Showing papers in "Advances in Applied Mechanics in 1997"

Delamination of Compressed Thin Films

Abstract: In this article, we specifically concern ourselves with the buckling-driven delamination mechanism, whereby a portion of the film buckles away from the substrate, thereby forming a blister (also termed buckle or wrinkle). Blisters may grow by interfacial fracture, a process which, under the appropriate conditions, may result in the catastrophic failure of the component. Blisters are often observed to adopt convoluted-even bizarre shapes and to fold into intricate patterns. A principal objective of this article is to review some recent developments based on the use of direct methods of the calculus of variations which have proven useful for understanding the mechanics of folding of thin films (Ortiz and Gioia, 1994). These developments are reviewed in Section III, which is extracted from the original publication. The remaining sections are devoted to the application of these principles to the problem of predicting the shape of thin-film blisters.

Computational Mechanics for Metal Deformation Processes Using Polycrystal Plasticity

Abstract: Publisher Summary This chapter discusses computational mechanics for metal deformation processes using polycrystal plasticity. The chapter presents a methodology for utilizing polycrystal plasticity as the constitutive description in simulations of large-strain metal-forming processes. An unstressed crystal lattice always retains the same internal arrangement of crystal planes and directions, regardless of the level of plastic strain. A crystal's orientation is simply that rotation needed to align a set of axes fixed to its lattice with a reference frame. The orientations of crystal lattices are discussed in terms of these rotations and the different parameterizations of such a rotation. With respect to the plastic deformation of crystals, equivalent orientations must exhibit both the identical geometric arrangement of atoms and identical strengths in the associated deformation mode. The inelastic response of a metal to an applied loading may involve one or more deformation mechanisms, such as crystallographic slip, diffusional creep, and twinning. The dominant mechanism, at any instant, depends on the regime of temperature and strain rate, as well as the microstructural condition of the material. The rotation of individual crystals during deformation modifies the orientation distribution of crystals that comprise the material. The evolution of the orientation distribution by using the finite-element method is also elaborated.

Buckling analysis of elastic structures : A computational approach

Abstract: Publisher Summary This chapter presents a computational approach to the buckling analysis of elastic structures A short description of the path-following method used for the computation of the static equilibrium branches, together with additional techniques that are needed for the analysis of these solutions, is presented The structural models are supposed to be purely elastic It is further assumed that an appropriate discretization procedure is available that allows to represent the state of the structure in terms of a vector of finite dimension One aspect of the formulation that needs consideration is the parametrization of the governing equations In the case of a one-parameter loading, the load intensity emerges as the natural parameter that steers the deformation process in the actual physical case The energy criterion states that if the potential energy of the structure at the equilibium state under consideration is a proper minimum, no matter how shallow or small it is, the equilibrium is stable The energy criterion can be interpreted as a geometrical analog of Lyapunov's dynamical criterion, because it can be seen as a rule that connects the geometrical properties of the potential energy function of the mechanical system at the equilibrium state, to the dynamical properties of the system at this state The stability and reactive forces at the critical states are also elaborated

Forced Generation of Solitary-Like Waves Related to Unstable Boundary Layers

Abstract: Publisher Summary This chapter elaborates the forced generation of solitary-like waves related to unstable boundary layers. In an incompressible, steady, two-dimensional boundary-layer flow on a flat plate, instability evolves in the form of Tollmien–Schlichting linear eigenmodes if the Reynolds number exceeds a certain critical value. A linear stage of the wave development can be kept approximately two-dimensional over a long distance, provided that a disturbing source is carefully controlled during measurements. The basic mechanism underlying the manifestation of the periodically produced solitary-like waves can be attributed to their excitation as nonlinear eigenmodes in both systems. On the other hand, the shapes of the corresponding limit cycles in the phase plane, display some intrinsic characteristics depending on the model. The instantaneous displacement thickness is evaluated simultaneously with the velocity field in the near-wall viscous sublayer. This feature makes the triple deck dissimilar to the classical boundary-layer theory of Prandtl. The truly nonlinear disturbances propagating through the Blasius boundary layer are described. Some characteristic features of forced oscillations are also presented.

The mathematical foundation of plasticity theory

Abstract: Supporting the mathematical theory of plasticity, two pillars constituting the modeling of yield behavior are the convexity and normality conditions on a yield function. The models so established have been time tested to hold for a wide class of ductile materials in many practical applications of the theory. Their logical basis was the belief that a material does not release energy during plastic defor- mation (nonnegative dissipation). Even though the theory is sound, the lack of a mathematical proof on normality still causes some researchers to call it a pos- tulate. In this paper, we shall dismiss this notion of assumption by introducing a generalized Holder inequality. The normality relation becomes a requirement for the inequality to be sharp (equality inclusive). This inequality also reveals the primal-dual relation of stress and strain rate. Even before this connection of the mathematical and physical implications, different duality relations were used in many known minimax theorems in plasticity. We shall claim that convexity, nor- mality, and duality, all properties of the generalized Holder inequality, complete the foundation for the constitutive modeling of the mathematical theory of plasticity. By using these models, the minimax formulations of plasticity problems can be derived in a systematic and unified approach.