Nonlinear finite elements for continua and structures / Ted Belytschko, Wing Kam Liu, Brian Moran, Khalil I. Elkhodary.

Includes bibliographical references and index.

Introduction -- Nonlinear finite elements in design -- Related books and a brief history of nonlinear finite elements -- Notation -- Mesh descriptions -- Classification of partial differential equations -- Exercises -- Lagrangian and Eulerian finite elements in one dimension -- Introduction -- Governing equations for total Lagrangian formulation -- Weak form for total Lagrangian formulation -- Finite element discretization in total Lagrangian formulation -- Element and global matrices -- Governing equations for updated Lagrangian formulation -- Weak form for updated Lagrangian formulation -- Element equations for updated Lagrangian formulation -- Governing equations for Eulerian formulation -- Weak forms for Eulerian mesh equations -- Finite element equations -- Solution methods -- Summary -- Exercises -- Continuum mechanics -- Introduction -- Deformation and motion -- Strain measures -- Stress measures -- Conservation equations -- Lagrangian. conservation equations -- Polar decomposition and frame-invariance -- Exercises -- Lagrangian meshes -- Introduction -- Governing equations -- Weak form: principle of virtual power -- Updated Lagrangian finite element discretization -- Implementation -- Corotational formulations -- Total Lagrangian formulation -- Total Lagrangian weak form -- Finite element semidiscretization -- Exercise -- Constitutive models -- Introduction -- The stress-strain curve -- One-dimensional elasticity -- Nonlinear elasticity -- One-dimensional plasticity -- Multiaxial plasticity -- Hyperelastic-plastic models -- Viscoelasticity -- Stress update algorithms -- Continuum mechanics and constitutive models -- Exercises -- Solution methods and stability -- Introduction -- Explicit methods -- Equilibrium solutions and implicit time integration -- Linearization -- Stability and continuation methods -- Numerical stability -- Material stability -- Exercises -- Arbitrary Lagrangian Eulerian formulations -- Introduction -- ALE continuum mechanics -- Conservation laws in ALE description -- ALE governing equations -- Weak forms -- Introduction to the Petrov-Galerkin method -- Petrov-Galerkin formulation of momentum equation -- Path-dependent materials -- Linearization of the discrete equations -- Mesh update equations -- Numerical example: an elastic-plastic wave propagation problem -- Total ALE formulations -- Element technology -- Introduction -- Element performance -- Element properties and patch tests -- Q4 and volumetric locking -- Multi-field weak forms and elements -- Multi-field quadrilaterals -- One-point quadrature elements -- Examples -- Stability -- Exercises -- Beams and shells -- Introduction -- Beam theories -- Continuum-based beam -- Analysis of CB beam -- Continuum-based shell implementation -- CB shell theory -- Shear and membrane locking -- Assumed strain elements -- One-point quadrature elements -- Exercises -- Contact-impact -- Introduction -- Contact interface equations -- Friction models -- Weak forms -- Finite element discretization -- On explicit methods -- XFEM -- INTRODUCTION -- PARTITION OF UNITY AND ENRICHMENTS -- ONE DIMENSIONAL XFEM -- MULTI-DIMENSION XFEM -- WEAK AND STRONG FORMS -- DISCRETE EQUATIONS -- LEVEL SET METHOD -- XFEM IMPLEMENTATION STRATEGY -- INTEGRATION -- AN EXAMPLE OF XFEM SIMULATION -- EXERCISE -- Introduction to multiresolution theory -- MOTIVATION: MATERIALS ARE STRUCTURED CONTINUA -- BULK DEFORMATION OF MICROSTRUCTURED CONTINUA -- GENERALIZING MECHANICS TO BULK MICROSTRUCTURED CONTINUA -- MULTISCALE MICROSTRUCTURES AND THE MULTIRESOLUTION CONTINUUM THEORY -- GOVERNING EQUATIONS FOR MCT -- CONSTRUCTING MCT CONSTITUTIVE RELATIONSHIPS -- BASIC GUIDELINES FOR RVE MODELS -- FINITE ELEMENT IMPLEMENTATION OF MCT -- NUMERICAL EXAMPLE -- FUTURE RESEARCH DIRECTION OF MCT MODELING -- EXERCISES -- Single-crystal plasticity -- Introduction -- Crystallographic description of cubic and non-cubic crystals -- Atomic origins of plasticity and the burgers vector in single crystals -- Defining slip planes and directions in general single crystals -- Kinematics of single crystal plasticity -- Dislocation density evolution -- Stress required for dislocation motion -- Stress update in rate-dependent single-crystal plasticity -- Algorithm for rate-dependent dislocation-density based crystal plasticity -- Numerical example -- Exercises -- Appendix 1. Voigt notation -- Appendix 2. Norms -- Appendix 3. Element shape functions -- Appendix 4. Euler angles from pole figures -- Appendix 5. Example of dislocation density evolutionary equations.

'Focuses on the formulation and solution of the discrete equations for various classes of problems encountered in the application of the finite element method to solid and structural mechanics'-- Provided by publisher.