Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. We adopt the Hellinger--Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. On applying the divergence theorem to the weak strain-displacement relations, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement-based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions. However, for flexibility in choosing basis functions, we also present a formulation that uses a penalty term to enforce the element equilibrium conditions. This method is referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the $L^2$ norm of the displacement, energy seminorm, and the $L^2$ norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.Comment: 49 pages, 49 figure

Simulating the pervasive fracture and fragmentation of materials and structures using randomly close-packed Voronoi tessellations.

Under extreme loading conditions most often the extent of material and structural fracture is pervasive in the sense that a multitude of cracks are nucleating, propagating in arbitrary directions, coalescing, and branching. Pervasive fracture is a highly nonlinear process involving complex material constitutive behavior, material softening, localization, surface generation, and ubiquitous contact. Two primary applications in which pervasive fracture is encountered are (1) weapons effects on structures and (2) geomechanics of highly jointed and faulted reservoirs. A pure Lagrangian computational method based on randomly close-packed Voronoi tessellations is proposed as a rational approach for simulating the pervasive fracture of materials and structures. Each Voronoi cell is formulated as a finite element using the reproducing kernel method. Fracture surfaces are allowed to nucleate only at the intercell faces. The randomly seeded Voronoi cells provide an unbiased network for representing cracks. In this initial study two approaches for allowing the new surfaces to initiate are studied: (1) dynamic mesh connectivity and the instantaneous insertion of a cohesive traction when localization is detected, and (2) a discontinuous Galerkin approach in which the interelement tractions are an integral part of the variational formulation, but only become active once localization is detected. Pervasive fracture problems are extremely sensitive to initial conditions and system parameters. Dynamic problems exhibit a form of transient chaos. The primary numerical challenge for this class of problems is the demonstration of model objectivity and, in particular, the identification and demonstration of a measure of convergence for engineering quantities of interest

Loss of the Heparan Sulfate Sulfotransferase, Ndst1, in Mammary Epithelial Cells Selectively Blocks Lobuloalveolar Development in Mice

Considerable evidence indicates that heparan sulfate is essential for the development of tissues consisting of branching ducts and tubules. However, there are few examples where specific sulfate residues regulate a specific stage in the formation of such tissues.We examined the role of heparan sulfation in mammary gland branching morphogenesis, lactation and lobuloalveolar development by inactivation of heparan sulfate GlcNAc N-deacetylase/N-sulfotransferase genes (Ndst) in mammary epithelial cells using the Cre-loxP system. Ndst1 deficiency resulted in an overall reduction in glucosamine N-sulfation and decreased binding of FGF to mammary epithelial cells in vitro and in vivo. Mammary epithelia lacking Ndst1 underwent branching morphogenesis, filling the gland with ductal tissue by sexual maturity to the same extent as wildtype epithelia. However, lobuloalveolar expansion did not occur in Ndst1-deficient animals, resulting in insufficient milk production to nurture newly born pups. Lactational differentiation of isolated mammary epithelial cells occurred appropriately via stat5 activation, further supporting the notion that the lack of milk production was due to lack of expansion of the lobuloalveoli.These findings demonstrate a selective, highly penetrant, cell autonomous effect of Ndst1-mediated sulfation on lobuloalveolar development

Two-way coupling of Presto v2.8 and CTH v8.1.

A loose two-way coupling of SNL's Presto v2.8 and CTH v8.1 analysis code has been developed to support the analysis of explosive loading of structures. Presto is a Lagrangian, three-dimensional explicit, transient dynamics code in the SIERRA mechanics suite for the analysis of structures subjected to impact-like loads. CTH is a hydro code for modeling complex multi-dimensional, multi-material problems that are characterized by large deformations and/or strong shocks. A fundamental assumption in this loose coupling is that the compliance of the structure modeled with Presto is significantly smaller than the compliance of the surrounding medium (e.g. air) modeled with CTH. A current limitation of the coupled code is that the interaction between CTH and thin structures modeled in Presto (e.g. shells) is not supported. Research is in progress to relax this thin-structure limitation

Model Generation Issues in a Simulation Support Environment

No longer available as a technical report. Contact authors re reprints of published article

Defining language impairments in a subgroup of children with autism spectrum disorder

Autism spectrum disorder (ASD) is diagnosed on the basis of core impairments in pragmatic language skills, which are found across all ages and subtypes. In contrast, there is significant heterogeneity in language phenotypes, ranging from nonverbal to superior linguistic abilities, as defined on standardized tests of vocabulary and grammatical knowledge. The majority of children are verbal but impaired in language, relative to age-matched peers. One hypothesis is that this subgroup has ASD and co-morbid specific language impairment (SLI). An experiment was conducted comparing children with ASD to children with SLI and typically developing controls on aspects of language processing that have been shown to be impaired in children with SLI: repetition of nonsense words. Patterns of performance among the children with ASD and language impairment were similar to those with SLI, and contrasted with the children with ASD and no language impairment and typical controls, providing further evidence for the hypothesis that a subgroup of children with ASD has co-morbid SLI. The findings are discussed in the context of brain imaging studies that have explored the neural bases of language impairment in ASD and SLI, and overlap in the genes associated with elevated risk for these disorders.M01 RR00533 - NCRR NIH HHS; R01 DC10290 - NIDCD NIH HHS; U19 DC03610 - NIDCD NIH HH

Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes

We have developed a general method for finding apparent horizons in 3D numerical relativity. Instead of solving for the partial differential equation describing the location of the apparent horizons, we expand the closed 2D surfaces in terms of symmetric trace--free tensors and solve for the expansion coefficients using a minimization procedure. Our method is applied to a number of different spacetimes, including numerically constructed spacetimes containing highly distorted axisymmetric black holes in spherical coordinates, and 3D rotating, and colliding black holes in Cartesian coordinates.Comment: 19 pages, 13 figures, LaTex, to appear in Phys. Rev. D. Minor changes mad

Pattern and Outcome of Chest Injuries at Bugando Medical Centre in Northwestern Tanzania.

Chest injuries constitute a continuing challenge to the trauma or general surgeon practicing in developing countries. This study was conducted to outline the etiological spectrum, injury patterns and short term outcome of these injuries in our setting. This was a prospective study involving chest injury patients admitted to Bugando Medical Centre over a six-month period from November 2009 to April 2010 inclusive. A total of 150 chest injury patients were studied. Males outnumbered females by a ratio of 3.8:1. Their ages ranged from 1 to 80 years (mean = 32.17 years). The majority of patients (72.7%) sustained blunt injuries. Road traffic crush was the most common cause of injuries affecting 50.7% of patients. Chest wall wounds, hemothorax and rib fractures were the most common type of injuries accounting for 30.0%, 21.3% and 20.7% respectively. Associated injuries were noted in 56.0% of patients and head/neck (33.3%) and musculoskeletal regions (26.7%) were commonly affected. The majority of patients (55.3%) were treated successfully with non-operative approach. Underwater seal drainage was performed in 39 patients (19.3%). One patient (0.7%) underwent thoracotomy due to hemopericardium. Thirty nine patients (26.0%) had complications of which wound sepsis (14.7%) and complications of long bone fractures (12.0%) were the most common complications. The mean LOS was 13.17 days and mortality rate was 3.3%. Using multivariate logistic regression analysis, associated injuries, the type of injury, trauma scores (ISS, RTS and PTS) were found to be significant predictors of the LOS (P < 0.001), whereas mortality was significantly associated with pre-morbid illness, associated injuries, trauma scores (ISS, RTS and PTS), the need for ICU admission and the presence of complications (P < 0.001). Chest injuries resulting from RTCs remain a major public health problem in this part of Tanzania. Urgent preventive measures targeting at reducing the occurrence of RTCs is necessary to reduce the incidence of chest injuries in this region