Tuesday, 18 April 2017

Mechanics of Materials and Interfaces - The Disturbed State Concept by Chandrakant S Desai - www.MechanicaLibrary.com





  1. Introduction
  2. The Disturbed State Concept: Preliminaries
  3. Relative Intact and Fully Adjusted States and Disturbance
  4. DSC Equations and Specializations
  5. Theory of Elasticity in the DSC
  6. Theory of Plasticity in the DSC
  7. Hierarchical Single-Surface Plasticity Models in the DSC
  8. Creep Behavior: Viscoelastic and Viscoplastic Models in the DSC
  9. The DSC for Saturated and Unsaturated Materials
  10. The DSC for Structured and Stiffened Materials
  11. The DSC for Interfaces and Joints
  12. Microstructure: Localization and Instability
  13. Implementation of the DSC in Computer Procedures
  14. Conclusions and Future Trends

Appendix I : Disturbed State, Critical-State, and Self-Organized Criticality Concepts
Appendix II : DSC Parameters: Optimization and Sensitivity


Engineering Materials :

Engineering materials are difficult to characterize in their initial natural or artificially manufactured states. Characterization of their behavior under a
variety of possible forces—natural, mechanical, and environmental—also poses a challenging problem. Human understanding of the behavior of materials, which are a mixture of “continuous” and “discontinuous” particle systems at the same time , involves mental (human), physical, and mathematical models; the latter are often used
to develop numerical models for solution by the artificial mind , which is the modern computer.

Continuous or Discontinuous or Mixture : 

The long pursuit of the mechanics of engineering materials has grappled with the notion that the materials’ systems can be treated as continuous , such that
particles or clusters at the level of interest do not separate or do not overlap. A moment’s mental reflection and probing would reveal that particles at any level are not continuous as there is always a gap, or void (“shunya” or space), between them. At the same time, there is some known and some unknown and mysterious thread or force or synchronous cohesion that connects the particles. Even if all physical and chemical forces that contribute to this connection are identified and quantified, there “appears” to exist a force beyond all quantifiable forces that remains to be identified and quantified. Some would say that when the complete understanding occurs there would be no further need to characterize materials, and all will become (again) one material whole. Also, this makes us aware of the fact that the models we develop to characterize the material behavior are only approximations, as they do not completely characterize the response of the entire, or holistic,
system. Thus, the limitation of our understanding of the complex discontinuous system requires us to treat materials as continuous. The reality appears to be that both continuous and discontinuous exist simultaneously, i.e., a particle at a given level is connected and disconnected to others at the same time. Hence, in a
general sense, almost all reasonably successful efforts and models, in physics and mechanics, until now, have involved some sort of superposition or imposition of discontinuity on continuity. Then, the available continuum models or theories are very often enhanced or enriched by models or constraints to simulate discontinuity.
It is with the foregoing appreciation of the limitation of our modelling that we will deal with materials that are both continuous and discontinuous at the same time.

The Disturbed State Concept: Preliminaries - Introduction :

A deforming material is considered to be a mixture of “continuous” and “discontinuous” parts. The latter can involve relative motions between particles due to microcracking, slippage, rotations, etc. As introduced in the previous chapter, the disturbed state concept (DSC) is based on the basic physical principle that the  behavior exhibited through the interacting mechanisms of components in a mixture can be expressed in terms of the responses of the components connected through a  coupling function, called the disturbance function ( D ). In the case of the mechanical response of deforming engineering materials, the components are considered to be reference material states. For the element of the same material, the reference material states are considered to be its (initial) continuum or relative intact (RI) state, and the fully adjusted (FA) state that results from the transformation of the material in the RI state due to factors such as particle (relative) motions and microcracking. We first consider the DSC for the case of deformations in the same material. Then we shall consider the DSC for deforming a material element composed of more than one (different) material.

Relative Intact and Fully Adjusted States, and Disturbance - Introduction :

density or void ratio (e), does not change significantly during deformation. In other words, as in the case of some metals, it is assumed that the density or void ratio of the material remains invariant during deformation. The linear elastic response can be considered to be the RI state in relation to the observed elastic–plastic (hardening) behavior. The elastic–plastic hardening response can be treated as an RI state in relation to the elastic perfectly plastic response. The linear elastic or the elastic–plastic hardening responses can be treated as RI in relation to the observed degradation or softening behavior.

Relative Intact Behavior : A loose material with an initial mean pressure (p0) may compact continuously during shear loading. In that case, the RI response can be characterized by excluding the effect of increased compaction, in which case the observed response can be stiffer than the RI response 

Theory of Plasticity in DSC :

The development and application of the theory of plasticity have occurred over the last many years (1–13). The intention here is to describe briefly the basic aspects of the theory and its use in the DSC. The theory of elasticity is applicable if the material is elastic; that is, upon removal of load, it returns to its original configuration along the same path. However, except for limited ranges of loading, most materials do not return to their original configuration; that is, they follow different paths during unloading. As a result, at the end of unloading, the material retains a part of the deformation or strain, which is referred to as irreversible,
inelastic, or plastic strain . Hence, the total strain, , at different points is assumed to be composed of the plastic, , and the elastic or recoverable parts.
If the material (element) is elastic up to point A and then yields plastically, it is referred to as elastoplastic material. If, after point A, it experiences continuing deformation under the constant yield stress ( y), it is called elastic perfectly plastic material. After the yield point A, if the material is unloaded, it will not return to its original configuration and will experience plastic strain. The “stiffness” of some materials may experience gradual decrease during
yielding; however, the stress under continuing loading increases after the yield point. In other words, every point during the loading is a “new” yield point, and the next yield stress is greater than the previous yield stress. Such behavior is called elastic-plastic hardening response.