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One of the largest improvements to CINEMA 4D R12 is in the dynamics engine that drives the Rigid and Soft Body dynamics. The relationship between these engines and the MoGraph elements are especially rewarding. Along with checking out the latest and greatest in dynamic simulations, we’ll also take a look at some of the best special effects options in the Hair and Cloth engines as well as CINEMA 4D's particle-effects powerhouse, PyroCluster.

Publisher Summary This chapter aims to present a brief coverage of the governing equations most widely adopted in the present element methods (DEM) approaches. It assumes that the general reader is familiar with the basics of continuum mechanics, the finite element method (FEM) as well as tensor analysis techniques. It provides Newton's equations of motion for particles. A rigid body characterized by a domain of constant volume and mass does not deform. The distance between any two points in a rigid body remains unchanged. A rigid body is an idealization as all bodies deform under the action of external forces. However, this idealization is acceptable in many rock engineering problems, especially large-scale block movements under low stress conditions. Rigid body dynamics is governed by Newton's law of motion and Euler's rotations of rigid bodies. The equations of motion for the deformable bodies are acceptable descriptions if the ‘small displacement’ assumption is accepted. However, the small deformation or rigid body assumptions are just two extreme cases of uncoupled deformation-motion conditions, and are not necessarily universally valid. Under certain circumstances, deformable bodies may undergo large-scale displacements but have small strains that need to be taken into account. The chapter also presents the basic equations for conductive heat transfer and some key thermal properties.

Numerous situations are encountered where treatment of the entire system as deformable bodies is neither necessary nor practical. This chapter presents the study of the first class of problems. This class of problems divides itself into two further subclasses: one where it is necessary to include some simple mechanisms of deformation in each body and the second in which the individual bodies have no deformation at all. The first class is called pseudo-rigid body deformational and the second rigid body behavior. This chapter illustrates how such behavior can be described and combined in a finite element system. It considers analysis of systems that are composed of many small bodies, each of which is assumed to undergo large displacements and a uniform deformation. A faceted shape can be constructed directly from a finite element discretization in which the elements are designated as all belonging to a single solid object or the individual bodies can be described by simple geometric forms, such as discs or ellipsoids. The pseudo-rigid body form can be directly extended to rigid bodies by using the polar decomposition on the deformation tensor.