Kumar K. Tamma

Microscale permeability predictions of porous fibrous media

A good understanding of woven fiber preform permeabilities is critical in the design and optimization of the composite molding processes encountered in resin transfer molding (RTM); yet these issues remain unresolved in the literature. Many have attempted to address permeability predictions for flat undeformed fiber preform, but few have investigated permeability variations for complex geometries of porous fibrous media. In this study, the objectives are to: (i) provide a brief review of existing methods for the prediction of the fiber mat permeability; (ii) postulate a more realistic representation of a unit cell to account for such fabric structures as crimp, tow spacing and the like; and (iii) apply computational approximations to predict effective permeabilities for use in modeling of structural composites manufacturing processes. The Stokes equation is used to model the flow in the inter-tow region of the unit cell, and in the intra-tow region, the Brinkmans equation is used. Initial permeability calculations are performed for a three-dimensional unit cell model representative of the PET-61 woven fabric composite. The results show good agreement with experimental data published in the literature.

The time dimension: A theory towards the evolution, classification, characterization and design of computational algorithms for transient/ dynamic applications

SummaryVia new perspectives, for the time dimension, the present exposition overviews new and recent advances describing a standardized formal theory towards the evolution, classification, characterization and generic design of time discretized operators for transient/dynamic applications. Of fundamental importance in the present exposition are the developments encompassing the evolution of time discretized operators leading to the theoretical design of computational algorithms and their subsequent classification and characterization. And, the overall developments are new and significantly different from the way traditional modal type and a wide variety of step-by-step time marching approaches which we are mostly familiar with have been developed and described in the research literature and in standard text books over the years. The theoretical ideas and basis towards the evolution of a generalized methodology and formulations emanate under the umbrella and framework and are explained via a generalized time weighted philosophy encompassing the semi-discretized equations pertinent to transient/dynamic systems. It is herein hypothesized that integral operators and the associated representations and a wide variety of the so-called integration operators pertain to and emanate from the same family, with the burden which is being carried by a virtual field or weighted time field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi-discretized equation system. Subsequently, the selection or burden carried by the virtual or weighted time fields originally introduced to facilitate the time discretization process determines the formal development and outcome of “exact integral operators”, “approximate integral operators”, including providing avenues leading to the design of new computational algorithms which have not been exploited and/or explored to-date and the recovery of most of the existing algorithms, and also bridging the relationships systematically leading to the evolution of a wide variety of “integration operators”. Thus, the overall developments not only serve as a prelude towards the formal developments for “exact integral operators”, but also demonstrate that the resulting “approximate integral operators” and a wide variety of “new and existing integration operators and known methods” are simply subsets of the generalizations of a standardizedWp-Family, and emanate from the principles presented herein. The developments first leading to integral operators in time, and the resulting consequences then systematically leading to not only providing new avenues but additionally also explaining a wide variety of generalized integration operators in time of which single-step time integration operators and various widely recognized algorithms which we are familiar are simply subsets, the associated multi-step time integration operators, and a class of finite element in time integration operators, and their relationships are particularly addressed. The theoretical design developments encompass and explain a variety of time discretized operators, the recovery of various original methods of algorithmic development, and the development of new computational algorithms which have not been exploited and/or explored to-date, and furthermore, permit time discretized operators to be uniquely classified and characterized by algorithmic markers. The resulting and so-called discrete numerically assigned [DNA] algorithmic markers not only serve as a prelude towards providing a standardized formal theory of development of time discretized operators and forum for selecting and identifying time discretized operators, but also permit lucid communication when referring to various time discretized operators. That which constitutes characterization of time discretized operators are the so-called DNA algorithmic markers which essentially comprise of both: (i) the weighted time fields introduced for enacting the time discretization process, and (ii) the corresponding conditions (if any) these weighted time fields impose (dictate) upon the approximations for the dependent field variables and updates in the theoretical development of time discretized operators. As such, recent advances encompassing the theoretical design and development of computational algorithms for transient/dynamic analysis of time dependent phenomenon encountered in engineering, mathematical and physical sciences are overviewed.

Asymptotic expansion homogenization for heterogeneous media: computational issues and applications

Developments in asymptotic expansion homogenization (AEH) are overviewed in the context of engineering multi-scale problems. The problems of multi-scales presently considered are those linking continuum level descriptions at two different length scales. Concurrent research in the literature is first described. A recipe of the AEH approach is then presented that can be used for future developments in many areas of material and geometric non-linear continuum mechanics. Then, a derivation is outlined using the finite element method that is useful for engineering applications that leads to coupled hierarchical partial differential equations in elasticity. The approach provides causal relationships between macro and micro scales wherein procedures for homogenization of properties and localization of small-scale response are built-in. A brief discussion of a physical paradox is introduced in the estimation of micro-stresses that tends to be a barrier in the understanding of the method. Computational issues are highlighted and illustrative applications in linear elasticity are then presented for composites containing microstructures with complex geometries.

Macroscale and microscale thermal transport and thermo-mechanical interactions: Some noteworthy perspectives

Some noteworthy and historical perspectives and an overview of macroscale and microscale heat transport behavior in materials and structures are presented. The topic of heat waves is also discussed. The significance of constitutive models for both macroscale and microscale heat conduction are described in conjunction with generalizations drawn concerning the physical relevance and the role of relaxation and retardation times emanating from the Jeffreys type heat flux constitutive model, with consequences to the Cattaneo heat flux model and subsequently to the Fourier heat flux model. Both macroscopic model formulations for applications to macroscopic heat conduction problems and two-step models for use in specialized applications to account for microscale heat transport mechanisms are overviewed with emphasis on the proposition of a Generalized Two-Step relaxation / retardation time-based heating model. So as to bring forth a variety of issues in a single forum, illustrative numerical applications are ove...

Woven fabric composites - Developments in engineering bounds, homogenization and applications

Various approaches for approximating upper and lower bounds for the elastic stiffness tensor for general woven fabric composites are first described. Well accepted minimum energy principles are briefly presented to establish the foundation for practical finite element procedures for determining these bounds. Secondly, comparisons of four common homogenization procedures are shown: the strain energy balance method, the plate approximation method, a direct approach via area averaging, and asymptotic expansion homogenization. As a limiting case, all of the methods obtain the well-known Rule of Mixtures for a unidirectional uniaxial specimen. In attempting to consolidate much of the existing knowledge of structural constitutive models for woven fabric composites, this research seeks to summarize and compare various homogenization methods via finite element analyses. Finally, some illustrative applications are presented. Copyright

Time discretized operators. Part 1: towards the theoretical design of a new generation of a generalized family of unconditionally stable implicit and explicit representations of arbitrary order for computational dynamics

The new generation of a generalized family of time discretized operators encompassing implicit and explicit representations that are unconditionally stable and which theoretically inherit Nth-order time accurate features developed in Part 1 are restricted here in Part 2 of the exposition to second-order time accurate operators. As such, unconditionally stable implicit representations are first described followed by unconditionally stable explicit representations. The theoretical design leading to computational algorithms with excellent algorithmic attributes for applicability to practical situations are also addressed for both the implicit and explicit unconditionally stable representations of time discretized operators. Attention is first focused on linear problems and extensions to nonlinear situations are subsequently briefly addressed.

Recent Developments Encompassing Non-Isothermal/Isothermal Liquid Composite Molding Process Modeling/Analysis: Physically Accurate, Computationally Effective, and Affordable Simulations and Validations

The mathematical and associated computational modeling and analysis of mold filling, heat transfer, and polymerization reaction kinetics in Resin Transfer Molding (RTM) are quite complex and not only require accurate computational approaches to capture the process physics during the simulations, but also must permit complex geometric configurations to be effectively analyzed. The process simulations at a macroscopic level require the representative macroscopic constitutive behavior which can be predicted from a microscopic analysis of the representative volume element (RVE) of the fiber preform configurations. This is first presented here for purposes of illustration in reference to determination of the preform flow permeabilities. Next, an effective integrated micro/macro approach and developments including a viable flow solution modeling and analysis methodology with emphasis on providing improved physical accuracy of solutions and computational advantages are described for the transient flow progression inside a mold cavity filled with a fiber preform under isothennal and non-isothermal flow conditions. The improved physical accuracy and the overall effectiveness of the new computational developments for realistic process modeling simulations are first demonstrated for isothermal conditions. Subsequently, the new integrated flow/ thermal methodology and developments are extended for non-isothermal conditions. The highly advective nature of the non-isothermal conditions involving thermal and polymerization reactions also require special numerical considerations and stabilization techniques and are also addressed here. Finally, validations and comparisons are presented with available analytical and experimental results whenever feasible. Emphasis is also placed upon demonstrations for practical engineering problems.

Specially tailored transfinite-element formulations for hyperbolic heat conduction involving non-Fourier effects

The phenomenon of hyperbolic heat conduction in contrast to the classical (parabolic) form of Fourier heat conduction involves thermal energy transport that propagates only at finite speeds as opposed to an infinite speed of thermal energy transport. To accommodate the finite speed of thermal wave propagation, a more precise form of heat flux law is involved, thereby modifying the heat flux originally postulated in the classical theory of heat conduction. As a consequence, for hyperbolic heat conduction problems, the thermal energy propagates with very sharp discontinuities at the wave front. The primary purpose of the present paper is to provide accurate solutions to a class of one-dimensional hyperbolic heat conduction problems involving non-Fourier effects that can precisely help understand the true response and furthermore can be used effectively for representative benchmark tests and for validating alternate schemes. As a consequence, the present paper purposely describes modeling/analysis formulatio...

Heat transfer - A review of 2001 literature

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Robust control of flexible manipulators via μ-synthesis

Abstract An experimental flexible arm serves as testbed to investigate the efficacy of the μ -synthesis design technique in the control of flexible manipulators. A linearized model of the testbed is derived for control design. Discrepancies and errors between the linearized model and the physical system are accounted for in the control design via uncertainty models. These uncertainties include: unmodeled high-frequency dynamics, errors in natural frequencies and damping levels and actuator and sensor errors. Colocated and noncolocated controllers are designed using μ -synthesis. It is observed, theoretically and experimentally, that the μ -synthesis design technique is a viable control tool for tip tracking with flexible manipulators.