Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Mechanics of Materials and Interfaces: The Disturbed State Concept

Abstract: INTRODUCTION Prelude Philosophical Motivation Reference States Engineering Materials and Matter Continuous , Discontinuous or Mixture Transformation and Self Adjustment Disturbed Sate Concept Disturbance and Damage Models DSC and Other Models Scope THE DISTURBED STATE CONCEPT: Preliminaries Introduction Engineering Behavior Mechanism Fully Adjusted State Characteristic Dimension Observed Behavior Formulation of DSC Alternative Formulations of DSC Material Element Composed of Two Materials DSC-Multi -Component System DSC For Porous Media Composite Materials Bonded Materials Self Organized Criticality RELATIVE INTACT AND FULLY ADJUSTED STATES AND DISTURBANCE Specializations Disturbance and Function Laboratory Tests Stiffening or Healing Representations of Disturbance Creep Behavior Rate Dependence Disturbance Based on Disorder (Entropy) and Free Energy Material Parameters DSC EQUATIONS AND SPECIALIZATIONS Relative Intact Response Fully Adjusted Response Specializations Thermal Effects Disturbance Models DSC With and Without Relative Motions Critical State for FA Response DSC Euqations with Critical State Strain Equations General Formulation Examples 1 to 4 THEORY OF ELASTICITY IN DSC Linear Elasticity Nonlinear Elasticity Relative Intact Behavior Fully Adjusted Behavior Disturbance Function Material Parameters Thermal Effects Examples 1 to 8 THEORY OF PLASTICITY IN DSC Mechanisms Theoretical Development Continuous Yielding or Hardening To Hierarchical Single Surface Models Incremental Equations Parameters and Determination from Laboratory Tests Thermoplasticity Examples 1 to 7 HIERARCHICAL SINGLE SURFACE PLASTICITY MODELS IN DSC Basic HISS Model Specializations of HISS Model Material Parameters Thermal Effects Rate Effects Repetitive Loading Derivation of Elastoplastic Equations Incremental Iterative Analysis Correction Procedures Thermoplasticity Examples including Validations 1 to 16 Sensitivity Analysis CREEP BEHAVIOR: VISCOELASTIC AND VISCOPLASTIC MODELS Elastoviscoplastic Model (Perzyna) Mechanism of Viscoplastic Solution Elastoviscoplastic Equations One-Dimensional Formulation of Perzyna's Model Disturbance Function Finite Element Equations Rate Dependent Behavior Parameters for Viscoplastic Model Temperature Dependence Multi-component DSC and Overlay Models Specializations: Elastic(e), Viscoelastic(ve), Elastoviscoplastic(evp), Material Parameters in Overlay Models Examples 1 to 9 DSC FOR SATURATED AND UNSATURATED MATERIALS Brief Review Fully Saturated Materials Equations Terzaghi's Equation Incremental DSC Equations Disturbance Effective Stress Parameter Residual Flow Concept HISS and DSC Models Softening, Degradation and Collapse Material Parameters Examples 1 to 3 DSC FOR STRUCTURED AND STIFFENED MATERIALS Definition of Disturbance Structured Soils Dislocation, Softening and Stiffening Reinforced and Jointed Systems Equivalent Composite Individual Solid and Joint Elements Rest Periods: Unloading Examples 1 to 3 DSC FOR INTERFACES AND JOINTS General Problem Review Thin Layer Interface Model Disturbed State Concept Disturbance Function Incremental Equations Determination of Parameters Mathematical and Physical Characteristics of DSC Testing Examples 1 to 11 Computer Implementation MICROSTRUCTURE, LOCALIZATION AND INSTABILITY Microstructure Wellposedness Localization Nonlocality and Characteristic Dimension Regularization and Nonlocal Models Rate Dependent Models Continuum Damage Model Nonlocal Continuum Strain and Energy Based Models Gradient Enrichment of Continuum Models Cosserat Continuum Stability Disturbed State Concept: Nonlocality, Micro-crack Interaction, Characteristic Mesh Dependence Instability Approximate Decoupled DSC Stability Analysis of DSC Examples 1 to 4 Appndix 12-1: Thermodynamical Analysis of DSC IMPLEMENTATION OF DSC IN COMPUTER PROCEDURES Finite Element Formulation Solution Schemes Algorithms for Creep Behavior Algorithms for Coupled Dynamic Behavior Partially Saturated Systems Cyclic and Repetitive Loading Initial Conditions Hierarchical Capabilities and Options Mesh Adaption Using DSC Examples of Applications: Field and Laboratory Simulated Tests 1 to 12 CONCLUSIONS AND FUTURE TRENDS APPENDIX I : DISTURBED STATE, CRITICAL STATE AND SELF ORGANIZED CRITICALITY CONCEPTS APPENDIX II : DSC PARAMETERS, OPTIMIZATION AND SENSITIVITY

Use of the distinct element method to perform stress analysis in rock with non-persistent joints and to study the effect of joint geometry parameters on the strength and deformability of rock masses

Abstract: To use the distinct element method, it is necessary to discretize the problem domain into polygons in two dimensions (2 D) or into polyhedra in three dimensions (3 D). To perform distinct element stress analysis in a rock mass which contains non-persistent finite size joints, it is necessary to generate some type of fictitious joints so that when they are combined with the non-persistent joints, they discretize the problem domain into polygons in 2 D or into polyhedra in 3 D. The question arises as to which deformation and strength parameter values should be assigned to these fictitious joints so that they behave as intact rock. In this paper, linear elastic, perfectly-plastic constitutive models with the Mohr-Coulomb failure criterion, including a tension cut-off, were used to represent the mechanical behaviour of both intact rock and fictitious joints. It was found that, by choosing the parameter values for the constitutive models as given below, it is possible to make the fictitious joints behave as intact rock, in a global sense. Some examples are given in the paper to illustrate how to use the distinct element method to perform stress analysis of rock blocks which contain non-persistent joints and to study the effect of joint geometry parameters on strength and deformability of rock masses.