Adjustment of the mechanical properties (apparent elastic modulus and compressive strength) in porous scaffolds is important for artificial implants and bone tissue engineering. In this study, a ...top-down design method based on Voronoi-Tessellation was proposed. This method was successful in obtaining the porous structures with specified and functionally graded porosity. The porous specimens were prepared by selective laser melting technology. Quasi-static compressive tests were conducted as well. The experiment results revealed that the mechanical properties were affected by both porosity and irregularity. The irregularity coefficient proposed in this study can achieve good accommodation and balance of “irregularity” and “controllability”. The method proposed in this study provides an efficient approach for the bionic design and topological optimization of scaffolds.
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Voronoi tessellation techniques are widely accepted methods for the generation of representative models of polycrystalline microstructures of metallurgic and ceramic materials. ...Contrary to most of the Voronoi-based tessellation methods developed, the Laguerre Voronoi technique provides control over the size and shape of the cells, therefore allowing to simulate accurately the grain structure of a wide range of materials. This paper presents a method for the generation of numerical models of 3D polycrystalline microstructures, based on the Laguerre-Voronoi tessellation technique. An innovative approach to define the additional parameters required by the Laguerre-Voronoi formulation for the generation of realistic 3D microstructures is presented, providing the algorithm with information on the given microstructure from a set of 2D micrographs easily obtainable experimentally. The method implemented efficiently avoids degenerated cells (affecting the quality of the final structure) and finds the most representative set of input values by comparing 2D sections of the numerical model against 2D imaging of real polished surfaces. In this paper, the capability of the method developed is verified by reproducing the microstructure of polycrystalline alumina with various ranges of grain sizes, deriving from different sintering procedures.
•A 3D Voronoi clump based model is established for brittle rock.•Complex micro-structure of rock is captured with an ergodic algorithm.•The sensitivity of model behavior to the micro-properties is ...identified.•A simple calibration method is proposed for the developed model.•The new model realistically reproduces failure behavior of LdB granite.
Particle-based model (PBM) has been extensively used to investigate progressive failure process of rock due to its advantage in modeling fracture development. In order to make the PBM reproduce rock failure behavior more realistically, this study develops an advanced clumped particle model for rock based on 3D Voronoi tessellation (VCPM). In the newly developed model, irregular clumps are identified by using an ergodic algorithm similar with that adopted by the Voronoi tessellation. Thus, structural similarity between convex clumps and Voronoi cells is guaranteed while computational efficiency of the clump logic is remained by the VCPM. The clump size and coordination number of the VCPM obey Inverse Gaussian and Gaussian distributions, respectively. Such characteristics enable the VCPM to simulate rock micro-cracking and macro-fracturing behaviors even in large-scale engineering problems. A comprehensive parametric study indicates both micro-geometric and micro-mechanical properties have significant influences on macro-mechanical properties of the VCPM. Linear or nonlinear mode of the predicted strength envelope can be controlled by the average particle number involved in the clump. Based on the revealed relationship between macro-mechanical responses and micro-properties, a calibration procedure is moreover established for the VCPM. The calibrated VCPM is then applied to simulate failure behavior of Lac du Bonnet granite to investigate its modeling capability. The predicted stress–strain response and strength envelope are in good accordance to the experimental data. The large magnitudes of the UCS-to-TS ratio and strength envelope slope imply the interlocking effect is greatly strengthened in the VCPM. In addition, the influences of the minor principal stress on the ductility, volumetric dilation and failure pattern of the granite as well as its splitting failure in the Brazilian test are also accurately captured by the VCPM. Such capabilities indicate the VCPM is of great potential in further investigation of rock fracturing behavior under more complex stress environment.
•A combined Voronoi tessellation and finite-discrete element method (FDEM) approach for modelling the post-fracture behaviour of laminated tempered glass was proposed.•Fragments of tempered glass ...with different surface compressive stresses were modelled as Voronoi cells.•Statistical distribution parameters such as the fragment face numbers, volume and sphericity were adopted to reconstruct the fracture morphology of tempered glass.•Post-fracture behaviour of one triple layered laminated tempered glass block under tension was modelled and validated with experimental data.•Key cohesive parameters for describing the residual interaction between glass fragments were determined.•The influence due to the fragments interaction property, bond levels and fracture morphology on the post-fracture behaviour of laminated tempered glass was investigated.
It is reported that the fractured glass panels can contribute to the residual load-bearing capability of laminated glass (LG) after cracking. In order to investigate the stiffness and failure characteristics of LG at the post-fracture stage, a combined Voronoi and finite-discrete element method (FDEM) approach was proposed, which includes reconstructing the post-fracture patterns and carrying out the structural simulation of the post-fracture behaviour. The fracture morphology was determined by introducing Voronoi tessellation defined with statistical parameters such as the fragment face numbers, volume and sphericity. The interaction between glass fragments was captured with the cohesive zone model. One fractured LG block under uniaxial tension, which was taken from a triple layered LG beam with ionoplast interlayers, was modelled and validated with experimentally recorded data. Through iteration analysis, the key cohesive parameters were selected. It was then followed by investigating the influence of the fragment interaction property, the bond level and fracture morphology on the post-fracture behaviour of laminated tempered glass. Results show that the combined cohesion and frictional properties can well represent the residual interaction behaviour between fragments. The frictional property has a significant effect on the post-fracture resistance, and whereas the effect on the stiffness is not that evident. Compared to other cohesive parameters, the cohesive stiffness factors have a predominant effect on both the post-fracture stiffness and resistance. The tension stiffening effect is found to be able to provide a clear increase in post-fracture resistance, which can be up to ten times the original resistance, if the glass-interlayer interface is perfectly bonded. The progressive debonding at glass-interlayer interfaces will lead to the degradation in the loading resistance of fractured LG. A higher bond level can promote the coupling effect between interlayers and mid glass layer for providing increased load resistance after the significant debonding has occurred at the outmost glass-interlayer interface. The effect of fracture morphology on post-fracture performance is not evident in most cases except that the increase in fragment size will lead to a great stiffness growth.
Combined Voronoi-FDEM concept for the post-fracture model of laminated tempered glass Display omitted
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•A combined method for the mesoscopic failure simulation in concrete has been presented, which is combined with (1) the stochastic aggregate distribution modelling approach based on ...morphological characteristics of real concrete, and (2) the finite element treatment for hybrid phase-field modeling. The case study of concrete specimen under tensile loading proves the effectiveness of application of phase-field method in computation of the crack propagation of concrete.•The increasing of aggregate fraction θ leads to the nonlinear growth of the concrete tensile strength. While, the effect of aggregate fraction θ on shear strength of concrete can be classified into two Modes, depending on whether the interact of aggregates occurs during the crack propagation. The shear strength of concrete is twice higher during the interact of aggregates (Mode I) than that in case of no-interact (Mode II).•As the elongation of aggregate raises, the probability of shear fracture Mode I increases, which leads to the improvement of the shear strength of concrete. While, the elongation and surface roughness of aggregates have little effect on the tensile strength of concrete.•In the case of tension failure and Mode II shear failure, the strength of the structure decreases as the pre-notch deepens. However, the depth of the pre-notch is not directly proportional to the structural shear strength in the case of Mode I shear failure, due to the effect of the pre-notch on the crack propagation path.
Concrete crack propagation is significantly affected by its complex mesoscopic structure, tracking which is of great importance for revealing the fracture failure modes and crack propagation patterns of concrete. This study presents a stochastic aggregate distribution modeling approach combining the Fourier-Voronoi method and techniques with XCT images. it enables the generation of stochastic aggregate distribution models that mimic real concrete's morphological characteristics. Meanwhile, with the hybrid phase-field theory and finite element method, a multi-field coupling model is established to simulate the crack propagation. In contrast to the isotropic or anisotropic phase-field theory, with the hybrid phase-field theory the stiffness degradation of concrete material in all directions during crack propagation are taken into consideration. With the proposed methodology, the effects of volume fraction, shape, roughness and pre-notch depth on the fracture behavior and strength of concrete are investigated. Results show that both the tensile and shear strength of concrete grows with the increase of aggregate volume fraction. Benefited from the application of hybrid phase-field theory, two shear fracture failure modes of concrete with distinct shear strengths are revealed, influenced by aggregate interaction during the shear fracture process.
•Effects of spatial scale on modeling radiative heat transfer of packed particle beds are analyzed.•Long-range scale (LR) model is accurate for large conductivity ks≫kr or Λ>10.•Short-range scale ...(SR) model is inaccurate for ks≫kr but accurate for ks~O(kr) at low temperature.•Microscopic-scale (MS) model is the most accurate model used for correcting other models.•Over- and underestimation of radiative and conductive heat cause better prediction of SR at ks~O(kr).
Thermal radiation is important in high temperature packed pebble bed, which is still poorly understood. The present work is to analyze the effect of spatial scale in modeling thermal radiation of packed pebble beds. The long-range model (full integral scale), short-range model (partial integral scale) and microscopic models (sub-particle scale) are compared and analyzed with reference to existing correlations. In high temperature packed pebble beds, the long-range model takes into account all possible radiation between surrounding spheres, even those that are not direct Voronoi neighbors, whereas the short-range model considers only a portion nearby. It is found that when solid conductivity is much greater than the effective thermal conductivity of radiation (ks≫kr or Λ>10), the long-range model provides better results than the short-range model in predicting the radiative heat exchange. The short-range model overestimates solid conductivity at low temperatures (lower than 1215°C) when ks~O(kr) (or Λ<10) while underestimating radiative heat exchange. It therefore still provides predictions for total heat exchange that is in good agreement with experimental data in cases where the errors cancel out. Moreover, the short-range radiation model is more computationally efficient than the long-range model and microscopic model to compute view factor between particles of Voronoi neighbors.
We present VoroIF‐GNN (Voronoi InterFace Graph Neural Network), a novel method for assessing inter‐subunit interfaces in a structural model of a protein–protein complex, relying solely on the input ...structure without any additional information. Given a multimeric protein structural model, we derive interface contacts from the Voronoi tessellation of atomic balls, construct a graph of those contacts, and predict the accuracy of every contact using an attention‐based GNN. The contact‐level predictions are then summarized to produce whole interface‐level scores. VoroIF‐GNN was blindly tested for its ability to estimate the accuracy of protein complexes during CASP15 and showed strong performance in selecting the best multimeric model out of many. The method implementation is freely available at https://kliment-olechnovic.github.io/voronota/expansion_js/.
This paper presents a study on in-plane wave propagation in two-dimensional polycrystalline microstructure with different grain distributions. The numerical simulations are performed using commercial ...finite element (FE) package and the microstructure is generated using Voronoi tessellation. The different grain distributions are generated using a regularity parameter, α. In-plane wave results in simultaneous P and S waves unlike conventional bulk wave, where only P or S wave is observed. Such in-plane wave propagation resulting from localized excitation is more realistic and has important applications in microstructural flaw detection. Here, an analogy is drawn with seismic wave in heterogeneous geophysical media to understand the in-plane waves in the polycrystalline microstructure. First, the effect of grain distributions on the attenuation and phase velocity behavior of in-plane wave is studied in the low-frequency Rayleigh regime. The numerical simulations are performed for Inconel-600 for grain sizes of 100 and 250
. Then, the numerical model is validated with experimental results using piezoelectric transducers on an Inconel-600 plate. The physical microstructure of Inconel-600 material is observed using a scanning electron microscope. The frequency dependency of attenuation for in-plane waves is close to unity similar to that of seismic wave. The attenuation and phase velocity vary with the change in regularity parameter, α. Additionally, it is observed that the scattering of P wave is higher than that of S wave during in-plane wave propagation, resulting in higher attenuation of P wave. Finally, an exponential expression is established between regularity parameter and attenuation, which will help in characterizing and predicting the grain distribution inversely.
In this report, classic molecular dynamics simulations based on the embedded atom method (EAM) are carried out to study the atomic arrangement in Ni3Al metallic glass. The short-range order (SRO) and ...medium-range order (MRO) in the rapidly quenched Ni3Al alloy are characterized by the both structural analysis methods; Radial distribution function (RDF) and Voronoi tessellation. From RDF, we found a splitting in the second peak that reflects the atomic packing beyond the nearest neighbors and it is a characteristic of the MRO. Furthermore, the transition from the supercooled state to the glassy state of Ni3Al alloy leads to an increased population of icosahedral-like clusters and their spatial connectivity via vertex-sharing (VS), edge-sharing (ES), face-sharing (FS) and intercross-sharing (IS). Interestingly, by comparing the position ratios of subpeaks in RDF with those of the shared cluster distance to the first peak in RDF, we suggest that the first subpeak originates from the face-sharing clusters while the second one results from the vertex-sharing clusters. However, the edge-sharing is hidden between the two subpeaks due to its smaller fraction in the system.
•The medium-range order of Ni3Al is characterized by icosahedral-like clusters.•The polyhedrons 〈0,1,10,2〉,〈0,2,8,4〉and〈0,0,12,0〉 are predominant in the system.•Majority of icosahedral clusters are connected by vertex, face and intercross-sharing.•Splitting of the 2nd peak in RDF is caused by the vertex, and face-sharing clusters.
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