A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory Element Technology discusses four-node, three-node, eight-node, and two-node element theories Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

A systematic introduction to the theories and formulations ofthe explicit finite element methodAs numerical technology continues to grow and evolve withindustrial applications, understanding the explicit finite elementmethod has become increasingly important, particularly in the areasof crashworthiness, metal forming, and impact engineering.Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is the first book to addressspecifically what is now accepted as the most successful numericaltool for nonlinear transient dynamics. The book aids readers inmastering the explicit finite element method and programming codewithout requiring extensive background knowledge of the generalfinite element.The authors present topics relating to the variationalprinciple, numerical procedure, mechanical formulation, andfundamental achievements of the convergence theory. In additionkey topics and techniques are provided in four clearly organizedsections:* Fundamentals explores a framework of the explicitfinite element method for nonlinear transient dynamics andhighlights achievements related to the convergence theory* Element Technology discusses four-nodethree-node, eight-node, and two-node element theories* Material Models outlines models of plasticity andother nonlinear materials as well as the mechanics model of ductiledamage* Contact and Constraint Conditions covers subjectsrelated to three-dimensional surface contact, with examples solvedanalytically, as well as discussions on kinematic constraintconditionsThroughout the book, vivid figures illustrate the ideas and keyfeatures of the explicit finite element method. Examples clearlypresent results, featuring both theoretical assessments andindustrial applications.Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is an ideal book for bothengineers who require more theoretical discussions and fortheoreticians searching for interesting and challenging researchtopics. The book also serves as an excellent resource for courseson applied mathematics, applied mechanics, and numerical methods atthe graduate level.

PART 1 Fundamentals1 Introduction1.1 Era of Simulation and Computer Aided Engineering1.2 Preliminaries2 Framework of Explicit Finite Element Method for Nonlinear Transient Dynamics2.1 Transient Structural Dynamics2.2 Variational Principles for Transient Dynamics2.3 Finite Element Equations and the Explicit Procedures2.4 Main Features of the Explicit Finite Element Method2.5 Assessment of Explicit Finite Element MethodPART 2 Element Technology3 Four-Node Shell Element (Reissner-Mindlin Plate Theory)3.1 Fundamentals of Plates and Shells3.2 Linear Theory of R-M Plate3.3 Interpolation for Four-Node R-M Plate Element3.4 Reduced Integration and Selective Reduced Integration3.5 Perturbation Hourglass Control - Belytschko-Tsay (B-T) Element3.6 Physical Hourglass Control - Belytschko-Leviathan (B-L) (QPH) Element3.7 Shear Projection Method - Bathe-Dvorkin (B-D) Element3.8 Assessment of Four-Node R-M Plate Element4 Three-Node Shell Element (Reissner-Mindlin Plate Theory)4.1 Fundamentals of a Three-Node C0 Element4.2 Decomposition Method for C0 Triangular Element with One Point Integration4.3 Discrete Kirchhoff Triangular (DKT) Element4.4 Assessment of Three-Node R-M Plate Element5 Eight-Node Solid Element5.1 Trilinear Interpolation for the Eight-Node Hexahedron Element5.2 Locking Issues of the Eight-Node Solid Element5.3 One- Point Reduced Integration and the Perturbed Hourglass Control5.4 Assumed Strain Method and Selective / Reduced Integration5.5 Assumed Deviatoric Strain5.6 An Enhanced Assumed Strain Method5.7 Taylor Expansion of Assumed Strain about the Element Center5.8 Evaluation of Eight-Node Solid Element6 Two-Node Element6.1 Truss and Rod Element6.2 Timoshenko Beam Element6.3 Spring Element6.4 Spot Weld ElementPART 3 Material Models7 Material Model of Plasticity7.1 Fundamentals of Plasticity7.2 Constitutive Equations7.3 Software Implementation7.4 Evaluation of Shell Elements with Plastic Deformation8 Continuum Mechanics Model of Ductile Damage8.1 Concept of Damage Mechanics8.2 Gurson's Model8.3 Chow's Isotropic Model of Continuum Damage Mechanics8.4 Chow's Anisotropic Model of Continuum Damage Mechanics9 Models of Nonlinear Materials9.1 Vicoelasticity9.2 Polymer and Engineering Plastics9.3 Rubber9.4 Foam9.5 Honeycomb9.6 Laminated GlazingPART 4 Contact and Constraint Conditions10 Three-Dimensional Surface Contact10.1 Examples of Contact Problems10.2 Description of Contact Conditions10.3 Variational Principle for the Dynamic Contact Problem10.4 Penalty Method and the Regularization of Variational Inequality11 Numerical Procedures for Three-Dimensional Surface Contact11.1 A Contact Algorithm with Slave Node Searching Master Segment11.2 A Contact Algorithm with Master Segment Searching Slave Node11.3 Method of Contact Territory and Defense Node11.4 Pin- Ball Contact Algorithm11.5 Edge (Line Segment) Contact11.6 Evaluation of Contact Algorithm with Penalty Method12 Kinematic Constraint Conditions12.1 Rigid Wall12.2 Rigid Body12.3 Explicit Finite Element Procedure with Constraint Conditions12.4 Application Examples with Constraint Conditions