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1

A 3D trabecular bone homogenization technique

Marques Marco Costa, Belinha J., Oliveira A. F., Manzanares Cespedes M.C., Natal Jorge R.M.

Acta of Bioengineering and Biomechanics

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2020

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Vol. 22, no. 3

139--152

EN

Purpose: Bone is a hierarchical material that can be characterized from the microscale to macroscale. Multiscale models make it possible to study bone remodeling, inducing bone adaptation by using information of bone multiple scales. This work proposes a computationally efficient homogenization methodology useful for multiscale analysis. This technique is capable to define the homogenized microscale mechanical properties of the trabecular bone highly heterogeneous medium. Methods: In this work, a morphology-based fabric tensor and a set of anisotropic phenomenological laws for bone tissue was used, in order to define the bone micro-scale mechanical properties. To validate the developed methodology, several examples were performed in order to analyze its numerical behavior. Thus, trabecular bone and fabricated benchmarks patches (representing special cases of trabecular bone morphologies) were analyzed under compression. Results: The results show that the developed technique is robust and capable to provide a consistent material homogenization, indicating that the homogeneous models were capable to accurately reproduce the micro-scale patch mechanical behavior. Conclusions: The developed method has shown to be robust, computationally less demanding and enabling the authors to obtain close results when comparing the heterogeneous models with equivalent homogenized models. Therefore, it is capable to accurately predict the micro-scale patch mechanical behavior in a fraction of the time required by classic homogenization techniques.

2

Combining radial point interpolation meshless method with a new homogenization technique for trabecular bone multiscale structural analyses

Marques Marco, Belinha Jorge, Oliveira António, Manzanares Céspedes, Jorge Renato Natal

Acta of Bioengineering and Biomechanics

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2019

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Vol. 21, no. 2

101--113

EN

Bone tissue is a dynamic tissue, possessing different functional requirements at different scales. This layered organization indicates the existence of a hierarchical structure, which can be characterized to distinguish macro-scale from micro-scale levels. Structurally, both scales can be linked by the use of classic multiscale homogenization techniques. Since in bone tissue each micro-scale domain is distinct form its neighbour, applying a classic multiscale homogenization technique to a complete bone structure could represent an inadmissible computational cost. Thus, this work proposes a homogenization methodology that is computationally efficient, presenting a reduced computational cost, and is capable to define the homogenized microscale mechanical properties of the trabecular bone highly heterogeneous medium. Methods: The methodology uses the fabric tensor concept in order to define the material principal directions. Then, using an anisotropic phenomenological law for bone tissue correlating the local apparent density with directional elasticity moduli, the anisotropic homogenized material properties of the micro-scale patch are fully defined. To validate the developed methodology, several numerical tests were performed, measuring the sensitivity of the technique to changes in the micro-patch size and preferential orientation. Results: The results show that the developed technique is robust and capable to provide a consistent material homogenization. Additionally, the technique was combined with two discrete numerical techniques: the finite element method and radial point interpolation meshless method. Conclusions: Structural analyses were performed using real trabecular patches, showing that the proposed methodology is capable to accurately predict the micro-scale patch mechanical behavior in a fraction of the time required by classic homogenization techniques.

3

Multiscale Processing Performance for Motion Capture

Jablonski B., Kulbacki M.

Machine Graphics and Vision

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2011

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Vol. 20, No. 3

251-266

EN

Motion capture systems help record human motion as a sequence of joint angle vectors and analyse it in multiple degrees of freedom with high accuracy. Motion, as many other signals, might contain information which is stored on many different scales. Hence the use of a multiscale model might help correctly distinguish or analyse motion properties. In this paper we analyse the capabilities of a multiscale motion model to help distinguish meaningful motion features, whilst the unnecessary components (like noise) get removed. We performed experiments based on real motion capture data to analyse the discriminative properties of the multiscale approach. The main goal of experiments was to check the clustering performance of a multiscale model. The detailed results are presented and discussed, showing the capabilities and advantages of multiscale model application.

4

Identification of stochastic material properties in multiscale modelling

Kuś W., Burczyński T.

Computer Methods in Materials Science

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2011

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Vol. 11, No. 4

524-530

EN

The paper is devoted to identification problems in multiscale modeling in stochastic conditions. The multiscale modeling is able to take into account materials or geometrical effects which occur in microscale and obtain more precise results in macroscale analysis. The identification allows to evaluate materials or geometrical parameters of a structure in microscale on the basis of statistical measurements in macroscale. The methodology presented in the paper takes into account stochastic nature of parameters in the microscale and the identification problem is formulated as minimization of a certain stochastic objective function. The problem is transformed into deterministic one in which a new objective functional dependent on mean values and variances is minimized with respect to moments of stochastic parameters. An approach based on evolutionary computing is presented in the minimization problem. The main advantage of the presented approach consists in the fact that a gradient of the objective functional is no needed and moreover there is a great probability of finding the global minimum. The computational homogenization is used to multiscale modelling of the structures. The problem formulation, description of optimization algorithm and a numerical example are shown in the paper.

PL

Artykuł jest poświęcony zagadnieniom identyfikacji parametrów modelu w skali mikro w ujęciu wieloskalowym. Pozwala to uwzględnić wpływ parametrów materiałowych oraz geometrycznych w skali mikro na rozwiązania w skali makro. Rozwiązanie zagadnienia identyfikacji umożliwia określenie parametrów struktury w skali mikro na podstawie pomiarów przeprowadzonych dla skali makro. Przedstawiona w pracy metodologia oparta jest na założeniu, że parametry w skali mikro mają naturę stochastyczną i można je wyznaczyć dysponując wynikami statystycznych pomiarów eksperymentalnych przemieszczeń i odkształceń w skali makro. Zagadnienie sprowadzono do minimalizacji różnicy między charakterystykami probabilistycznymi przemieszczeń i odkształceń obliczonych dla modelu stochastycznego oraz obiektu rzeczywistego. W tym celu zastosowano koncepcję homogenizacji komputerowej, metodę Monte Carlo oraz algorytm ewolucyjny. Opracowaną koncepcję identyfikacji w warunkach stochastycznych zweryfikowano pozytywnie na przykładzie numerycznym.

5

New models of fracture in solids at meso- and nanoscales

Wnuk M.

Czasopismo Techniczne. Mechanika

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2010

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R. 107, z. 4-M

167-180

EN

Novel properties of the present cohesive crack models provide a better insight and an effective tool to explain multiscale nature of fracture process and the associated transitions from macroto meso- and nano-levels of material response to deformation and fracture. Fracture testing of materials with cementitious bonding such as concrete and certain types of ceramics demonstrates that fractal cracks are commonly observed. In the limit of vanishing fracture quantum and/ or reduced degree of fractality the quantized cohesive model of a fractal crack, as presented here, reduces to the well-known classic models of Dugdale-Barenblatt or to the linear elastic fracture mechanics or the quantized fracture mechanics theories. Therefore, the basic concepts of linear elastic fracture mechanics, quantized fracture mechanics and fractal geometry are all incorporated into the present theory.

PL

Nowe właściwości materiału oraz jego zachowania w procesie deformacji i pękania zostały opisane teoretycznie na podstawie dyskretnego modelu kohezyjnego szczeliny, uwzględniającego również geometrię fraktalną. Okazuje się, że dla makroszczelin różnice między nowym opisem oraz klasycznymi teoriami zniszczenia, takimi jak teoria Griffitha oraz LEFM (liniowo-sprężysta mechanika zniszczenia), nie są zbyt istotne. Natomiast w zakresie nanoszczelin, kiedy długość szczeliny jest porównywalna z kwantum propagacji a[0], różnice te są istotne. Uwzględnienie geometrii fraktalnej oraz dyskretnej natury propagacji szczeliny ma znaczący wpływ na końcowe rezultaty teorii dotyczącej tzw. wytrzymałości rezydualnej materiału niedoskonałego zawierającego początkowe defekty.

6

Sensitivity testing practice on pre-processing parameters in hard and soft coupled modeling

Ignaszak Z., Hajkowski J., Hajkowski M.

Archives of Foundry Engineering

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2010

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Vol. 10, iss. 1

51-58

EN

This paper pays attention to the problem of practical applicability of coupled modeling with the use of hard and soft models types and necessity of adapted to that models data base possession. The data base tests results for cylindrical 30 mm diameter casting made of AlSi7Mg alloy were presented. In simulation tests that were applied the Calcosoft system with CAFE (Cellular Automaton Finite Element) module. This module which belongs to "multiphysics" models enables structure prediction of complete casting with division of columnar and equiaxed crystals zones of [alpha]phase. Sensitivity tests of coupled model on the particular values parameters changing were made. On these basis it was determined the relations of CET (columnar-to-equaiaxed transition) zone position influence. The example of virtual structure validation based on real structure with CET zone location and grain size was shown.

7

Template matching by means of correlation coefficient for detecting cancerous masses in mammograms

Bator M., Nieniewski M.

Machine Graphics and Vision

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2007

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Vol. 16, No. 3/4

329-345

EN

The paper presents the authors' experiences with the detection of cancerous masses in mammograms. The described detection method is based on the use of multiscale template matching and multiresolution. As a measure of similarity, the correlation coefficient is adapted. The main conclusion drawn from the conducted experiments is that by sufficiently dense scaling of the templates one can achieve FROC (Free Response Operating Characteristics) curves of the same quality as the curves obtained in the literature with considerably more sophisticated methods. The results were calculated for full mammograms of the entire MIAS database, in contrast to the literature, where the results are often given for regions of interest or for selected images. Several options for the templates were investigated, including three variants based on the hemispherical gray level distribution, as well as the optimal choice of the increasing scale of templates covering the whole range of diameters of masses.

8

Application of CAFE multiscale model to description of microstructure development during dynamic recrystallization

Gawąd J., Pietrzyk M.

Archives of Metallurgy and Materials

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2007

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Vol. 52, iss. 2

257-266

EN

Multiscale CAFE (Cellular Automata – Finite Element) model of the material undergoing dynamic recrystallization is presented in the paper. The coupled model consists of dislocation and microstructure development description based on Cellular Automata (CA) and continuum macroscale simulation using Finite Element (FE) method. The model is capable of simulate various characteristics of the material, including multi-peak and single-peak flow stress behaviour. Several improvements to the CA model are proposed in the paper. The connection between flow stress characteristic and grain size is properly described by the model with respect to the structural criterion. Additionally, distribution of grain size can be calculated at arbitrary stage of the process. Analysis of recrystallization cycles observed in the material is discussed. The results show good qualitative agreement with the experimental flow stress curves commonly observed in literature.

PL

W artykule zaprezentowano wieloskalowy model CAFE (Cellular Automata – Finite Element). Model ten złożony jest z symulacji rozwoju mikrostruktury i gęstości dyslokacji, opartej o metodę Automatów Komórkowych (AK, CA) oraz modelu skali makro, opartego o Metodę Elementów Skończonych (MES, FE). Zaproponowano szereg usprawnień do modelu skali mikro. Model ten umożliwia uwzględnienie różnych charakterystyk naprężenia uplastyczniajacego, w tym jednopikowego i wielopikowego. Model poprawnie odwzorowuje kryterium strukturalne, łączące charakter krzywej naprężenia uplastyczniajacego z wielkością ziarna. Zaletą modelu jest dostarczanie zarówno informacji o średniej wielkości ziarna jak i o rozkładzie wielkości. W pracy przeanalizowano krzywe opisujące ułamki cykli rekrystalizacji w materiale. Uzyskane z modelu krzywe naprężenia uplastyczniającego wykazuje dobrą zgodność jakościową z powszechnie znanymi z literatury danymi doświadczalnymi.

9

Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics

Hadjiconstantinou N.G.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2005

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Vol. 53, nr 4

335-342

EN

We discuss recent progress in hybrid atomistic-continuum methods with particular emphasis on developments in boundary condition imposition in molecular simulations, an essential ingredient of hybrid methods. Both Dirichlet (state variable) and flux boundary conditions are discussed. We also briefly review various coupling approaches and discuss the effects of compressibility and molecular fluctuations on the choice of coupling method. Common elements between hybrid methods and related multiscale simulation approaches are also briefly discussed.