Learning hyperelastic anisotropy from data via a tensor basis neural network

Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel neural network layers, and L1 regularization. The proposed tensor-basis neural network can discover both the type and orientation of the anisotropy and provide an accurate model of the stress response. The method is demonstrated with data from hyperelastic materials with off-axis transverse isotropy and orthotropy, as well as materials with less well-defined symmetries induced by fibers or spherical inclusions. Both plain feed-forward neural networks and input-convex neural network formulations are developed and tested. Using the latter, a polyconvex potential can be established, which, by satisfying the growth condition can guarantee the existence of boundary value problem solutions.Comment: 36 pages, 20 figure

Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen

Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent generalization performance. In these models, the stress prediction follows from a linear combination of invariant-dependent coefficient functions and known tensor basis generators. However, thus far the formulations have been limited to stress representations based on the classical Rivlin and Ericksen form, while the performance of alternative representations has yet to be investigated. In this work, we survey a variety of tensor basis neural network models for modeling hyperelastic materials in a finite deformation context, including a number of so far unexplored formulations which use theoretically equivalent invariants and generators to Finger-Rivlin-Ericksen. Furthermore, we compare potential-based and coefficient-based approaches, as well as different calibration techniques. Nine variants are tested against both noisy and noiseless datasets for three different materials. Theoretical and practical insights into the performance of each formulation are given.Comment: 32 pages, 20 figures, 4 appendice

The clinical pharmacology of intranasal l-methamphetamine.

BackgroundWe studied the pharmacology of l-methamphetamine, the less abused isomer, when used as a nasal decongestant.Methods12 subjects self-administered l-methamphetamine from a nonprescription inhaler at the recommended dose (16 inhalations over 6 hours) then at 2 and 4 (32 and 64 inhalations) times this dose. In a separate session intravenous phenylephrine (200 microg) and l-methamphetamine (5 mg) were given to define alpha agonist pharmacology and bioavailability. Physiological, cardiovascular, pharmacokinetic, and subjective effects were measured.ResultsPlasma l-methamphetamine levels were often below the level of quantification so bioavailability was estimated by comparing urinary excretion of the intravenous and inhaled doses, yielding delivered dose estimates of 74.0 +/- 56.1, 124.7 +/- 106.6, and 268.1 +/- 220.5 microg for ascending exposures (mean 4.2 +/- 3.3 microg/inhalation). Physiological changes were minimal and not dose-dependent. Small decreases in stroke volume and cardiac output suggesting mild cardiodepression were seen.ConclusionInhaled l-methamphetamine delivered from a non-prescription product produced minimal effects but may be a cardiodepressant

Mechanisms of Silica Fracture in Aqueous Electrolyte Solutions

Glassy silicates are substantially weaker when in contact with aqueous electrolyte solutions than in vacuum due to chemical interactions with preexisting cracks. To investigate this silicate weakening phenomenon, classical molecular dynamics (MD) simulations of silica fracture were performed using the bond-order based, reactive force field ReaxFF. Four different environmental conditions were investigated: vacuum, water, and two salt solutions (1M NaCl, 1M NaOH) that form relatively acidic and basic solutions, respectively. Any aqueous environment weakens the silica, with NaOH additions resulting in the largest decreases in the effective fracture toughness (eKIC) of silica or the loading rate at which the fracture begins to propagate. The basic solution leads to higher surface deprotonation, narrower radius of curvature of the crack tip, and greater weakening of the silica, compared with the more acidic environment. The results from the two different electrolyte solutions correspond to phenomena observed in experiments and provide a unique atomistic insight into how anions alter the chemical-mechanical fracture response of silica