{"product_id":"large-strain-finite-element-method-isbn-9781118405307","title":"Large Strain Finite Element Method","description":"\u003cp\u003e\u003cb\u003eAn introductory approach to the subject of large strains and large displacements in finite elements.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLarge Strain Finite Element Method: A Practical Course\u003c\/i\u003e, takes an introductory approach to the subject of large strains and large displacements in finite elements and starts from the basic concepts of finite strain deformability, including finite rotations and finite displacements. The necessary elements of vector analysis and tensorial calculus on the lines of modern understanding of the concept of tensor will also be introduced.\u003c\/p\u003e \u003cp\u003eThis book explains how tensors and vectors can be described using matrices and also introduces different stress and strain tensors. Building on these, step by step finite element techniques for both hyper and hypo-elastic approach will be considered.\u003c\/p\u003e \u003cp\u003eMaterial models including isotropic, unisotropic, plastic and viscoplastic materials will be independently discussed to facilitate clarity and ease of learning. Elements of transient dynamics will also be covered and key explicit and iterative solvers including the direct numerical integration, relaxation techniques and conjugate gradient method will also be explored.\u003c\/p\u003e \u003cp\u003eThis book contains a large number of easy to follow illustrations, examples and source code details that facilitate both reading and understanding. \u003c\/p\u003e \u003cul\u003e \u003cli\u003eTakes an introductory approach to the subject of large strains and large displacements in finite elements. No prior knowledge of the subject is required.\u003c\/li\u003e \u003cli\u003eDiscusses computational methods and algorithms to tackle large strains and teaches the basic knowledge required to be able to critically gauge the results of computational models.\u003c\/li\u003e \u003cli\u003eContains a large number of easy to follow illustrations, examples and source code details.\u003c\/li\u003e \u003cli\u003eAccompanied by a website hosting code examples.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgements xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART ONE FUNDAMENTALS 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Assumption of Small Displacements 3\u003c\/p\u003e \u003cp\u003e1.2 Assumption of Small Strains 6\u003c\/p\u003e \u003cp\u003e1.3 Geometric Nonlinearity 6\u003c\/p\u003e \u003cp\u003e1.4 Stretches 8\u003c\/p\u003e \u003cp\u003e1.5 Some Examples of Large Displacement Large Strain Finite Element Formulation 8\u003c\/p\u003e \u003cp\u003e1.6 The Scope and Layout of the Book 13\u003c\/p\u003e \u003cp\u003e1.7 Summary 13\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Matrices 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Matrices in General 15\u003c\/p\u003e \u003cp\u003e2.2 Matrix Algebra 16\u003c\/p\u003e \u003cp\u003e2.3 Special Types of Matrices 21\u003c\/p\u003e \u003cp\u003e2.4 Determinant of a Square Matrix 22\u003c\/p\u003e \u003cp\u003e2.5 Quadratic Form 24\u003c\/p\u003e \u003cp\u003e2.6 Eigenvalues and Eigenvectors 24\u003c\/p\u003e \u003cp\u003e2.7 Positive Definite Matrix 26\u003c\/p\u003e \u003cp\u003e2.8 Gaussian Elimination 26\u003c\/p\u003e \u003cp\u003e2.9 Inverse of a Square Matrix 28\u003c\/p\u003e \u003cp\u003e2.10 Column Matrices 30\u003c\/p\u003e \u003cp\u003e2.11 Summary 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Some Explicit and Iterative Solvers 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Central Difference Solver 35\u003c\/p\u003e \u003cp\u003e3.2 Generalized Direction Methods 43\u003c\/p\u003e \u003cp\u003e3.3 The Method of Conjugate Directions 50\u003c\/p\u003e \u003cp\u003e3.4 Summary 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Numerical Integration 65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Newton-Cotes Numerical Integration 65\u003c\/p\u003e \u003cp\u003e4.2 Gaussian Numerical Integration 67\u003c\/p\u003e \u003cp\u003e4.3 Gaussian Integration in 2D 70\u003c\/p\u003e \u003cp\u003e4.4 Gaussian Integration in 3D 71\u003c\/p\u003e \u003cp\u003e4.5 Summary 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Work of Internal Forces on Virtual Displacements 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Principle of Virtual Work 75\u003c\/p\u003e \u003cp\u003e5.2 Summary 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART TWO PHYSICAL QUANTITIES 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Scalars 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Scalars in General 81\u003c\/p\u003e \u003cp\u003e6.2 Scalar Functions 81\u003c\/p\u003e \u003cp\u003e6.3 Scalar Graphs 82\u003c\/p\u003e \u003cp\u003e6.4 Empirical Formulas 82\u003c\/p\u003e \u003cp\u003e6.5 Fonts 83\u003c\/p\u003e \u003cp\u003e6.6 Units 83\u003c\/p\u003e \u003cp\u003e6.7 Base and Derived Scalar Variables 85\u003c\/p\u003e \u003cp\u003e6.8 Summary 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Vectors in 2D 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Vectors in General 87\u003c\/p\u003e \u003cp\u003e7.2 Vector Notation 91\u003c\/p\u003e \u003cp\u003e7.3 Matrix Representation of Vectors 91\u003c\/p\u003e \u003cp\u003e7.4 Scalar Product 92\u003c\/p\u003e \u003cp\u003e7.5 General Vector Base in 2D 93\u003c\/p\u003e \u003cp\u003e7.6 Dual Base 94\u003c\/p\u003e \u003cp\u003e7.7 Changing Vector Base 95\u003c\/p\u003e \u003cp\u003e7.8 Self-duality of the Orthonormal Base 97\u003c\/p\u003e \u003cp\u003e7.9 Combining Bases 98\u003c\/p\u003e \u003cp\u003e7.10 Examples 104\u003c\/p\u003e \u003cp\u003e7.11 Summary 108\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Vectors in 3D 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Vectors in 3D 109\u003c\/p\u003e \u003cp\u003e8.2 Vector Bases 111\u003c\/p\u003e \u003cp\u003e8.3 Summary 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Vectors in n-Dimensional Space 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Extension from 3D to 4-Dimensional Space 117\u003c\/p\u003e \u003cp\u003e9.2 The Dual Base in 4D 118\u003c\/p\u003e \u003cp\u003e9.3 Changing the Base in 4D 120\u003c\/p\u003e \u003cp\u003e9.4 Generalization to n-Dimensional Space 121\u003c\/p\u003e \u003cp\u003e9.5 Changing the Base in n-Dimensional Space 124\u003c\/p\u003e \u003cp\u003e9.6 Summary 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 First Order Tensors 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Slope Tensor 129\u003c\/p\u003e \u003cp\u003e10.2 First Order Tensors in 2D 131\u003c\/p\u003e \u003cp\u003e10.3 Using First Order Tensors 132\u003c\/p\u003e \u003cp\u003e10.4 Using Different Vector Bases in 2D 134\u003c\/p\u003e \u003cp\u003e10.5 Differential of a 2D Scalar Field as the First Order Tensor 137\u003c\/p\u003e \u003cp\u003e10.6 First Order Tensors in 3D 141\u003c\/p\u003e \u003cp\u003e10.7 Changing the Vector Base in 3D 142\u003c\/p\u003e \u003cp\u003e10.8 First Order Tensor in 4D 143\u003c\/p\u003e \u003cp\u003e10.9 First Order Tensor in n-Dimensions 147\u003c\/p\u003e \u003cp\u003e10.10 Differential of a 3D Scalar Field as the First Order Tensor 149\u003c\/p\u003e \u003cp\u003e10.11 Scalar Field in n-Dimensional Space 152\u003c\/p\u003e \u003cp\u003e10.12 Summary 153\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Second Order Tensors in 2D 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Stress Tensor in 2D 155\u003c\/p\u003e \u003cp\u003e11.2 Second Order Tensor in 2D 158\u003c\/p\u003e \u003cp\u003e11.3 Physical Meaning of Tensor Matrix in 2D 159\u003c\/p\u003e \u003cp\u003e11.4 Changing the Base 161\u003c\/p\u003e \u003cp\u003e11.5 Using Two Different Bases in 2D 163\u003c\/p\u003e \u003cp\u003e11.6 Some Special Cases of Stress Tensor Matrices in 2D 167\u003c\/p\u003e \u003cp\u003e11.7 The First Piola-Kirchhoff Stress Tensor Matrix 168\u003c\/p\u003e \u003cp\u003e11.8 The Second Piola-Kirchhoff Stress Tensor Matrix 169\u003c\/p\u003e \u003cp\u003e11.9 Summary 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Second Order Tensors in 3D 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Stress Tensor in 3D 175\u003c\/p\u003e \u003cp\u003e12.2 General Base for Surfaces 179\u003c\/p\u003e \u003cp\u003e12.3 General Base for Forces 182\u003c\/p\u003e \u003cp\u003e12.4 General Base for Forces and Surfaces 184\u003c\/p\u003e \u003cp\u003e12.5 The Cauchy Stress Tensor Matrix in 3D 186\u003c\/p\u003e \u003cp\u003e12.6 The First Piola-Kirchhoff Stress Tensor Matrix in 3D 186\u003c\/p\u003e \u003cp\u003e12.7 The Second Piola-Kirchhoff Stress Tensor Matrix in 3D 188\u003c\/p\u003e \u003cp\u003e12.8 Summary 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Second Order Tensors in nD 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Second Order Tensor in n-Dimensions 191\u003c\/p\u003e \u003cp\u003e13.2 Summary 200\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART THREE DEFORMABILITY AND MATERIAL MODELING 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Kinematics of Deformation in 1D 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Geometric Nonlinearity in General 203\u003c\/p\u003e \u003cp\u003e14.2 Stretch 205\u003c\/p\u003e \u003cp\u003e14.3 Material Element and Continuum Assumption 208\u003c\/p\u003e \u003cp\u003e14.4 Strain 209\u003c\/p\u003e \u003cp\u003e14.5 Stress 213\u003c\/p\u003e \u003cp\u003e14.6 Summary 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Kinematics of Deformation in 2D 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Isotropic Solids 217\u003c\/p\u003e \u003cp\u003e15.2 Homogeneous Solids 217\u003c\/p\u003e \u003cp\u003e15.3 Homogeneous and Isotropic Solids 217\u003c\/p\u003e \u003cp\u003e15.4 Nonhomogeneous and Anisotropic Solids 218\u003c\/p\u003e \u003cp\u003e15.5 Material Element Deformation 221\u003c\/p\u003e \u003cp\u003e15.6 Cauchy Stress Matrix for the Solid Element 225\u003c\/p\u003e \u003cp\u003e15.7 Coordinate Systems in 2D 227\u003c\/p\u003e \u003cp\u003e15.8 The Solid- and the Material-Embedded Vector Bases 228\u003c\/p\u003e \u003cp\u003e15.9 Kinematics of 2D Deformation 229\u003c\/p\u003e \u003cp\u003e15.10 2D Equilibrium Using the Virtual Work of Internal Forces 231\u003c\/p\u003e \u003cp\u003e15.11 Examples 235\u003c\/p\u003e \u003cp\u003e15.12 Summary 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Kinematics of Deformation in 3D 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 The Cartesian Coordinate System in 3D 241\u003c\/p\u003e \u003cp\u003e16.2 The Solid-Embedded Coordinate System 241\u003c\/p\u003e \u003cp\u003e16.3 The Global and the Solid-Embedded Vector Bases 243\u003c\/p\u003e \u003cp\u003e16.4 Deformation of the Solid 244\u003c\/p\u003e \u003cp\u003e16.5 Generalized Material Element 246\u003c\/p\u003e \u003cp\u003e16.6 Kinematic of Deformation in 3D 247\u003c\/p\u003e \u003cp\u003e16.7 The Virtual Work of Internal Forces 249\u003c\/p\u003e \u003cp\u003e16.8 Summary 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 The Unified Constitutive Approach in 2D 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 257\u003c\/p\u003e \u003cp\u003e17.2 Material Axes 259\u003c\/p\u003e \u003cp\u003e17.3 Micromechanical Aspects and Homogenization 260\u003c\/p\u003e \u003cp\u003e17.4 Generalized Homogenization 263\u003c\/p\u003e \u003cp\u003e17.5 The Material Package 264\u003c\/p\u003e \u003cp\u003e17.6 Hyper-Elastic Constitutive Law 265\u003c\/p\u003e \u003cp\u003e17.7 Hypo-Elastic Constitutive Law 266\u003c\/p\u003e \u003cp\u003e17.8 A Unified Framework for Developing Anisotropic Material Models in 2D 267\u003c\/p\u003e \u003cp\u003e17.9 Generalized Hyper-Elastic Material 267\u003c\/p\u003e \u003cp\u003e17.10 Converting the Munjiza Stress Matrix to the Cauchy Stress Matrix 274\u003c\/p\u003e \u003cp\u003e17.11 Developing Constitutive Laws 279\u003c\/p\u003e \u003cp\u003e17.12 Generalized Hypo-Elastic Material 288\u003c\/p\u003e \u003cp\u003e17.13 Unified Constitutive Approach for Strain Rate and Viscosity 292\u003c\/p\u003e \u003cp\u003e17.14 Summary 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 The Unified Constitutive Approach in 3D 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Material Package Framework 295\u003c\/p\u003e \u003cp\u003e18.2 Generalized Hyper-Elastic Material 295\u003c\/p\u003e \u003cp\u003e18.3 Generalized Hypo-Elastic Material 299\u003c\/p\u003e \u003cp\u003e18.4 Developing Material Models 302\u003c\/p\u003e \u003cp\u003e18.5 Calculation of the Cauchy Stress Tensor Matrix 302\u003c\/p\u003e \u003cp\u003e18.6 Summary 312\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART FOUR THE FINITE ELEMENT METHOD IN 2D 315\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 2D Finite Element: Deformation Kinematics Using the Homogeneous Deformation Triangle 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 The Finite Element Mesh 317\u003c\/p\u003e \u003cp\u003e19.2 The Homogeneous Deformation Finite Element 317\u003c\/p\u003e \u003cp\u003e19.3 Summary 326\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 2D Finite Element: Deformation Kinematics Using Iso-Parametric Finite Elements 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 The Finite Element Library 327\u003c\/p\u003e \u003cp\u003e20.2 The Shape Functions 327\u003c\/p\u003e \u003cp\u003e20.3 Nodal Positions 330\u003c\/p\u003e \u003cp\u003e20.4 Positions of Material Points inside a Single Finite Element 331\u003c\/p\u003e \u003cp\u003e20.5 The Solid-Embedded Vector Base 332\u003c\/p\u003e \u003cp\u003e20.6 The Material-Embedded Vector Base 334\u003c\/p\u003e \u003cp\u003e20.7 Some Examples of 2D Finite Elements 337\u003c\/p\u003e \u003cp\u003e20.8 Summary 340\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Integration of Nodal Forces over Volume of 2D Finite Elements 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 The Principle of Virtual Work in the 2D Finite Element Method 343\u003c\/p\u003e \u003cp\u003e21.2 Nodal Forces for the Homogeneous Deformation Triangle 348\u003c\/p\u003e \u003cp\u003e21.3 Nodal Forces for the Six-Noded Triangle 352\u003c\/p\u003e \u003cp\u003e21.4 Nodal Forces for the Four-Noded Quadrilateral 353\u003c\/p\u003e \u003cp\u003e21.5 Summary 355\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Reduced and Selective Integration of Nodal Forces over Volume of 2D Finite Elements 357\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Volumetric Locking 357\u003c\/p\u003e \u003cp\u003e22.2 Reduced Integration 358\u003c\/p\u003e \u003cp\u003e22.3 Selective Integration 359\u003c\/p\u003e \u003cp\u003e22.4 Shear Locking 362\u003c\/p\u003e \u003cp\u003e22.5 Summary 364\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART FIVE THE FINITE ELEMENT METHOD IN 3D 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 3D Deformation Kinematics Using the Homogeneous Deformation Tetrahedron Finite Element 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 367\u003c\/p\u003e \u003cp\u003e23.2 The Homogeneous Deformation Four-Noded Tetrahedron Finite Element 368\u003c\/p\u003e \u003cp\u003e23.3 Summary 377\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 3D Deformation Kinematics Using Iso-Parametric Finite Elements 379\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 The Finite Element Library 379\u003c\/p\u003e \u003cp\u003e24.2 The Shape Functions 379\u003c\/p\u003e \u003cp\u003e24.3 Nodal Positions 381\u003c\/p\u003e \u003cp\u003e24.4 Positions of Material Points inside a Single Finite Element 382\u003c\/p\u003e \u003cp\u003e24.5 The Solid-Embedded Infinitesimal Vector Base 383\u003c\/p\u003e \u003cp\u003e24.6 The Material-Embedded Infinitesimal Vector Base 386\u003c\/p\u003e \u003cp\u003e24.7 Examples of Deformation Kinematics 387\u003c\/p\u003e \u003cp\u003e24.8 Summary 392\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Integration of Nodal Forces over Volume of 3D Finite Elements 393\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Nodal Forces Using Virtual Work 393\u003c\/p\u003e \u003cp\u003e25.2 Four-Noded Tetrahedron Finite Element 396\u003c\/p\u003e \u003cp\u003e25.3 Reduce Integration for Eight-Noded 3D Solid 399\u003c\/p\u003e \u003cp\u003e25.4 Selective Stretch Sampling-Based Integration for the Eight-Noded Solid Finite Element 400\u003c\/p\u003e \u003cp\u003e25.5 Summary 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Integration of Nodal Forces over Boundaries of Finite Elements 403\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e26.1 Stress at Element Boundaries 403\u003c\/p\u003e \u003cp\u003e26.2 Integration of the Equivalent Nodal Forces over the Triangle Finite Element 404\u003c\/p\u003e \u003cp\u003e26.3 Integration over the Boundary of the Composite Triangle 407\u003c\/p\u003e \u003cp\u003e26.4 Integration over the Boundary of the Six-Noded Triangle 408\u003c\/p\u003e \u003cp\u003e26.5 Integration of the Equivalent Internal Nodal Forces over the Tetrahedron Boundaries 409\u003c\/p\u003e \u003cp\u003e26.6 Summary 412\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART SIX THE FINITE ELEMENT METHOD IN 2.5D 415\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Deformation in 2.5D Using Membrane Finite Elements 417\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e27.1 Solids in 2.5D 417\u003c\/p\u003e \u003cp\u003e27.2 The Homogeneous Deformation Three-Noded Triangular Membrane Finite Element 419\u003c\/p\u003e \u003cp\u003e27.3 Summary 438\u003c\/p\u003e \u003cp\u003e\u003cb\u003e28 Deformation in 2.5D Using Shell Finite Elements 439\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e28.1 Introduction 439\u003c\/p\u003e \u003cp\u003e28.2 The Six-Noded Triangular Shell Finite Element 440\u003c\/p\u003e \u003cp\u003e28.3 The Solid-Embedded Coordinate System 441\u003c\/p\u003e \u003cp\u003e28.4 Nodal Coordinates 442\u003c\/p\u003e \u003cp\u003e28.5 The Coordinates of the Finite Element’s Material Points 443\u003c\/p\u003e \u003cp\u003e28.6 The Solid-Embedded Infinitesimal Vector Base 444\u003c\/p\u003e \u003cp\u003e28.7 The Solid-Embedded Vector Base versus the Material-Embedded Vector Base 447\u003c\/p\u003e \u003cp\u003e28.8 The Constitutive Law 449\u003c\/p\u003e \u003cp\u003e28.9 Selective Stretch Sampling Based Integration of the Equivalent Nodal Forces 449\u003c\/p\u003e \u003cp\u003e28.10 Multi-Layered Shell as an Assembly of Single Layer Shells 455\u003c\/p\u003e \u003cp\u003e28.11 Improving the CPU Performance of the Shell Element 456\u003c\/p\u003e \u003cp\u003e28.12 Summary 462\u003c\/p\u003e \u003cp\u003eIndex 463\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eAntonio A. Munjiza, Queen Mary College, London, UK\u003c\/strong\u003e\u003cbr\u003eAntonio Munjiza is a professor of computational mechanics in the Department of Computational Mechanics at Queen Mary College, London. His research interests include finite element methods, discrete element methods, molecular dynamics, structures and solids, structural dynamics, software engineering, blasts, impacts, and nanomaterials. He has authored two books, \u003cem\u003eThe Combined Finite-Discrete Element Method\u003c\/em\u003e (Wiley 2004) and \u003cem\u003eComputational Mechanics of Discontinua\u003c\/em\u003e (Wiley 2011) and over 110 refereed journal papers. In addition, he is on the editorial board of seven international journals. Dr Munjiza is also an accomplished software engineer with three research codes behind him and one commercial code all based on his technology. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eEarl E. Knight, Esteban Rougier and Ted Carney, Los Alamos National Laboratories, USA\u003c\/strong\u003e\u003cbr\u003eEarl Knight is a Team Leader in the Geodynamics Team at Los Alamos National Laboratory. His research interests include geodynamic modeling, rock mechanical modeling for deep water oil reservoirs and ground based nuclear explosion monitoring. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eEsteban Rougier\u003c\/strong\u003e is a Post Doctoral Research Associate at LANL. He has received his Ph.D. from Queen Mary, University of London in 2008` on Computational Mechanics of Discontinuum and its Application to the Simulation of Micro-Flows.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989510176997,"sku":"NP9781118405307","price":99.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118405307.jpg?v=1761784395","url":"https:\/\/k12savings.com\/es\/products\/large-strain-finite-element-method-isbn-9781118405307","provider":"K12savings","version":"1.0","type":"link"}