scholarly journals Bayesian stochastic multi-scale analysis via energy considerations

Author(s):  
Muhammad S. Sarfaraz ◽  
Bojana V. Rosić ◽  
Hermann G. Matthies ◽  
Adnan Ibrahimbegović

AbstractMulti-scale processes governed on each scale by separate principles for evolution or equilibrium are coupled by matching the stored energy and dissipation in line with the Hill-Mandel principle. We are interested in cementitious materials, and consider here the macro- and meso-scale behaviour of such a material. The accurate representations of stored energy and dissipation are essential for the depiction of irreversible material behaviour, and here a Bayesian approach is used to match these quantities on different scales. This is a probabilistic upscaling and as such allows to capture, among other things, the loss of resolution due to scale coarsening, possible model errors, localisation effects, and the geometric and material randomness of the meso-scale constituents in the upscaling. On the coarser (macro) scale, optimal material parameters are estimated probabilistically for certain possible behaviours from the class of generalised standard material models by employing a nonlinear approximation of Bayes’s rule. To reduce the overall computational cost, a model reduction of the meso-scale simulation is achieved by combining unsupervised learning techniques based on a Bayesian copula variational inference with functional approximation forms.

2021 ◽  
Author(s):  
Jie Wang ◽  
Peng Wang ◽  
Nahiène Hamila ◽  
Philippe Boisse

During the forming stage in the RTM process, deformations and orientations of yarns at the mesoscopic scale are essential to evaluate mechanical behaviors of final composite products and calculate the permeability of the reinforcement. However, due to the high computational cost, it is very difficult to carry out a mesoscopic draping simulation for the entire reinforcement. In this paper, a macro-meso scale simulation of composite reinforcements is presented in order to predict mesoscopic deformations of the fabric in a reasonable calculation time. The proposed multi-scale method allows linking the macroscopic simulation of the reinforcement with the mesoscopic modelling of the RVE through a macromeso embedded analysis. On the base of macroscopic simulations using a hyperelastic constitutive law of the reinforcement, an embedded mesoscopic geometry is first deduced from the macroscopic simulation of the draping. To overcome the inconvenience of the macro-meso embedded solution which leads to unreal excessive yarn extensions, local mesoscopic simulations based on the embedded analysis are carried out on a single RVE by defining specific boundary conditions. Finally, the multi-scale forming simulations are investigated in comparison with the experimental results, illustrating the efficiency of the proposed approach, in terms of accuracy and CPU time.


Materials ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 3693 ◽  
Author(s):  
Pham ◽  
Döbrich ◽  
Trümper ◽  
Gereke ◽  
Cherif

Weft-knitted fabrics offer an excellent formability into complex shapes for composite application. In biaxial weft-knitted fabric, additional yarns are inserted in the warp (wale-wise) and weft (course-wise) directions as a reinforcement. Due to these straight yarns, the mechanical properties of such fabrics are better than those of unreinforced weft-knitted fabrics. The forming process of flat fabrics into 3D preforms is challenging and requires numerical simulation. In this paper, the mechanical behavior of biaxial weft-knitted fabrics is simulated by means of macro- and meso-scale finite element method (FEM) models. The macro-scale modelling approach is based on a shell element formulation and offers reasonable computational costs but has some limitations by the description of fabric mechanical characteristics and forming behavior. The meso-scale modelling approach based on beam elements can describe the fabric’s mechanical and forming characteristics better at a higher computational cost. The FEM models were validated by comparing the results of various simulations with the equivalent experiments. With the help of the parametric models, the forming of biaxial weft-knitted fabrics into complex shapes can be simulated. These models help to predict material and process parameters for optimized forming conditions without the necessity of costly experimental trials.


2017 ◽  
Vol 372 ◽  
pp. 170-179
Author(s):  
Daniel A. Kestering ◽  
Flavia F.S. Zinani ◽  
George C. Bleyer

In computational fluid dynamics (CFD) of fluidization processes, the modeling of drag between fluid and particles has a direct effect on the results. The EMMS (Energy Minimization Multi-Scale) models are based on the micro-scale of individual particles and the macro scale of equipment to model the meso-scale phenomena related to particle clustering, which directly affect the drag between fluid and particles. The EMMS/bubbling model was introduced as a change from the classic EMMS model to specific bubbling fluid bed conditions. The present work aims to apply the EMMS/bubbling model in the CFD of Geldart-D particles fluidized by air. The results were compared with results from the literature. It was observed that, for particles of Geldart groups A and B, the results using the EMMS/bubbling model agreed well with the literature. The CFD results for Geldart-D particles showed good agreement with the literature results for this method using coarse grids.


2014 ◽  
Vol 627 ◽  
pp. 349-352 ◽  
Author(s):  
Javier Oliver ◽  
M. Caicedo ◽  
E. Roubin ◽  
A.E. Huespe

This paper presents a FE2 multi-scale framework for numerical modeling of the structural failure of heterogeneous quasi-brittle materials. The model is assessed by application to cementitious materials. Using the Continuum Strong Discontinuity Approach (CSD), innovative numerical tools, such as strain injection and crack path field techniques, provide a robust, and mesh-size, mesh-bias and RVE-size objective, procedure to model crack onset and propagation at the macro-scale.


2011 ◽  
Vol 243-249 ◽  
pp. 2084-2090 ◽  
Author(s):  
Li Wang ◽  
Da Hu Rui ◽  
Jian Hui Yang

Multi-scale science is the challenge and opportunity of science in the 21th century, and turbulence of liquid and fracture of solid will be the classical problems of multi-scale mechanics. The failure process of brittle materials displayed a multi-scale mechanics feature that amounts of micro damages grow large trans-scale and nonlinear and evolve to a macro catastrophic transition in the end. So, the concepts of scale and hierarchy of material are inescapable in strength theory to be used explaining solid fracture, it is the main puzzle of the strength theory at present. In the paper, in order to show the phenomena of multi-scale fracture, numeric method is used to simulate the failure process of brittle material, during which micro cracks initiate, grow large, aggregate and in the end form a run-through fracture band in the sample. The result of the numeric simulation shows that the micro cracks of a meso-scale size initiate due to tensile strain and the sample of a macro-scale size breaks down due to tensile-shearing strain under uniaxial tensile or due to compression-shearing strain under uniaxial compression. It powerfully disabused the puzzles in teaching strength theory of brittle material. The further discussion concluded that for a brittle material grain of meso-scale size, the theory of Maximum Tensile Strain is reasonable in explaining the strength, as for a brittle material sample of a macro-scale size, the mohr-columb theory is reasonable for its strength owing to the two important factors of cohesive strength and friction factorwere introduced.


2016 ◽  
Vol 12 (1) ◽  
pp. 151-176 ◽  
Author(s):  
Garrison Stevens ◽  
Sez Atamturktur ◽  
Ricardo Lebensohn ◽  
George Kaschner

Purpose – Highly anisotropic zirconium is a material used in the cladding of nuclear fuel rods, ensuring containment of the radioactive material within. The complex material structure of anisotropic zirconium requires model developers to replicate not only the macro-scale stresses but also the meso-scale material behavior as the crystal structure evolves; leading to strongly coupled multi-scale plasticity models. Such strongly coupled models can be achieved through partitioned analysis techniques, which couple independently developed constituent models through an iterative exchange of inputs and outputs. Throughout this iterative process, biases, and uncertainties inherent within constituent model predictions are inevitably transferred between constituents either compensating for each other or accumulating during iterations. The paper aims to discuss these issues. Design/methodology/approach – A finite element model at the macro-scale is coupled in an iterative manner with a meso-scale viscoplastic self-consistent model, where the former supplies the stress input and latter represents the changing material properties. The authors present a systematic framework for experiment-based validation taking advantage of both separate-effect experiments conducted within each constituent’s domain to calibrate the constituents in their respective scales and integral-effect experiments executed within the coupled domain to test the validity of the coupled system. Findings – This framework developed is shown to improve predictive capability of a multi-scale plasticity model of highly anisotropic zirconium. Originality/value – For multi-scale models to be implemented to support high-consequence decisions, such as the containment of radioactive material, this transfer of biases and uncertainties must be evaluated to ensure accuracy of the predictions of the coupled model. This framework takes advantage of the transparency of partitioned analysis to reduce the accumulation of errors and uncertainties.


2021 ◽  
Vol 15 (3) ◽  
pp. 1399-1422
Author(s):  
Jan Nitzbon ◽  
Moritz Langer ◽  
Léo C. P. Martin ◽  
Sebastian Westermann ◽  
Thomas Schneider von Deimling ◽  
...  

Abstract. In continuous permafrost lowlands, thawing of ice-rich deposits and melting of massive ground ice lead to abrupt landscape changes called thermokarst, which have widespread consequences on the thermal, hydrological, and biogeochemical state of the subsurface. However, macro-scale land surface models (LSMs) do not resolve such localized subgrid-scale processes and could hence miss key feedback mechanisms and complexities which affect permafrost degradation and the potential liberation of soil organic carbon in high latitudes. Here, we extend the CryoGrid 3 permafrost model with a multi-scale tiling scheme which represents the spatial heterogeneities of surface and subsurface conditions in ice-rich permafrost lowlands. We conducted numerical simulations using stylized model setups to assess how different representations of micro- and meso-scale heterogeneities affect landscape evolution pathways and the amount of permafrost degradation in response to climate warming. At the micro-scale, the terrain was assumed to be either homogeneous or composed of ice-wedge polygons, and at the meso-scale it was assumed to be either homogeneous or resembling a low-gradient slope. We found that by using different model setups and parameter sets, a multitude of landscape evolution pathways could be simulated which correspond well to observed thermokarst landscape dynamics across the Arctic. These pathways include the formation, growth, and gradual drainage of thaw lakes; the transition from low-centred to high-centred ice-wedge polygons; and the formation of landscape-wide drainage systems due to melting of ice wedges. Moreover, we identified several feedback mechanisms due to lateral transport processes which either stabilize or destabilize the thermokarst terrain. The amount of permafrost degradation in response to climate warming was found to depend primarily on the prevailing hydrological conditions, which in turn are crucially affected by whether or not micro- and/or meso-scale heterogeneities were considered in the model setup. Our results suggest that the multi-scale tiling scheme allows for simulating ice-rich permafrost landscape dynamics in a more realistic way than simplistic one-dimensional models and thus facilitates more robust assessments of permafrost degradation pathways in response to climate warming. Our modelling work improves the understanding of how micro- and meso-scale processes affect the evolution of ice-rich permafrost landscapes, and it informs macro-scale modellers focusing on high-latitude land surface processes about the necessities and possibilities for the inclusion of subgrid-scale processes such as thermokarst within their models.


Author(s):  
Rafael Cámara Artigas ◽  
Fernando Díaz del Olmo ◽  
Jose Ramon Martinez Batlle

An analytical and cartographic method of biomass distribution and plant formations at a multi-scalar level is developed based on bioclimatic variables extracted from the Thornthwaite Water Balance (WB) and the Bioclimatic Balances (BB) of Montero de Burgos & González Rebollar. As a result, a distribution map involving Types of Bioclimatic Regimens (TBR) is obtained leading to the identification of a multi-scale classification at different levels: zonal (macro-scale) with 5 types, regional (meso-scale) with 27 types, and local (micro-scale) with 162 plant formations subtypes, conditioned by lithology-soils, the relief exposure to wind or sunstroke respectively and obtained through the combination of TBR and ombroclimates.


Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 106 ◽  
Author(s):  
Konstantinos Tserpes ◽  
Christos Kora

This is the second of a two-paper series describing a multi-scale modeling approach developed to simulate crack sensing in polymer fibrous composites by exploiting interruption of electrically conductive carbon nanotube (CNT) networks. The approach is based on the finite element (FE) method. Numerical models at three different scales, namely the micro-scale, the meso-scale and the macro-scale, have been developed using the ANSYS APDL environment. In the present paper, the meso- and macro-scale analyses are described. In the meso-scale, a two-dimensional model of the CNT/polymer matrix reinforced by carbon fibers is used to develop a crack sensing methodology from a parametric study which relates the crack position and length with the reduction of current flow. In the meso-model, the effective electrical conductivity of the CNT/polymer computed from the micro-scale is used as input. In the macro-scale, the final implementation of the crack sensing methodology is performed on a CNT/polymer/carbon fiber composite volume using as input the electrical response of the cracked CNT/polymer derived at the micro-scale and the crack sensing methodology. Analyses have been performed for cracks of two different lengths. In both cases, the numerical model predicts with good accuracy both the length and position of the crack. These results highlight the prospect of conductive CNT networks to be used as a localized structural health monitoring technique.


Author(s):  
Konstantinos Tserpes ◽  
Christos Kora

This is the second of a two-paper series describing a multi-scale modeling approach developed to simulate crack sensing in polymer fibrous composites by exploiting interruption of electrically conductive carbon nanotube (CNT) networks. The approach is based on the finite element (FE) method. FE models at three different scales, namely the micro-scale, the meso-scale and the macro-scale, have been developed using the ANSYS PDL environment. In the present paper, the meso- and macro-scale analyses are described. In the meso-scale, a two-dimensional model of the CNT/polymer matrix reinforced by carbon fibers is used to develop a crack sensing methodology from a parametric study which relates the crack position and length with the reduction of current flow. In the meso-model, the effective electrical conductivity of the CNT/polymer computed from the micro-scale is used as input. In the macro-scale, the final implementation of the crack sensing methodology is performed on a CNT/polymer/carbon fiber composite volume using as input the electrical response of the cracked CNT/polymer derived at the micro-scale and the crack sensing methodology. Analyses have been performed for cracks of two different lengths. In both cases, the numerical model predicts with good accuracy both the length and position of the crack. These results highlight the prospect of conductive CNT networks to be used as a localized structural health monitoring technique.


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