The combined finite-discrete element method [[electronic resource] /] / Ante Munjiza

• Record Nr.: UNINA9910831049103321
• Autore: Munjiza Ante
• Pubbl/distr/stampa: Hoboken, NJ, : Wiley, c2004
• ISBN: 1-280-27485-9; 9780470020172; 9786610274857; 0-470-02017-2; 0-470-02018-0
• Descrizione fisica: 1 online resource (349 p.)
• Disciplina: 620.00151535; 620.1/123/015118; 620.1123015118
• Soggetti: Deformations (Mechanics) - Mathematical models; Finite element method
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [319]-330) and index.
• Nota di contenuto: The Combined Finite-Discrete Element Method; Contents; Preface; Acknowledgements; 1 Introduction; 1.1 General Formulation of Continuum Problems; 1.2 General Formulation of Discontinuum Problems; 1.3 A Typical Problem of Computational Mechanics of Discontinua; 1.4 Combined Continua-Discontinua Problems; 1.5 Transition from Continua to Discontinua; 1.6 The Combined Finite-Discrete Element Method; 1.7 Algorithmic and Computational Challenge of the Combined Finite-Discrete Element Method; 2 Processing of Contact Interaction in the Combined Finite Discrete Element Method; 2.1 Introduction; 2.2 The Penalty Function Method2.3 Potential Contact Force in 2D; 2.4 Discretisation of Contact Force in 2D; 2.5 Implementation Details for Discretised Contact Force in 2D; 2.6 Potential Contact Force in 3D; 2.6.1 Evaluation of contact force; 2.6.2 Computational aspects; 2.6.3 Physical interpretation of the penalty parameter; 2.6.4 Contact damping; 2.7 Alternative Implementation of the Potential Contact ; Force; 3 Contact Detection; 3.1 Introduction; 3.2 Direct Checking Contact Detection Algorithm; 3.2.1 Circular bounding box; 3.2.2 Square bounding object; 3.2.3 Complex bounding box; 3.3 Formulation of Contact Detection Problem for Bodies of Similar Size in 2D3.4 Binary Tree Based Contact Detection Algorithm for Discrete Elements of Similar Size; 3.5 Direct Mapping Algorithm for Discrete Elements of Similar Size; 3.6 Screening Contact Detection Algorithm for Discrete Elements of Similar Size; 3.7 Sorting Contact Detection Algorithm for Discrete Elements of a Similar Size; 3.8 Munjiza-NBS Contact Detection Algorithm in 2D; 3.8.1 Space decomposition; 3.8.2 Mapping of discrete elements onto cells; 3.8.3 Mapping of discrete elements onto rows and columns of cells; 3.8.4 Representation of mapping3.9 Selection of Contact Detection Algorithm; 3.10 Generalisation of Contact Detection Algorithms to 3D Space; 3.10.1 Direct checking contact detection algorithm; 3.10.2 Binary tree search; 3.10.3 Screening contact detection algorithm; 3.10.4 Direct mapping contact detection algorithm; 3.11 Generalisation of Munjiza-NBS Contact Detection Algorithm to Multidimensional Space; 3.12 Shape and Size Generalisation-Williams C-GRID Algorithm; 4 Deformability of Discrete Elements; 4.1 Deformation; 4.2 Deformation Gradient; 4.2.1 Frames of reference; 4.2.2 Transformation matrices4.3 Homogeneous Deformation; 4.4 Strain; 4.5 Stress; 4.5.1 Cauchy stress tensor; 4.5.2 First Piola-Kirchhoff stress tensor; 4.5.3 Second Piola-Kirchhoff stress tensor; 4.6 Constitutive Law; 4.7 Constant Strain Triangle Finite Element; 4.8 Constant Strain Tetrahedron Finite Element; 4.9 Numerical Demonstration of Finite Rotation Elasticity in the Combined Finite-Discrete Element Method; 5 Temporal Discretisation; 5.1 The Central Difference Time Integration Scheme; 5.1.1 Stability of the central difference time integration scheme; 5.2 Dynamics of Irregular Discrete Elements Subject to Finite Rotations in 3D
• Sommario/riassunto: The combined finite discrete element method is a relatively new computational tool aimed at problems involving static and / or dynamic behaviour of systems involving a large number of solid deformable bodies. Such problems include fragmentation using explosives (e.g rock blasting), impacts, demolition (collapsing buildings), blast loads, digging and loading processes, and powder technology.The combined finite-discrete element method - a natural extension of both discrete and finite element methods - allows researchers to model problems involving the deformability of either one solid body,