Zeroth-order finite similitude and scaling of complex geometries in biomechanical experimentation

Scaled experimentation provides an alternative approach to full-scale biomechanical (and biological) testing but is known to suffer from scale effects, where the underlying system behaviour changes with scale. This phenomenon is arguably the overriding principal obstacle to the many advantages that scaled experimentation provides. These include reduced costs, materials and time, along with the eschewal of ethical compliance concerns with the application of substitute artificial materials as opposed to the use of hazardous biological agents. This paper examines the role scale effects play in biomechanical experimentation involving strain measurement and introduces a formulation that overtly captures scale dependencies arising from geometrical change. The basic idea underpinning the new scaling approach is the concept of space scaling, where a biomechanical experiment is scaled by the metaphysical mechanism of space contraction. The scaling approach is verified and validated with finite-element (FE) models and actual physical-trial experimentation using digital image correlation software applied to synthetic composite bone. The experimental design aspect of the approach allows for the selection of three-dimensional printing materials for trial-space analysis in a complex pelvis geometry. This aspect takes advantage of recent advancements in additive manufacturing technologies with the objective of countering behavioural distorting scale effects. Analysis is carried out using a laser confocal microscope to compare the trial and physical space materials and subsequently measured using surface roughness parameters. FE models were constructed for the left hemipelvis and results show similar strain patterns (average percentage error less than 10%) for two of the three trial-space material combinations. A Bland–Altman statistical analysis shows a good agreement between the FE models and physical experimentation and a good agreement between the physical-trial experimentation, providing good supporting evidence of the applicability of the new scaling approach in a wider range of experiments

Modelling chemistry in the nocturnal boundary layer above tropical rainforest and a generalised effective nocturnal ozone deposition velocity for sub-ppbv NOx conditions

Measurements of atmospheric composition have been made over a remote rainforest landscape. A box model has previously been demonstrated to model the observed daytime chemistry well. However the box model is unable to explain the nocturnal measurements of relatively high [NO] and [O3], but relatively low observed [NO2]. It is shown that a one-dimensional (1-D) column model with simple O3 -NOx chemistry and a simple representation of vertical transport is able to explain the observed nocturnal concentrations and predict the likely vertical profiles of these species in the nocturnal boundary layer (NBL). Concentrations of tracers carried over from the end of the night can affect the atmospheric chemistry of the following day. To ascertain the anomaly introduced by using the box model to represent the NBL, vertically-averaged NBL concentrations at the end of the night are compared between the 1-D model and the box model. It is found that, under low to medium [NOx] conditions (NOx <1 ppbv), a simple parametrisation can be used to modify the box model deposition velocity of ozone, in order to achieve good agreement between the box and 1-D models for these end-of-night concentrations of NOx and O3. This parametrisation would could also be used in global climate-chemistry models with limited vertical resolution near the surface. Box-model results for the following day differ significantly if this effective nocturnal deposition velocity for ozone is implemented; for instance, there is a 9% increase in the following day’s peak ozone concentration. However under medium to high [NOx] conditions (NOx > 1 ppbv), the effect on the chemistry due to the vertical distribution of the species means no box model can adequately represent chemistry in the NBL without modifying reaction rate constants

Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of the method lies in its treatment of the equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM), that have already been developed to treat non-linear operators within reduced order models. The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov–Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions.A demonstration of the capabilities of this new approach is provided by solving the incompressible Navier–Stokes equations for simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the Mohr–Coulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots

Are CT-Based Finite Element Model Predictions of Femoral Bone Strengthening Clinically Useful?

Purpose of Review: This study reviews the available literature to compare the accuracy of areal bone mineral density derived from dual X-ray absorptiometry (DXA-aBMD) and of subject-specific finite element models derived from quantitative computed tomography (QCT-SSFE) in predicting bone strength measured experimentally on cadaver bones, as well as their clinical accuracy both in terms of discrimination and prediction. Based on this information, some basic cost-effectiveness calculations are performed to explore the use of QCT-SSFE instead of DXA-aBMD in (a) clinical studies with femoral strength as endpoint, (b) predictor of the risk of hip fracture in low bone mass patients. Recent Findings: Recent improvements involving the use of smooth-boundary meshes, better anatomical referencing for proximal-only scans, multiple side-fall directions, and refined boundary conditions increase the predictive accuracy of QCT-SSFE. Summary: If these improvements are adopted, QCT-SSFE is always preferable over DXA-aBMD in clinical studies with femoral strength as the endpoint, while it is not yet cost-effective as a hip fracture risk predictor, although pathways that combine both QCT-SSFE and DXA-aBMD are promising