Search Results

At a basic level, cognitive search involves several parameters: Under what circumstances should a search be initiated, and how should the goal be specified? What are the criteria by which the search is judged a success or failure? How are corrective actions implemented when search strategies are judged insufficient? Studies of cognitive control have the potential to address each of these questions. In this chapter, a number of issues related to executive control of search are discussed, including the way in which hierarchical search goals are monitored and updated. A new theory of cognitive control is proposed to begin to answer these questions, and open questions that remain are highlighted for future enquiry.

Some essential preliminaries introduce the failure-theory problem by considering the different roles assumed by analytical forms that involve parameters as opposed to those that involve properties of the material. The first section of the derivation of the failure theory is entitled “The Organizing Principle”, and therein it is found that only two properties are allowed for the failure theory calibration and that they must be the uniaxial tensile and compressive strengths, T and C. Furthermore, it is established that the ratio T/C varies between the limits of 0 and 1, and covers the entire spectrum of materials types from the most brittle types to the most ductile types, and all those in between. Next, a polynomial expansion in the isotropic invariants of stress is used to define the representation for the elastic energy of the body, and most importantly, also used independently for the representation defining the limits of this constitutive form. This latter result is then the polynomial invariants failure criterion. Although this criterion provides the basic and guiding theoretical form, it is shown that it cannot provide the complete and all-inclusive failure description. There must be a competitive fracture criterion in certain ranges of T/C, and this fracture criterion is found to be controlled by the maximum principal stress. These two failure criteria, controlled by only T and C, cover all the types of isotropic materials where failure represents the cessation of linear elastic behavior, whether the failure event is that of brittle fracture or plastic flow.

The characterization of failure for materials has been a longstanding, even classical topic. The incentive to define failure criteria for application to all types of materials under all types of stress states has always been a primary, vital objective. The history of these endeavors is rich with the noble efforts of some the worlds greatest scientists. The history is also littered with a huge variety of vain and failed attempts at prescribing failure criteria. The great scientists and serious investigators, in no particular order, include: Coulomb, Maxwell, Lord Kelvin, von Mises, Mohr, von Karman, Rankine, Saint-Venant, Lame, G. I. Taylor, Timoshenko, Drucker, Prager, Griffith, and many others. None succeeded in producing a complete and useful general theory of failure, only fragmentary steps of advancement were made. In defining the meaning of failure for materials it is necessary to be very careful and fully explicit on the meaning of homogeneity and its scale significance and upon the qualifications that must attend the concept of macroscopic failure. It is also important to recognize the role of fracture mechanics and its contributions to the separate development of failure criteria for homogeneous materials.

This chapter presents conditions for determining the limits of elastic behaviour for isotropic materials. The stress invariants of equivalent pressure, equivalent shear stress, and equivalent tensile stress are defined. These are then used to define common yield conditions, viz. the pressure-independent Mises and Tresca yield conditions, as well as the pressure-dependent Coulomb-Mohr and the Drucker-Prager yield conditions. Rankine’s failure criterion for brittle materials in tension, that is failure in a brittle material will initiate when the maximum principal stress at a point in the body reaches a critical value, is also discussed.

Definitions of yield stress and failure stress (strength) have always been subject to great variations in understanding and implementation. There is no agreement on the proper definitions of these properties that are needed for the use of failure criteria. There are only individual preferences that usually are not even stated when reporting data-derived properties. Rational definitions are derived for both the yield stress and the failure stress. The yield stress definition is that of the stress at which the second derivative of the stress versus strain attains a maximum. Unfortunately this definition is difficult to implement from typical testing data, so an approximation is derived in an “offset” form. The failure-stress definition is specified in terms of some energy characteristics that are easily found from the stress–strain curves. Both definitions for yield stress and failure stress can be used with the failure criteria derived from relevant failure theories.

There has always been some confusion about the separate roles of fracture mechanics and failure criteria for homogeneous and isotropic materials. To clarify this situation the historical development of fracture mechanics is briefly reviewed so that it can be seen side by side with the failure theory for the homogeneous materials discussed in the book. To further amplify the differences and the unique capabilities of both disciplines, two typical problems are posed and examined—one for fracture mechanics and one for failure criteria. The fracture-mechanics problem involves the critical size for an edge crack in a structural member. The failure-criteria problem is that of deducing the location of the local failure for a rigid spherical inclusion embedded in an infinite elastic medium under far-field load. The complementary capabilities and individual advantages of the two fields are placed in proper perspective.

Managing an infectious disease threat requires, first, determining the extent of the threat, and, second, identifying the nature of the threat. This is often not straightforward. Once the nature and severity of the threat have been identified, it is essential to develop a management plan. Management plans require the following: clear objectives; evaluation of costs, benefits, and risks; capacity for adaptation; and clear success and failure criteria, together with stopping rules. Objectives might include: (i) preventing arrival and establishment of an infectious agent; (ii) eliminating an infectious agent from a population, region, or even globally; (iii) allowing the continued persistence of a population in the presence of disease; or (iv) using an infectious agent for the biological control of an invasive or pest species. These objectives are explored in detail in Chapters 12–15. Disease management also raises ethical questions, dealt with in Chapter 16 of the book.