In this chapter, roughly three perspectives are presented and discussed based on the author’s own views, which are at least conceptually informative and expected to greatly help enrich the understanding of “corporation” aspects of multiscale plasticity, either directly or indirectly. The topics chosen are “small world network,” “global analysis,” and “bio-inspired mechanics.” The first subject is related to an issue how the microscopic and macroscopic degrees of freedoms are organically interrelated in hierarchically constituted complex material systems. The last topic is about much more complex systems than the materials, that is, bio-systems, from which we expect to gain numerous insights for tackling our problems in more advanced fashion. Roughly two implications are picked up here, that is, “irreducible structure of life” and “tight coupling versus loose coupling” controversy in terms of the mechanism of bio-motors. The latter is evidently associated with the previously mentioned “weak ties.”

Like the previous question about “FCC versus BCC” posed in Chapter 1, here is another interesting question of a very fundamental kind that few might be able to answer clearly and appropriately: What is (are) the substantial distinction(s) between single crystals and polycrystals in terms of plasticity? Of course the secondary and tertiary factors such as the effect of “textures” should be excluded. This question is extensively discussed in this section.

This chapter intends to overview the field theory of multiscale plasticity (FTMP) in terms of the key concepts (keywords), the basic theories, and the fundamental hierarchical recognition (i.e., the identification of important scales). This will be followed by the introductions of several new features that the author himself has found and introduced afresh. Practically, the theory is applied via the crystal plasticity formalism-based framework as a tentative and convenient vehicle. So, the constitutive framework together with some detailed sets of modeling for the evolution equations therein is are also presented in the present chapter, i.e., strain gradient terms for the dislocation-density and the incompatibility tensors.

As we have seen in Chapter 3, much of the microscopic “specificities” are renormalized into a limited number of degrees of freedom at dislocation substructure scale (Scale A), especially into those with “cellular” morphology, essentially extending over 3D crystalline space. Therefore, as a critical step toward the successful multiscale plasticity, we are required to be ready to answer the following questions about the 3D cell structure; “why do they need the 3D ‘cellular’ morphology?,” “what is the substantial role, especially against the mechanical properties?,” why does the well-documented ‘universality’ manifested as a similitude law, hold?, and “how the microscopic degrees of freedom (information) are stored and when will they be released?” The first goal of this chapter is to derive an effective theory governing the dislocation substructure evolutions, particularly, cellular patterning, from a dislocation theory-based microscopic description of Hamiltonian through a rational “coarse-graining” procedure provided by the method of quantum field theory (QFT) (see Chapter 8). Secondly, after presenting some representative simulation results, an extensive series of discussions on the cell formation mechanisms and the mechanical roles are discussed and identified.

The completion of the theory for MMMs (multiscale modeling of materials) is manifested itself partially as an identification of the right “flow-evolutionary” law explicitly, which describes generally the evolution of the inhomogeneous fields and the attendant local plastic flow accompanied by energy dissipation. The notion “duality” ought to be embodied by this law, although it still is a “working hypothesis,” deserving further investigations. Specifically, it represents the interrelationship between the locally stored strain energy and the local plastic flow as has been discussed in the context of polycrystalline plasticity in Chapter 12 for Scale C. In this final chapter, we will derive explicitly a candidate form of the flow-evolutionary law as a possible embodiment of the duality, which is followed by application examples.

In Chapter 11, we studied the forces in machine systems in which all forces on the bodies were in balance, and therefore the systems were in either static or dynamic equilibrium. However, in real machines this is seldom, if ever, the case except when the machine is stopped. We learned in Chapter 4 that although the input crank of a machine may be driven at constant speed, this does not mean that all points of the input crank have constant velocity vectors or that other links of the machine operate at constant speeds. In general, there will be accelerations, and therefore machines with moving parts having mass are not balanced.

The existence of vibrating elements in a mechanical system produces unwanted noise, high stresses, wear, poor reliability, and, frequently, premature failure of one or more of the parts. The moving parts of all machines are inherently vibration producers, and for this reason engineers must expect vibrations to exist in the devices they design. But there is a great deal they can do during the design of the system to anticipate a vibration problem and to minimize its undesirable effects.

Balancing is defined here as the process of correcting or eliminating unwanted inertia forces and moments in rotating machinery. In previous chapters, we have seen that shaking forces on the frame can vary significantly during a cycle of operation. Such forces can cause vibrations that at times may reach dangerous amplitudes. Even if they are not dangerous, vibrations increase component stresses and subject bearings to repeated loads that may cause parts to fail prematurely by fatigue. Thus, in the design of machinery, it is not sufficient merely to avoid operation near the critical speeds; we must eliminate, or at least reduce, the dynamic forces that produce these vibrations in the first place.

In the previous chapters we learned how to analyze the kinematic characteristics of a given mechanism. We were given the design of a mechanism, and we studied ways to determine its mobility, its posture, its velocity, and its acceleration, and we even discussed its suitability for given types of tasks. However, we have said little about how the mechanism is designed – that is, how the sizes and shapes of the links are chosen by the designer.

In our studies of kinematic analysis in the previous chapters, we limited ourselves to consideration of the geometry of the motions and of the relationships between displacement and time. The forces required to produce those motions or the motion that would result from the application of a given set of forces were not considered. We are now ready for a study of the dynamics of machines and systems. Such a study is usually simplified by starting with the statics of such systems.

The large majority of mechanisms in use today have planar motion, that is, the motions of all points produce paths that lie in a single plane or in parallel planes. This means that all motions can be seen in true size and shape from a single viewing direction and that graphic methods of analysis require only a single view. If the coordinate system is chosen with the x and y axes parallel to the plane(s) of motion, then all z values remain constant, and the problem can be solved, either graphically or analytically, with only two-dimensional methods. Although this is usually the case, it is not a necessity. Mechanisms having three-dimensional point paths do exist and are called spatial mechanisms. Another special category, called spherical mechanisms, have point paths that lie on concentric spherical surfaces.