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At least 217 records · Page 12

Application of fiber bridging models to fatigue crack growth in unidirectional titanium matrix composites

Several fiber bridging models were reviewed and applied to study the matrix fatigue crack growth behavior in center notched (0)(sub 8) SCS-6/Ti-15-3 and (0)(sub 4) SCS-6/Ti-6Al-4V laminates. Observations revealed that fatigue damage consisted primarily of matrix cracks and fiber matrix interfacial failure in the (0)(sub 8) SCS-6/Ti-15-3 laminates. Fiber-matrix interface failure included fracture of the brittle reaction zone and cracking between the two carbon rich fiber coatings. Intact fibers in the wake of the matrix cracks reduce the stress intensity factor range. Thus, an applied stress intensity factor range is inappropriate to characterize matrix crack growth behavior. Fiber bridging models were used to determine the matrix stress intensity factor range in titanium metal matrix composites. In these models, the fibers in the wake of the crack are idealized as a closure pressure. An unknown constant frictional shear stress is assumed to act along the debond or slip length of the bridging fibers. The frictional shear stress was used as a curve fitting parameter to available data (crack growth data, crack opening displacement data, and debond length data). Large variations in the frictional shear stress required to fit the experimental data indicate that the fiber bridging models in their present form lack predictive capabilities. However, these models provide an efficient and relatively simple engineering method for conducting parametric studies of the matrix growth behavior based on constituent properties.

Bakuckas, J. G., Jr.↗

Recursive dynamics for flexible multibody systems using spatial operators

Due to their structural flexibility, spacecraft and space manipulators are multibody systems with complex dynamics and possess a large number of degrees of freedom. Here the spatial operator algebra methodology is used to develop a new dynamics formulation and spatially recursive algorithms for such flexible multibody systems. A key feature of the formulation is that the operator description of the flexible system dynamics is identical in form to the corresponding operator description of the dynamics of rigid multibody systems. A significant advantage of this unifying approach is that it allows ideas and techniques for rigid multibody systems to be easily applied to flexible multibody systems. The algorithms use standard finite-element and assumed modes models for the individual body deformation. A Newton-Euler Operator Factorization of the mass matrix of the multibody system is first developed. It forms the basis for recursive algorithms such as for the inverse dynamics, the computation of the mass matrix, and the composite body forward dynamics for the system. Subsequently, an alternative Innovations Operator Factorization of the mass matrix, each of whose factors is invertible, is developed. It leads to an operator expression for the inverse of the mass matrix, and forms the basis for the recursive articulated body forward dynamics algorithm for the flexible multibody system. For simplicity, most of the development here focuses on serial chain multibody systems. However, extensions of the algorithms to general topology flexible multibody systems are described. While the computational cost of the algorithms depends on factors such as the topology and the amount of flexibility in the multibody system, in general, it appears that in contrast to the rigid multibody case, the articulated body forward dynamics algorithm is the more efficient algorithm for flexible multibody systems containing even a small number of flexible bodies. The variety of algorithms described here permits a user to choose the algorithm which is optimal for the multibody system at hand. The availability of a number of algorithms is even more important for real-time applications, where implementation on parallel processors or custom computing hardware is often necessary to maximize speed.

Jain, A.↗

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗

Ionizing radiation induces heritable disruption of epithelial cell interactions

Ionizing radiation (IR) is a known human breast carcinogen. Although the mutagenic capacity of IR is widely acknowledged as the basis for its action as a carcinogen, we and others have shown that IR can also induce growth factors and extracellular matrix remodeling. As a consequence, we have proposed that an additional factor contributing to IR carcinogenesis is the potential disruption of critical constraints that are imposed by normal cell interactions. To test this hypothesis, we asked whether IR affected the ability of nonmalignant human mammary epithelial cells (HMEC) to undergo tissue-specific morphogenesis in culture by using confocal microscopy and imaging bioinformatics. We found that irradiated single HMEC gave rise to colonies exhibiting decreased localization of E-cadherin, beta-catenin, and connexin-43, proteins necessary for the establishment of polarity and communication. Severely compromised acinar organization was manifested by the majority of irradiated HMEC progeny as quantified by image analysis. Disrupted cell-cell communication, aberrant cell-extracellular matrix interactions, and loss of tissue-specific architecture observed in the daughters of irradiated HMEC are characteristic of neoplastic progression. These data point to a heritable, nonmutational mechanism whereby IR compromises cell polarity and multicellular organization.

Non-NASA Center↗

Potential molecular targets for intervention in pelvic organ prolapse

Pelvic organ prolapse (POP) is a concerning gynecological benign illness in middle-aged and senior women. Its etiology is complex, the incidence rate is high, symptoms are clinically subjective, and its influence tends to be polarized. At present, for those who need medical treatment, whether surgical or non-surgical, complications cannot be ignored, and treatment effect needs to be optimized. However, there is a lack of accurate molecular biological interventions for the prevention, diagnosis, progression delay, and treatment of POP. Here, we reviewed the current state of understanding of the molecular mechanisms and factors associated with POP etiology. These factors include cyclins, matrix metal peptidases/tissue inhibitors of metalloproteinases, microRNAs, homeobox A11, transforming growth factor β1, insulin-like growth factor 1, fibulin 5, lysyl oxidase-like 1, oxidative stress, inflammatory response, estrogen, and other potential biomarkers associated with POP. In addition, relevant molecular targets that may be used to intervene in POP are summarized. The aim of this review was to provide more information to identify accurate potential biomarkers and/or molecular targets for the prevention, diagnosis, progression delay, and treatment of POP, with the goal of improving medical treatment for patients at-risk for POP or having POP. Continued research is needed to identify additional details of currently accepted molecular mechanisms and to identify additional mechanisms that contribute to POP.

Wu, Xia↗

Stress Intensity Factor Solutions for Multiple Edge Cracks in Ceramic Matrix Composites

NASA Lewis Research Center conducted a study to determine the stress intensity factor solutions for periodic arrays of bridged cracks for various crack spacings and crack lengths. Initially, the stress intensity factor of an array of unbridged multiple edge cracks was determined under constant global displacement as well as at a point load along the crack wake. These solutions are expected to contribute toward the development of a damage-based life-prediction methodology for CMC engine components.

Ghosn, Louis↗

Mechanical signaling and the cellular response to extracellular matrix in angiogenesis and cardiovascular physiology

Great advances have been made in the identification of the soluble angiogenic factors, insoluble extracellular matrix (ECM) molecules, and receptor signaling pathways that mediate control of angiogenesis--the growth of blood capillaries. This review focuses on work that explores how endothelial cells integrate these chemical signals with mechanical cues from their local tissue microenvironment so as to produce functional capillary networks that exhibit specialized form as well as function. These studies have revealed that ECM governs whether an endothelial cell will switch between growth, differentiation, motility, or apoptosis programs in response to a soluble stimulus based on its ability to mechanically resist cell tractional forces and thereby produce cell and cytoskeletal distortion. Transmembrane integrin receptors play a key role in this mechanochemical transduction process because they both organize a cytoskeletal signaling complex within the focal adhesion and preferentially focus mechanical forces on this site. Molecular filaments within the internal cytoskeleton--microfilaments, microtubules, and intermediate filaments--also contribute to the cell's structural and functional response to mechanical stress through their role as discrete support elements within a tensegrity-stabilized cytoskeletal array. Importantly, a similar form of mechanical control also has been shown to be involved in the regulation of contractility in vascular smooth muscle cells and cardiac myocytes. Thus, the mechanism by which cells perform mechanochemical transduction and the implications of these findings for morphogenetic control are discussed in the wider context of vascular development and cardiovascular physiology.

Non-NASA Center↗

Design for temperature and thermal buckling constraints employing a noneigenvalue formulation

A numerical procedure for simultaneous consideration of structural/thermal interactions during aircraft design is presented, with an emphasis on reentry vehicles such as the Orbiter. It has been shown that sequential design is inappropriate for reentry vehicles, due to the degradation of the material properties at elevated reentry temperatures. Attention is focused on thermal buckling, using an analytical technique that involves requiring that the stability matrix be positive definite, with the diagonal terms on the Gauss-Doolittle factor of the matrix also constrained to be positive. A finite element method is employed to calculate the derivative of the diagonal matrix, with optimization achieved by minimization of the mass of the structure and thermal protection system. Sample calculations are presented in terms of the aluminum structure and insulation for a section of the Orbiter wing bay.

Haftka, R. T.↗

A globally well-posed finite element algorithm for aerodynamics applications

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Iannelli, G. S.↗

Triangular covariance factorizations for

An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.

Thornton, C. L.↗

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I - Q(QTQ)-1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I - QTQT, with correction matrix T. When T = (QTQ)-1, and T is triangular, it is postulated that the best achievable orthogonality is $\mathcal{O}(ε)\mathcal{K}(A)$. We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a $\mathcal{O}(ε)\mathcal{K}[r_0, AV_m])$ stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Finally, further improvements in performance are achieved by accelerating GMRES on GPUs.

97 MATHEMATICS AND COMPUTING↗

Tensegrity: the architectural basis of cellular mechanotransduction

Physical forces of gravity, hemodynamic stresses, and movement play a critical role in tissue development. Yet, little is known about how cells convert these mechanical signals into a chemical response. This review attempts to place the potential molecular mediators of mechanotransduction (e.g. stretch-sensitive ion channels, signaling molecules, cytoskeleton, integrins) within the context of the structural complexity of living cells. The model presented relies on recent experimental findings, which suggests that cells use tensegrity architecture for their organization. Tensegrity predicts that cells are hard-wired to respond immediately to mechanical stresses transmitted over cell surface receptors that physically couple the cytoskeleton to extracellular matrix (e.g. integrins) or to other cells (cadherins, selectins, CAMs). Many signal transducing molecules that are activated by cell binding to growth factors and extracellular matrix associate with cytoskeletal scaffolds within focal adhesion complexes. Mechanical signals, therefore, may be integrated with other environmental signals and transduced into a biochemical response through force-dependent changes in scaffold geometry or molecular mechanics. Tensegrity also provides a mechanism to focus mechanical energy on molecular transducers and to orchestrate and tune the cellular response.

Review↗

Fibrous anisotropy and mineral gradients within the radula stylus of chiton: Controlled stiffness and damage tolerance in a flexible biological composite

Over hundreds of millions of years, organisms have evolved architected structures via precise control over hierarchically assembled components, including the integration of dissimilar materials. One such example is found in the radula system of chitons, intertidal mollusks that feed on algae growing on the rock. Their radula consists of multiple rows of ultrahard teeth, each integrated with a foldable belt-like substrate via a stiff, yet flexible stylus, which is essential for efficient rasping during the feeding process. Here, we investigate the nano and micro-scale components and architectures as well as regional mechanical properties of the stylus, and their subsequent role during the rasping of Cryptochiton stelleri. Three important factors were determined to contribute to the regio-specific stiffness of the stylus: the presence of mineral components, highly oriented chitinous fibers, and a chemically cross-linked protein matrix. All these factors are varied throughout the stylus. There is a high mineral content on the trailing edge close to the tooth and a cross-linked matrix on the leading edge, both with orientational specific oriented chitin fibers that provide force transduction to the tooth. Conversely, there is a significant lack of mineral or cross-linked matrix in the proximal end as well as a low degree of fiber orientation, resulting in a flexible region that can accommodate torsion and flexure during rasping. Understanding the graded composite structure of the stylus and applying this unique design to various engineering fields such as soft robotics, biotechnology, and the medical industry, can inspire the production of high-performance materials.

Lee, Jung-Eun↗

Tensor-GMRES method for large sparse systems of nonlinear equations

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Feng, Dan↗

Strain intensity factor approach for predicting the strength of continuously reinforced metal matrix composites

A method was previously developed to predict the fracture toughness (stress intensity factor at failure) of composites in terms of the elastic constants and the tensile failing strain of the fibers. The method was applied to boron/aluminum composites made with various proportions of 0 deg and +/- 45 deg plies. Predicted values of fracture toughness were in gross error because widespread yielding of the aluminum matrix made the compliance very nonlinear. An alternate method was develolped to predict the strain intensity factor at failure rather than the stress intensity factor because the singular strain field was not affected by yielding as much as the stress field. Far-field strains at failure were calculated from the strain intensity factor, and then strengths were calculated from the far-field strains using uniaxial stress-strain curves. The predicted strengths were in good agreement with experimental values, even for the very nonlinear laminates that contained only +/- 45 deg plies. This approach should be valid for other metal matrix composites that have continuous fibers.

Poe, Clarence C., Jr.↗

Strain intensity factor approach for predicting the strength of continuously reinforced metal matrix composites

A method was previously developed to predict the fracture toughness (stress intensity factor at failure) of composites in terms of the elastic constants and the tensile failing strain of the fibers. The method was applied to boron/aluminum composites made with various proportions of 0 to + or - 45 deg plies. Predicted values of fracture toughness were in gross error because widespread yielding of the aluminum matrix made the compliance very nonlinear. An alternate method was developed to predict the strain intensity factor at failure rather than the stress intensity factor because the singular strain field was not affected by yielding as much as the stress field. Strengths of specimens containing crack-like slits were calculated from predicted failing strains using uniaxial stress-strain curves. Predicted strengths were in good agreement with experimental values, even for the very nonlinear laminates that contained only + or - 45 deg plies. This approach should be valid for other metal matrix composites that have continuous fibers.

Poe, C. C., Jr.↗