rotations
9.2.3.1. Infinitesimal rotations
9.2.3.2. Two successive finite rotations
9.2.3.3. Update of finite nodal rotations
9.3. Element local coordinate systems
9.3.1. Euler angles
9.3.2. Orienting plate and shell elements in three dimensions
9.4. Corotational finite element formulation
9.4.1. Corotational coordinate systems
9.4.1.1. Notation
9.4.1.2. Element triads
9.4.1.3. Nodal triads
9.4.1.4. Nodal rotational freedoms
9.4.2. Incremental nodal degrees of freedom
9.4.2.1. Incremental nodal displacements
9.4.2.2. Incremental nodal rotations
9.4.3. Incremental variation of element frame.
9.4.4. Incremental variation of the nodal triad
9.4.4.1. Corotated incremental nodal rotations
9.4.5. Corotated incremental element freedoms combined
9.4.5.1. Geometric stiffness
9.4.5.2. Variation of LambdaTaui contracted with a nodal moment vector mi
9.4.5.3. Tangent stiffness summary
9.4.6. Discussion of a CR versus UDL formulation
10.1. Introduction
10.2. Modeling of shell structures
10.3.3D Structural element formulations
10.3.1. Kirchhoff beam, plate, and shell finite elements
10.3.1.1. Flat plate and shell elements
10.3.1.2. General form of geometric stiffness
10.3.1.3. Remarks
10.3.1.4. Synthesis of space frame stiffness matrices
10.3.1.5. Space frame geometric stiffness
10.3.1.6. Planar bending
10.3.1.7. Plane frame stiffness matrices
10.3.1.8. Remarks
10.3.1.9. Elastic tangent stiffness matrices
10.3.2. Mindlin plate theory
10.3.3. Degeneration of isoparametric solid elements.
10.3.4. Mindlin plate and flat shell finite elements
10.3.4.1. Bending stiffness
10.3.4.2. Shear stiffness
10.3.4.3. In-plane response
10.3.4.4. Geometric stiffness
10.3.4.5. Membrane stiffness
10.3.4.6. Performance of Mindlin elements
10.3.4.7. Shear locking, zero-energy modes, and hourglass control
10.3.4.8. Membrane locking
10.4. Isoparametric curved shell elements
10.4.1. Normal rotation in classic thin-shell theory
10.4.2. Isoparametric modeling of curved shell geometry
10.4.3. Nodal surface coordinate system
10.4.4. Jacobian matrix
10.4.5. Lamina Cartesian coordinate system
10.4.6. Summary of coordinate systems and transformations
10.4.7. Displacement interpolation
10.4.8. Approximations
10.4.9. Lamina kinematics
10.4.10. Lamina stresses
10.4.11. Virtual work density
10.4.12. Rotational freedoms
10.4.13.Comments on the UDL formulation
10.5. Nonlinear material behavior.
10.5.1. Through-thickness numerical integration
10.5.2. Layered models
11.1. Introduction
11.2. Pure incremental (Euler-Cauchy) method
11.3. Incremental method with equilibrium correction
11.4. Incremental-Iterative (Newton-Raphson) method
11.5. Modified Newton-Raphson method
11.6. Critical points on the equilibrium path
11.6.1. Characterization of critical points
11.6.2. Monitoring the incremental solution on the primary path
11.6.3. Determinant of the tangent stiffness
11.6.4. Current stiffness parameter
11.7. Arc-length solution methods
11.7.1. Crisfield's spherical method
11.7.2. Ramm's normal plane method
11.8. Lattice dome example
11.8.1. Load-deflection response of hexagonal dome
11.9. Secondary solution paths
11.10. Structural imperfections
11.10.1. Application to hexagonal dome example
12.1. Introduction
12.2. Multilayer neural networks
12.2.1. Training of neural networks.
12.3. Hard computing versus soft computing
12.4. Neural networks in material modeling
12.5. Nested adaptive neural networks
12.6. Neural network modeling of hysteretic behavior of materials
12.7. Acquisition of training data for neural network material models
12.8. Neural network material models in finite element analysis
12.9. Autoprogressive algorithm
12.9.1. Autoprogressive algorithm in modeling composite materials
12.9.2. Autoprogressive algorithm in structural mechanics and in geomechanics
12.9.3. Autoprogressive algorithm in biomedicine.

Nonlinear computational solid mechanics

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