Borja R.I. Plasticity: Modeling & Computation

Springer-Verlag Berlin Heidelberg, 2013. X, 255 p. — ISBN: 978-3-642-38546-9, ISBN: 978-3-642-38547-6 (eBook), DOI 10.1007/978-3-642-38547-6.There have been many excellent books written on the subject of plastic deformation in solids, but rarely can one find a textbook on this subject. Plasticity Modeling & Computation is a textbook written specifically for students who want to learn the theoretical, mathematical, and computational aspects of inelastic deformation in solids. It adopts a simple narrative style that is not mathematically overbearing, and has been written to emulate a professor giving a lecture on this subject inside a classroom. Each section is written to provide a balance between the relevant equations and the explanations behind them. Where relevant, sections end with one or more exercises designed to reinforce the understanding of the lecture. Color figures enhance the presentation and make the book very pleasant to read. For professors planning to use this textbook for their classes, the contents are sufficient for Parts A and B that can be taught in sequence over a period of two semesters or quarters.Motivations and ScopeProblem Statement
Finite Element Equations
Newton’s Method
The Line Search
Preconditioned Conjugate Gradients
Solved ProblemOne-Dimensional ProblemElastoplastic Problemin One Dimension
Yield Function, Flow Rule, and Hardening/Softening
Loading/Unloading and Consistency Conditions
Isotropic and Kinematic Hardening
Energy and Plastic Dissipation
Some Propertiesof the Yield Function
Algorithmfor Isotropic Hardening
Algorithm for Kinematic Hardening
Algorithm for Nonlinear Hardening
Uniqueness of Solution
Solved ProblemJ2 PlasticityThe J2 Yield Criterion
Perfect Plasticity
Radial Return Algorithm
Isotropic Hardening
Combined Isotropic-Kinematic Hardening
Algorithm for Combined Hardening
Algorithmic Tangent Operator
Maximum Plastic Dissipation
Non-associative Plasticity
Numerical SimulationsIsotropic FunctionsSpectral Representation
Spinof a Tensor
Constitutive Operators in Spectral Form
Lode’s Angle
The Mohr-Coulomb Yield Criterion
Smooth Approximations of th eMCYield Surface
Pressure-Dependent FrictionAngle
Flow Rule and Plastic Dilatancy
Cohesion and Friction Hardening
Return Mappingin Principa lAxes
Algorithmic Tangent Operator
Return Mappingin Invariant Space
Numerical ExampleFinite DeformationBasic Kinematics
Spectral Representation
Stress Tensors
Objectivity and Isotropy
Multiplicative Plasticity: Kinematics
FreeEnergy, YieldFunction, and Plastic Flow Evolution
Elastoplastic Tangent Operator
Momentum Balance and Weak Form
Stress-PointIntegration
Algorithmic Tangent OperatorCap ModelsInfinitesimal Strain Hyperelasticity
Critical State Theory
Hyperelastic Law for MCC Model
Three-Invariant Formulation
Derivatives of Lode’s Angle
APlasticity Model for Sand
APlasticity Model for Concrete
Return Mappingin Strain Space
Finite Deformation
Plane Strain Compression of a SandDiscontinuitiesContact with Cohesion andF riction
Lagrange Multipliers Method
Penalty and Augmented Lagrangian Methods
Enriched Finite Elements
Extended Finite Element Method
Stabilized Formulation
Strong Discontinuity
Assumed Enhanced Strain Method
Crack Tip Enrichment
Slip WeakeningCrysta lPlasticityKinematics of Crystal Slip
Constitutive Framework
Ultimate Algorithm
Uniqueness of Crystal Stress
Large Deformation
Multiscale Fields
Discrete Formulation
Stress-PointIntegration
Multislip Systems
Twisting and Stretching of a Hollow CylinderBifurcationStability of Incrementally Linear Solids
Stability of Elastoplastic Solids
DeformationBands
SpectralRepresentation
E-modes
Finite Deformation Bifurcation
Persistent Shear Band