Lie-group interpolation and variational recovery for internal variables

We propose a variational procedure for the recovery of internal variables, in effect extending them from integration points to the entire domain. The objective is to perform the recovery with minimum error and at the same time guarantee that the internal variables remain in their admissible spaces. The minimization of the error is achieved by a three-field finite element formulation. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an L2 projection that minimizes the distance between the source and target internal variables as measured in the L2 norm of the internal variable space. To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space

On the toughening of brittle materials by grain bridging:promoting intergranular fracture through grain angle, strength, andtoughness

The structural reliability of many brittle materials such asstructural ceramics relies on the occurrence of intergranular, as opposedto transgranular, fracture in order to induce toughening by grainbridging. For a constant grain boundary strength and grain boundarytoughness, the current work examines the role of grain strength, graintoughness, and grain angle in promoting intergranular fracture in orderto maintain such toughening. Previous studies have illustrated that anintergranular path and the consequent grain bridging process can bepartitioned into five distinct regimes, namely: propagate, kink, arrest,stall and bridge. To determine the validity of the assumed intergranularpath, the classical penentration/deflection problem of a crack impingingon an interface is reexamined within a cohesive zone framework forintergranular and transgranular fracture. Results considering both modesof propagation, i.e., a transgranular and intergranular path, reveal thatcrack-tip shielding is a natural outcome of the cohesive zone approach tofracture. Cohesive zone growth in one mode shields the opposing mode fromthe stresses required for cohesive zone initiation. Although stablepropagation occurs when the required driving force is equivalent to thetoughness for either transgranular or intergranular fracture, the mode ofpropagation depends on the normalized grain strength, normalized graintoughness, and grain angle. For each grain angle, the intersection ofsingle path and multiple path solutions demarcates "strong" grains thatincrease the macroscopic toughness and "weak" grains that decrease it.The unstable transition to intergranular fracture reveals that anincreasinggrain toughness requires a growing region of the transgranularcohesive zone be at and near the peak cohesive strength. The inability ofthe body to provide the requisite stress field yields an overdriven andunstable configuration. The current results provide restrictions for theachievement of substantial toughening through intergranularfracture

Construction of repeat-free fluorescence in situ hybridization probes

FISH probes are generally made out of BAC clones with genomic DNA containing a variable amount of repetitive DNA that will need to be removed or blocked for FISH analysis. To generate repeat free (RF) Probes without loss in genomic coverage, a random library is made from BAC clones by whole-genome amplification (WGA). Libraries are denatured in the presence of excess C0t-1 DNA and allowed to re-anneal followed by digestion of all double-stranded elements by duplex-specific nuclease (DSN). Selective amplification of all elements not containing repetitive sequences is realized by a sequential amplification. The final RF products can be re-amplified and used as a stock for future probe production. The RF probes have a lower background, the signal intensity build up is faster and there is no need for blocking DNA. The signal to background ratio of the RF was higher as compared to repeat containing probes

On the toughening of brittle materials by grain bridging: promoting intergranular fracture through grain angle, strength, and toughness

Abstract The structural reliability of many brittle materials such as structural ceramics relies on the occurrence of intergranular, as opposed to transgranular, fracture in order to induce toughening by grain bridging. For a constant grain boundary strength and grain boundary toughness, the current work examines the role of grain strength, grain toughness, and grain angle in promoting intergranular fracture in order to maintain such toughening. Previous studies have illustrated that an intergranular path and the consequent grain bridging process can be partitioned into five distinct regimes, namely: propagate, kink, arrest, stall and bridge. To determine the validity of the assumed intergranular path, the classical penentration/deflection problem of a crack impinging on an interface is reexamined within a cohesive zone framework for intergranular and transgranular fracture. Results considering both modes of propagation, i.e., a transgranular and intergranular path, reveal that crack-tip shielding is a natural outcome of the cohesive zone approach to fracture. Cohesive zone growth in one mode shields the opposing mode from the stresses required for cohesive zone initiation. Although stable propagation occurs when the required driving force is equivalent to the toughness for either transgranular or intergranular fracture, the mode of propagation depends on the normalized grain strength, normalized grain toughness, and grain angle. For each grain angle, the intersection of single path and multiple path solutions demarcates "strong" grains that increase the macroscopic toughness and "weak" grains that decrease it. The unstable transition to intergranular fracture reveals that an increasing grain toughness requires a growing region of the transgranular cohesive zone be at and near the peak cohesive strength. The Preprint submitted to Journal of the Mechanics and Physics of Solids 30 November 2007 inability of the body to provide the requisite stress field yields an overdriven and unstable configuration. The current results provide restrictions for the achievement of substantial toughening through intergranular fracture

A micromechanical basis for partitioning the evolution of grainbridging in brittle materials

A micromechanical model is developed for grain bridging inmonolithic ceramics. Specifically, bridge formation of a single,non-equiaxed grain spanning adjacent grains is addressed. A cohesive zoneframework enables crack initiation and propagation along grainboundaries. The evolution of the bridge is investigated through avariance in both grain angle and aspect ratio. We propose that thebridging process can be partitioned into five distinct regimes ofresistance: propagate, kink, arrest, stall, and bridge. Although crackpropagation and kinking are well understood, crack arrest and subsequent"stall" have been largely overlooked. Resistance during the stall regimeexposes large volumes of microstructure to stresses well in excess of thegrain boundary strength. Bridging can occur through continued propagationor reinitiation ahead of the stalled crack tip. The driving forcerequired to reinitiate is substantially greater than the driving forcerequired to kink. In addition, the critical driving force to reinitiateis sensitive to grain aspect ratio but relatively insensitive to grainangle. The marked increase in crack resistance occurs prior to bridgeformation and provides an interpretation for the rapidly risingresistance curves which govern the strength of many brittle materials atrealistically small flaw sizes

Adhesive Joint and Composites Modeling in SIERRA

Polymers and fiber-reinforced polymer matrix composites play an important role in many Defense Program applications. Recently an advanced nonlinear viscoelastic model for polymers has been developed and incorporated into ADAGIO, Sandia's SIERRA-based quasi-static analysis code. Standard linear elastic shell and continuum models for fiber-reinforced polymer-matrix composites have also been added to ADAGIO. This report details the use of these models for advanced adhesive joint and composites simulations carried out as part of an Advanced Simulation and Computing Advanced Deployment (ASC AD) project. More specifically, the thermo-mechanical response of an adhesive joint when loaded during repeated thermal cycling is simulated, the response of some composite rings under internal pressurization is calculated, and the performance of a composite container subjected to internal pressurization, thermal loading, and distributed mechanical loading is determined. Finally, general comparisons between the continuum and shell element approaches for modeling composites using ADAGIO are given

A mechanism-based approach to modeling ductile fracture.

Ductile fracture in metals has been observed to result from the nucleation, growth, and coalescence of voids. The evolution of this damage is inherently history dependent, affected by how time-varying stresses drive the formation of defect structures in the material. At some critically damaged state, the softening response of the material leads to strain localization across a surface that, under continued loading, becomes the faces of a crack in the material. Modeling localization of strain requires introduction of a length scale to make the energy dissipated in the localized zone well-defined. In this work, a cohesive zone approach is used to describe the post-bifurcation evolution of material within the localized zone. The relations are developed within a thermodynamically consistent framework that incorporates temperature and rate-dependent evolution relationships motivated by dislocation mechanics. As such, we do not prescribe the evolution of tractions with opening displacements across the localized zone a priori. The evolution of tractions is itself an outcome of the solution of particular, initial boundary value problems. The stress and internal state of the material at the point of bifurcation provides the initial conditions for the subsequent evolution of the cohesive zone. The models we develop are motivated by in-situ scanning electron microscopy of three-point bending experiments using 6061-T6 aluminum and 304L stainless steel, The in situ observations of the initiation and evolution of fracture zones reveal the scale over which the failure mechanisms act. In addition, these observations are essential for motivating the micromechanically-based models of the decohesion process that incorporate the effects of loading mode mixity, temperature, and loading rate. The response of these new cohesive zone relations is demonstrated by modeling the three-point bending configuration used for the experiments. In addition, we survey other methods with the potential to provide more detailed information about the near tip deformation fields

Stacked crop rotations and cultural practices for canola and flax yield and quality

Canola (Brassica napus L.) and flax (Linum usitatissimum L.) are important oilseed crops, but improved management practices to enhance their yields and quality are needed. We studied the effect of stacked versus alternate‐year crop rotations and traditional versus improved cultural practices on canola and flax growth, seed yield, oil concentration, and N‐use efficiency from 2006 to 2011 in the northern Great Plains, USA. Stacked rotations were durum (Triticum turgidum L.)‐durum‐canola‐pea (Pisum sativum L.) (DDCP) and durum‐durum‐flax‐pea (DDFP). Alternate‐year rotations were durum‐canola‐durum‐pea (DCDP) and durum‐flax‐durum‐pea (DFDP). The traditional cultural practice included a combination of conventional tillage, recommended seed rate, broadcast N fertilization, and reduced stubble height. The improved cultural practice included a combination of no‐tillage, increased seed rate, banded N fertilization, and increased stubble height. Canola stand count was 36–123% greater with the improved than the traditional cultural practice in 2006, 2009, 2010, and 2011. Canola pod number and oil concentration were 3–36% greater in the improved than the traditional practice in 2007 and 2010, but trends reversed by 5–19% in 2008. Flax stand count was 28% greater with DFDP than DDFP in 2007 and 56% greater in the improved than the traditional practice in 2010. Flax pod number, seed weight, seed yield, N content, N‐use efficiency, and N‐removal index varied with crop rotations, cultural practices, and years. Canola growth and oil concentration increased with the improved cultural practice as well as flax growth, yield, and quality enhanced with alternate‐year crop rotation and the improved cultural practice in wet years

G-quadruplex structures mark human regulatory chromatin

G-quadruplex (G4) structural motifs have been linked to transcription, replication and genome instability and are implicated in cancer and other diseases. However, it is crucial to demonstrate the bona fide formation of G4 structures within an endogenous chromatin context. Herein we address this through the development of G4 ChIP-seq, an antibody-based G4 chromatin immunoprecipitation and high-throughput sequencing approach. We find ∼10,000 G4 structures in human chromatin, predominantly in regulatory, nucleosome-depleted regions. G4 structures are enriched in the promoters and 5' UTRs of highly transcribed genes, particularly in genes related to cancer and in somatic copy number amplifications, such as $\textit{MYC}$. Strikingly, $\textit{de novo}$ and enhanced G4 formation are associated with increased transcriptional activity, as shown by HDAC inhibitor-induced chromatin relaxation and observed in immortalized as compared to normal cellular states. Our findings show that regulatory, nucleosome-depleted chromatin and elevated transcription shape the endogenous human G4 DNA landscape.European Molecular Biology Organization (EMBO Long-Term Fellowship), University of Cambridge, Cancer Research UK (Grant ID: C14303/A17197), Wellcome Trust (Grant ID: 099232/z/12/z