The simulation of high-rate deformation and failure of metals is has traditionally been performed using Lagrangian finite element methods or Eulerian hydrocodes. Lagrangian mesh-based methods are limited by issues involving mesh entanglement under large deformation and considerable complexity in handling contact. On the other hand, Eulerian hydrocodes are prone to material diffusion. In the Material Point Method (MPM), the material state is defined on solid Lagrangian particles. The particles interact with other particles in the same body, with other solid bodies, or with fluids through a background mesh. Thus, some of the problems associated with finite element codes and hydrocodes are alleviated. Another attractive feature of the material point method is the ease with which large deformation, fully coupled, fluid-structure interaction problems can be handled. In this work, we present MPM simulations that involve large plastic deformations, contact, material failure and fragmentation, and fluid-structure interaction.

Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean momentum balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.

Recent efforts by the present authors have focused on the fundamental multiscaling behaviors of the time averaged dynamical equations of wall turbulence. These efforts have generated a number of new results relating to dynamical structure, as well as a new mathematical foundation. Central to this has been the development of the so-called method of scaling patches. This method provides a formalism for determining scaling behaviors directly from the indeterminate equations. A general description of this methodology is provided herein, and in doing so its connections to well-established scaling notions are identified. Example problems for which the method has been successfully applied includes turbulent boundary layer, pipe and channel flows, turbulent Couette-Poiseuille flow, fully developed turbulent heat transfer in a channel, and favorable pressure gradient boundary layers.

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid flow with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment based on the concept of a scaling patch that justifies and greatly extends these empirical results. The primary hypothesis in this development is the monotone and limiting Peclet number dependence (at fixed Reynolds number) of the difference between the specially scaled centerline and wall temperatures. This fact is well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Peclet numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like mean temperature profiles are established. Throughout the paper, the classical arguments based on an assumed overlapping of regions where the inner and outer scalings are valid are avoided.

Experimental and numerical data of the Reynolds shear stress in turbulent channel and pipe flows under a mesonormalization are presented. The mesolength scale associated with this normalization is intermediate to the traditional inner and outer lengths. Justification,for the mesoscales is provided by a direct analysis of the mean momentum equation. Specifically, the mesonormalization is revealed through a resealing that appropriately reflects the physics of an internal mesolayer within which a balance breaking, and subsequent balance exchange of terms in the mean momentum equation takes place. Direct numerical simulation and experimental data are examined and. shown to be in good agreement with the new scaling, supporting the new theory.

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment which justifies and greatly extends these empirical results. The main hypothesis in this development is the monotone and limiting dependence of the difference between the specially scaled centerline and wall temperatures on the Prandtl number, a fact well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Prandtl numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like profiles are found.

This paper provides a multiscale analytical study of steady incompressible turbulent flow through a channel of either Couette or pressure-driven Poiseuille type. Mathematically, the paper's two most novel features are that (1) the analysis begins with an underdetermined singular perturbation problem, namely the Reynolds averaged mean momentum balance equation, and (2) it leads to the existence of an infinite number of length scales. (These two features are probably linked, but the linkage will not be pursued.) The paper develops a credible assumption of a mathematical nature which, when added to the initial underdetermined problem, results in a knowledge of almost the complete layer (scaling) structure of the mean velocity and Reynolds stress profiles. This structure in turn provides a lot of other important information about those profiles. The possibility of almost-logarithmic sections of the mean velocity profile is given special attention. The sense in which the length scales are asymptotically proportional to the distance from the wall is determined. Most traditional theoretical analyses of these wall-bounded flows are based ultimately on either the classical overlap hypothesis, mixing length concepts, or similarity arguments. The present paper avoids those approaches and their attendant assumptions. Empirical data are also not used, except that the Reynolds stress takes on positive values. Instead, reasonable criteria are proposed for recognizing scaling layers in the flow, and they are then used to determine the scaling structure and much more information.

Steady Couette and pressure-driven turbulent channel flows have large regions in which the gradients of the viscous and Reynolds stresses are approximately in balance (stress gradient balance regions). In the case of Couette flow, this region occupies the entire channel. Moreover, the relevant features of pressure-driven channel flow throughout the channel can be obtained from those of Couette flow by a simple transformation. It is shown that stress gradient balance regions are characterized by an intrinsic hierarchy of ‘scaling layers’ (analogous to the inner and outer domains), filling out the stress gradient balance region except for locations near the wall. The spatial extent of each scaling layer is found asymptotically to be proportional to its distance from the wall. There is a rigorous connection between the scaling hierarchy and the mean velocity profile. This connection is through a certain function $A(y^+)$ defined in terms of the hierarchy, which remains $O(1)$ for all $y^+$. The mean velocity satisfies an exact logarithmic growth law in an interval of the hierarchy if and only if $A$ is constant. Although $A$ is generally not constant in any such interval, it is arguably almost constant under certain circumstances in some regions. These results are obtained completely independently of classical inner/outer/overlap scaling arguments, which require more restrictive assumptions. The possible physical implications of these theoretical results are discussed.

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available high-quality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds number approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds number and have the same order of magnitude, there is additional theoretical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

A known difficulty with using the Clauser chart method to determine the friction velocity in wall bounded flows is that it assumes, a priori, a logarithmic law for the mean velocity profile. Using both experimental and DNS data in the literature, this note explicitly shows how friction velocities obtained using the Clauser chart method can potentially mask subtle Reynolds-number-dependent behavior.

Domain formation is modeled on the surface of giant unilamellar vesicles using a Landau field theory model for phase coexistence coupled to elastic deformation mechanics (e.g., membrane curvature). Smooth particle applied mechanics, a form of smoothed particle continuum mechanics, is used to solve either the time-dependent Landau-Ginzburg or Cahn-Hilliard free-energy models for the composition dynamics. At the same time, the underlying elastic membrane is modeled using smooth particle applied mechanics, resulting in a unified computational scheme capable of treating the response of the composition fields to arbitrary deformations of the vesicle and vice versa. The results indicate that curvature coupling, along with the field theory model for composition free energy, gives domain formations that are correlated with surface defects on the vesicle. In the case that external deformations are included, the domain structures are seen to respond to such deformations. The present simulation capability provides a significant step forward toward the simulation of realistic cellular membrane processes.

An approach to solving tightly coupled, large deformation, uid structure interac- tion problems is presented. The approach uses a theoretical model for the averaged behavior of multiple materials, called the \multield model". Solutions to the mul- tield model equations are obtained using a scheme that combines a Lagrangian technique called the \Material Point Method" with a multield Eulerian method. In this scheme, the thermodynamic state of each eld is integrated forward in time using one of two frames of reference. Embedded structures are integrated in the Lagrangian frame, uids are integrated in the Eulerian frame. The MPM divides a solid structure into a collection of nite masses and uses a computational grid to aect the update of their states in the Lagrangian frame. A common reference frame is required for evaluation of the interactions associated with exchange of mass, momentum, and energy among elds; for these interactions, the Eulerian frame is chosen. The theoretical model is outlined briey and the numerical scheme is described in detail. Findings from a numerical order of accuracy study are pre- sented. Results from simulations of three dieren t scenarios are compared with corresponding known solutions to validate the approach. Finally a demonstration calculation is presented to illustrate some of the unique capabilities of the approach.

An approach to solving tightly coupled, large deformation, uid structure interaction problems is presented. The approach uses a theoretical model for the averaged behavior of multiple materials, called the \multield model. Solutions to the multield model equations are obtained using a scheme that combines a Lagrangian technique called the \Material Point Method with a multield Eulerian method. In this scheme, the thermodynamic state of each eld is integrated forward in time using one of two frames of reference. Embedded structures are integrated in the Lagrangian frame, uids are integrated in the Eulerian frame. The MPM divides a solid structure into a collection of nite masses and uses a computational grid to aect the update of their states in the Lagrangian frame. A common reference frame is required for evaluation of the interactions associated with exchange of mass, momentum, and energy among elds; for these interactions, the Eulerian frame is chosen. The theoretical model is outlined briey and the numerical scheme is described in detail. Findings from a numerical order of accuracy study are presented. Results from simulations of three dieren t scenarios are compared with corresponding known solutions to validate the approach. Finally a demonstration calculation is presented to illustrate some of the unique capabilities of the approach.

A numerical algorithm for tightly coupled, high-deformation fluid-structure interaction problems is presented. The foundation of the method is the integration of a Lagrangian particle technique (the Material Point Method, or MPM) with a multimaterial Eulerian code. In this approach, each material is described and evolves in its preferred reference frame (e.g., Lagrangian for solids, Eulerian for fluids). The MPM uses a background mesh to update particle states. By using the Eulerian multi-material mesh as the background mesh to update particle states, the solid materials have a dual representation in the Lagrangian and Eulerian frame. It is in this common reference frame that coupling interactions among materials are computed through momentum and energy exchange terms in the multi-field equations. The approach is outlined and results from a numerical order-of-accuracy study are presented. Simulation results are compared with known solutions for the stress distribution in a pressurized cylinder. It is shown that the combined approach has the same order-of accuracy as the stand-alone material point method and gives excellent agreement with exact solutions for this geometry.

A tightly coupled fluid-structure interaction (FSI) solution technique incorporating fluid and solid mechanics, phase change and chemical reactions is presented. The continuum equations are solved with a cell-centered, multi-material ICE solution method. This formulation is integrated with a Lagrangian, particle based, solid mechanics technique, known as the Material Point Method, as described by Kashiwa et al. [1] and Guilkey et al. [2]. The combined method can handle large deformations and phase change within a single grid, without the need of separate domains for fluids and solids, or the passing of boundary conditions. This paper discusses algorithmic issues involved in accounting for chemical reactions and phase transition among material phases (e.g., solid --> gas). Validation is presented as are simulations showing large deformation with phase change. These simulations were performed within a computational framework that contains tools for parallelization, performance analysis, data management, algorithm integration, and data visualization. Features of this framework are described.