Time-vectorized numerical integration for systems of ODEs

Stiff systems of ordinary differential equations (ODEs) and sparse training data are common in scientific problems. This paper describes efficient, implicit, vectorized methods for integrating stiff systems of ordinary differential equations through time and calculating parameter gradients with the adjoint method. The main innovation is to vectorize the problem both over the number of independent times series and over a batch or "chunk" of sequential time steps, effectively vectorizing the assembly of the implicit system of ODEs. The block-bidiagonal structure of the linearized implicit system for the backward Euler method allows for further vectorization using parallel cyclic reduction (PCR). Vectorizing over both axes of the input data provides a higher bandwidth of calculations to the computing device, allowing even problems with comparatively sparse data to fully utilize modern GPUs and achieving speed ups of greater than 100x, compared to standard, sequential time integration. We demonstrate the advantages of implicit, vectorized time integration with several example problems, drawn from both analytical stiff and non-stiff ODE models as well as neural ODE models. We also describe and provide a freely available open-source implementation of the methods developed here

Essential role of stem cell factor–c‐Kit signalling pathway in bleomycin‐induced pulmonary fibrosis

Stem cell factor ( SCF ) and its receptor c‐Kit have been implicated in tissue remodelling and fibrosis. Alveolar fibroblasts from patients with diffuse interstitial fibrosis secrete more SCF . However, its precise role remains unclear. In this study the potential role of the SCF –c‐Kit axis in pulmonary fibrosis was examined. Fibrosis was induced by intratracheal instillation of bleomycin ( BLM ), which caused increased SCF levels in plasma, bronchoalveolar lavage fluid ( BALF ) and lung tissue, as well as increased expression by lung fibroblasts. These changes were accompanied by increased numbers of bone marrow‐derived c‐Kit + cells in the lung, with corresponding depletion in bone marrow. Both recombinant SCF and lung extracts from BLM ‐treated animals induced bone‐marrow cell migration, which was blocked by c‐Kit inhibitor. The migrated cells promoted myofibroblast differentiation when co‐cultured with fibroblasts, suggesting a paracrine pathogenic role. Interestingly, lung fibroblast cultures contained a subpopulation of cells that expressed functionally active c‐Kit, which were significantly greater and more responsive to SCF induction when isolated from fibrotic lungs, including those from patients with idiopathic pulmonary fibrosis ( IPF ). This c‐Kit + subpopulation was α SMA ‐negative and expressed lower levels of collagen I but significantly higher levels of TGF β than c‐Kit‐negative cells. SCF deficiency achieved by intratracheal treatment with neutralizing anti‐ SCF antibody or by use of Kitl Sl / Kitl Sl ‐d mutant mice in vivo resulted in significant reduction in pulmonary fibrosis. Taken together, the SCF –c‐Kit pathway was activated in BLM ‐injured lung and might play a direct role in pulmonary fibrosis by the recruitment of bone marrow progenitor cells capable of promoting lung myofibroblast differentiation. Copyright © 2013 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98368/1/path4177.pd

Understanding the deformation mechanisms in Ni-based superalloys with using crystal plasticity finite element method

“Ni-based superalloy is considered as a good candidate due to its excellent resistance to elevated temperature deformation for long term period application. Understanding the deformation and failure mechanisms of Ni-Based superalloys is very helpful for providing design guidelines for processing Ni-based superalloys. Experimental characterization indicates that the deformation mechanisms of Ni based superalloy is strongly microstructure dependent. Besides, damage transform from the void nucleation to the macro cracks by voids growth leading to the failure of the Ni-based superalloys are also showing strong microstructure sensitivity. Therefore, this work focuses on the prediction and comprehension of the deformation and void growth behavior in Ni based superalloy at different working conditions via crystal plasticity finite element modeling and simulation. Physically based crystal plasticity frameworks were developed for newly Ni-based superalloy Haynes 282. It was found that dislocation shearing through the precipitates were acting as the main contributor to the strength of Haynes 282 at room temperature and 8150⁰ C. Our analysis of the creeping behavior of Haynes 282 exhibited that resistance of general climb replaced by the resistance induced by the deposited climb dislocation density. In addition, in the study of void growth behavior, our simulation results demonstrated that as the main loading axis perpendicular to the grain boundary (GB), voids grow more slowly on tilt GBs in bicrystals than those in single and bicrystals with twist GBs. And tilt GBs would promote the void grow into irregular shape”--Abstract, page iv

Effect of the Grain Size and Distribution of Nanograins on the Deformation of Nanodomained Heterogeneous Nickel

We studied the effect of embedded nanograins on the strength and deformation of nanodomained heterogeneous nickel (Ni) via a novel discrete-crystal plasticity model. Nanodomained structures exhibited higher strength than those of heterogeneous lamella structures and rule of mixtures. Due to the mismatch of strengths between the nanograins and coarse grains, geometrically necessary dislocations (GND) accumulated around nanograins and increased with the strain. In addition, smaller nanograins are more effective to generate GND in both nanodomained and heterogeneous lamella structures. These findings shed light on the role of dislocation mechanisms in the plasticity of heterogeneous nanostructured metals

Crystal Plasticity Modeling the Deformation in Nanodomained Heterogenous Structures

Nanodomained heterogenous structures characterized by randomly dispersed nanograins (NGs) embedded in the coarser grains (CGs) have demonstrated an exciting potential to break the strength-ductility trade-off, providing high strength without the loss of ductility. Here, using a combination of discrete crystal plasticity finite element (discrete-CPFE) model and dislocation density-based CPFE model, we study the effects of grain size, volume fraction of nanograins on the strength and deformation in nanodomained materials. Our analysis shows that the overall flow stresses of nanodomained samples are equal or higher than the strengths predicted by rule of mixtures. Smaller NGs or higher volume fraction of NGs can make the nanodomained samples stronger, as they can be more effective to promote the dislocation accumulations inside the CGs and eventually raise the critical resolved shear stress for each slip system during the plastic flow. Areas surrounding NGs stored higher dislocation densities and less plastic strain, due to the restricted dislocation motion. Furthermore, NGs grain embedded in the CGs can effectively reduce the anisotropy of strength in the nanodomained samples

Crystal Plasticity Modeling of Fretting Fatigue Behavior of an Aluminum Alloy

Aluminum alloy (AA)7075 is widely used to fabricate parts and components on aircrafts, which are subjected to contact loading that may induce fretting fatigue and catastrophic failure. In this work, a crystal plasticity finite element (CPFE) model accounting for the microstructural features is developed for simulating the fretting fatigue of AA7075-T651. A submodel technology is adopted to refine the contact region to obtain more accurate simulation data. An energy-based criterion is developed for prediction of crack initiation life. The hotspots for the fretting fatigue crack nucleation are identified by the maximum of plastic strain energy density. The proposed CPFE model achieves high accuracy on predicting the fretting fatigue crack initiation and validated by fretting fatigue experimental results