Modelling of Environmental Ageing of Polymers and Polymer Composites—Modular and Multiscale Methods

Service lifetimes of polymers and polymer composites are impacted by environmental ageing. The validation of new composites and their environmental durability involves costly testing programs, thus calling for more affordable and safe alternatives, and modelling is seen as such an alternative. The state-of-the-art models are systematized in this work. The review offers a comprehensive overview of the modular and multiscale modelling approaches. These approaches provide means to predict the environmental ageing and degradation of polymers and polymer composites. Furthermore, the systematization of methods and models presented herein leads to a deeper and reliable understanding of the physical and chemical principles of environmental ageing. As a result, it provides better confidence in the modelling methods for predicting the environmental durability of polymeric materials and fibre-reinforced composites.

Evaluating Scaling Frameworks for Multiscale Geomorphometric Analysis

Multiscale methods have become progressively valuable in geomorphometric analysis as data have become increasingly detailed. This paper evaluates the theoretical and empirical properties of several common scaling approaches in geomorphometry. Direct interpolation (DI), cubic convolution resampling (RES), mean aggregation (MA), local quadratic regression (LQR), and an efficiency optimized Gaussian scale-space implementation (fGSS) method were tested. The results showed that when manipulating resolution, the choice of interpolator had a negligible impact relative to the effects of manipulating scale. The LQR method was not ideal for rigorous multiscale analyses due to the inherently non-linear processing time of the algorithm and an increasingly poor fit with the surface. The fGSS method combined several desirable properties and was identified as an optimal scaling method for geomorphometric analysis. The results support the efficacy of Gaussian scale-space as a general scaling framework for geomorphometric analyses.

Scalable Graphics Processing Unit–Based Multiscale Linear Solvers for Reservoir Simulation

Summary In this work, the scalability of two key multiscale solvers for the pressure equation arising from incompressible flow in heterogeneous porous media, namely, the multiscale finite volume (MSFV) solver, and the restriction-smoothed basis multiscale (MsRSB) solver, are investigated on the graphics processing unit (GPU) massively parallel architecture. The robustness and scalability of both solvers are compared against their corresponding carefully optimized implementation on the shared-memory multicore architecture in a structured problem setting. Although several components in MSFV and MsRSB algorithms are directly parallelizable, their scalability on the GPU architecture depends heavily on the underlying algorithmic details and data-structure design of every step, where one needs to ensure favorable control and data flow on the GPU, while extracting enough parallel work for a massively parallel environment. In addition, the type of algorithm chosen for each step greatly influences the overall robustness of the solver. Thus, we extend the work on the parallel multiscale methods of Manea et al. (2016) to map the MSFV and MsRSB special kernels to the massively parallel GPU architecture. The scalability of our optimized parallel MSFV and MsRSB GPU implementations are demonstrated using highly heterogeneous structured 3D problems derived from the SPE10 Benchmark (Christie and Blunt 2001). Those problems range in size from millions to tens of millions of cells. For both solvers, the multicore implementations are benchmarked on a shared-memory multicore architecture consisting of two packages of Intel® Cascade Lake Xeon Gold 6246 central processing unit (CPU), whereas the GPU implementations are benchmarked on a massively parallel architecture consisting of NVIDIA Volta V100 GPUs. We compare the multicore implementations to the GPU implementations for both the setup and solution stages. Finally, we compare the parallel MsRSB scalability to the scalability of MSFV on the multicore (Manea et al. 2016) and GPU architectures. To the best of our knowledge, this is the first parallel implementation and demonstration of these versatile multiscale solvers on the GPU architecture. NOTE: This paper is published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features

Multiscale computational modelling is challenging due to the high computational cost of direct numerical simulation by finite elements. To address this issue, concurrent multiscale methods use the solution of cheaper macroscale surrogates as boundary conditions to microscale sliding windows. The microscale problems remain a numerically challenging operation both in terms of implementation and cost. In this work we propose to replace the local microscale solution by an Encoder-Decoder Convolutional Neural Network that will generate fine-scale stress corrections to coarse predictions around unresolved microscale features, without prior parametrisation of local microscale problems. We deploy a Bayesian approach providing credible intervals to evaluate the uncertainty of the predictions, which is then used to investigate the merits of a selective learning framework. We will demonstrate the capability of the approach to predict equivalent stress fields in porous structures using linearised and finite strain elasticity theories.

Discrimination of Surface Topographies Created by Two-Stage Process by Means of Multiscale Analysis

The fundamental issue in surface metrology is to provide methods that can allow the establishment of correlations between measured topographies and performance or processes, or that can discriminate confidently topographies that are processed or performed differently. This article presents a set of topographies from two-staged processed steel rings, measured with a 3D contact profilometer. Data were captured individually from four different regions, namely the top, bottom, inner, and outer surfaces. The rings were manufactured by drop forging and hot rolling. Final surface texture was achieved by mass finishing with spherical ceramic media or cut wire. In this study, we compared four different multiscale methods: sliding bandpass filtering, three geometric length- and area-scale analyses, and the multiscale curvature tensor approach. In the first method, ISO standard parameters were evaluated as a function of the central wavelength and bandwidth for measured textures. In the second and third method, complexity and relative length and area were utilized. In the last, multiscale curvature tensor statistics were calculated for a range of scales from the original sampling interval to its forty-five times multiplication. These characterization parameters were then utilized to determine how confident we can discriminate (through F-test) topographies between regions of the same specimen and between topographies resulting from processing with various technological parameters. Characterization methods that focus on the geometrical properties of topographic features allowed for discrimination at the finest scales only. Bandpass filtration and basic height parameters Sa and Sq proved to confidently discriminate against all factors at all three considered bandwidths.

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in [Formula: see text], where [Formula: see text] represents the characteristic length of the small scale oscillations and [Formula: see text] is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in [Formula: see text]. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.

Multiscale Complexity Analysis of Rainfall in Northeast Brazil

In this work, we analyze the complexity of monthly rainfall temporal series recorded from 1962 to 2012, at 133 gauge stations in the state of Pernambuco, northeastern Brazil. To this end, we employ the modified multiscale entropy method (MMSE), which is well suited for short time series, to analyze the rainfall regularity across a wide range of temporal scales, from one month to one year. We identify the temporal scales that distinguish rainfall regularity in the inland semiarid Sertão region, the transitional inland Agreste region, and the coastal, tropical humid Zona da Mata region, by comparing the results for stations across the study area and performing statistical significance tests. Our work contributes to the establishment of multiscale methods based on information theory in climatological studies.

Discharge Energy as a Key Contributing Factor Determining Microgeometry of Aluminum Samples Created by Electrical Discharge Machining

The aim of this study is first to determine the effect of the discharge energy on the surface microgeometry of aluminum samples created by electrical discharge machining (EDM). Secondly, an additional purpose is to demonstrate the differences between the geometric multiscale methods: length-, area-scale, and curvature. Eleven samples were manufactured using discharge energies ranging from 0.486 mJ to 1389.18 mJ and, subsequently, measured with focus variation microscopy. Standard ISO and multiscale parameters were calculated and used for surface discrimination and regression analysis. The results of linear, logarithmic, and exponential regression analyses revealed a strong correlation (R2 > 0.9) between the geometrical features of the surface topography and the discharge energy. The approach presented in this paper shows that it is possible to shape surface microgeometry by changing the energy of electrical discharges, and these dependencies are visible in various scales of observation. The similarities of the results produced by curvature and length-scale methods were observed, despite the significant differences in the essence of those methods.