Multi-Scale Modelling of Materials

Numerical simulations have recently shown their potential as a robust, cheap and reliable tool for predicting the quality of components produced by metal additive manufacturing (MAM) processes. Despite the advantages of the MAM processes over conventional manufacturing methods, there is still a lack of thorough understanding on how different defects can form and originate during MAM processing. In that respect, advanced numerical techniques recently developed have the ability to predict the occurrence of such defects. These techniques have paved the way to efficiently obtain the optimal processing window for targeted mechanical properties to satisfy the end-use design requirements. The aim of this review paper is hence to present and classify numerical simulations of MAM, not solely based on their length-scale as often seen, but also based on the involved physics, as well as the modeling strategies at both the meso-scale and part-scale. The paper is arranged in the following way: First, literature describing purely conduction-based heat transfer simulations at meso-scale are presented. This is followed by a review of fluid-based simulations of increasing complexity based on the treatment of free surface of the melt pool at meso-scale. Finally, contributions based on different part-scale modeling approaches with a focus on thermo-mechanical behavior are reviewed.

The electrochemical properties of high strength 7xxx aluminium alloys strongly depend on the substitutional occupancy of Zn by Cu and Al in the strengthening η-phase with the two-sublattice structure, and its microstructural and compositional prediction is the key to design of new generation corrosion resistant alloys. In this work, we have developed a chemical-potential-based phase-field model capable of describing multi-component and two-sublattice ordered phases, during commercial multi-stage artificial ageing treatments, by directly incorporating the compound energy CALPHAD formalism. The model developed has been employed to explore the complex compositional pathway for the formation of the η-phase in Al-Zn-Mg-Cu alloys during heat treatments. In particular, the influence of alloy composition, solute diffusivity, and heat treatment parameters on the microstructural and compositional evolution of η-phase precipitates, was systematically investigated from a thermodynamic and kinetic perspective and compared to electron probe microanalysis validation data. The simulated η-phase growth kinetics and the matrix residual solute evolution in the AA7050 alloy indicates that Zn depletion mainly controlled the η-phase growth process during the early stage of ageing, resulting in fast η-phase growth kinetics, enrichment of Zn in the η-phase, and an excess in residual Cu in the matrix. The gradual substitution of Zn by Cu atoms in the η-phase during the later ageing stage was in principle a kinetically controlled process, owing to the slower diffusivity of Cu relative to Zn in the matrix. It was also found that the higher nominal Zn content in alloys like the AA7085 alloy, compared to the AA7050 alloy, could significantly enhance the chemical potential of Zn, but this had a minor influence on Cu, which essentially led to the higher Zn content (and consequently lower Cu) seen in the η-phase. Finally, substantial depletion of Zn and supersaturation of Cu in the matrix of the AA7050 alloy was predicted after 24 h ageing at 120 • C , whereas the second higher-temperature ageing stage at 180 • C markedly enhanced the diffusion of Cu from the supersaturated matrix into the η-phase, while the matrix residual Zn content was only slightly affected.

This research is part of a European project (namely, CODICE project), main objective of which is modelling, at a multi-scale, the evolution of the mechanical performance of non-degraded and degraded cementitious matrices. For that, a series of experiments were planned with pure synthetic tri-calcium silicate (C3S) and bi-calcium silicate (C2S) (main components of the Portland cement clinker) to obtain different calcium–silicate–hydrate (C–S–H) gel structures during their hydration. The characterization of those C–S–H gels and matrices will provide experimental parameters for the validation of the multi-scale modelling scheme proposed. In this article, a quantitative method, based on thermal analyses, has been used for the determination of the chemical composition of the C–S–H gel together with the degree of hydration and quantitative evolution of all the components of the pastes. Besides, the microstructure and type of silicate tetrahedron and mean chain length (MCL) were studied by scanning electron microscopy (SEM) and 29Si magic-angle-spinning (MAS) NMR, respectively. The main results showed that the chemical compositions for the C–S–H gels have a CaO/SiO2 M ratio almost constant of 1.7 for both C3S and C2S compounds. Small differences were found in the gel water content: the H2O/SiO2 M ratio ranged from 2.9 ± 0.2 to 2.6 ± 0.2 for the C3S (decrease) and from 2.4 ± 0.2 to 3.2 ± 0.2 for the C2S (increase). The MCL values of the C–S–H gels, determined from 29Si MAS NMR, were 3.5 and 4 silicate tetrahedron, for the hydrated C3S and C2S, respectively, remaining almost constant at all hydration periods.

Finite element models of single-walled and multi-walled carbon nanotubes in their perfect and fundamental forms (zigzag and armchair) were constructed. Then, after obtaining the mechanical properties of perfect carbon nanotubes, three types of imperfections, ie, doping with Si atoms, carbon vacancy and perturbation of the ideal location of the carbon atom were introduced in different amounts to the perfect models to make them imperfect. Finally, the mechanical properties of the imperfect carbon nanotubes were numerically simulated and ...

This paper deals with the integrated numerical analysis of iceberg collisions with ship sides. A nonlinear explicit commercial code LS-DYNA 971 was used in the analysis. The deformations and fracture of both the ship structure and iceberg are considered. The RTCL failure criterion is applied to simulate steel fracture, whereas the iceberg fracture model is simulated by a plastic strain and pressure-based empirical failure criterion. Material models for steel and iceberg are implemented in the commercial code through a user-defined subroutine. For simplicity, the ship-iceberg collision is split into external and internal mechanics. Thus, only part of the ship structure and iceberg is modelled in the numerical simulations. The ship structure is based on the drawings of an ice-strengthened FPSO, and only the side structure is modelled. The structure model has been enlarged to minimise boundary influences. Different shapes for the leading edges of the iceberg are proposed, namely so-called " sharp " , " blunt " and " intermediate " icebergs. The iceberg shapes are simply represented by revolving a parabolic or circular profile line about its symmetry axis. Four profiles are proposed. Three different collision locations were simulated as well. Rigid analyses have also been performed. Finally, 24 numerical simulations have been carried out. The results for the maximum deflection of the outer and inner shells and the total internal energy are presented. Discussions and conclusions based on the results are provided as well. Introduction Arctic waters are attracting researchers and engineers due to the large reserves of oil and gas and the potential for new sailing routes through this area. It is expected that ship traffic will increase in this area in the near future. Thus, the probability of ship/iceberg collision increases, and it is necessary to investigate ship and iceberg collision problems in Arctic and sub-Arctic waters. This paper presents a study on the numerical simulation of iceberg collisions with ship sides.

Dielectric function, absorption coefficient, reflectivity, optical conductivity, energy loss spectra, index of
refraction and extinction coefficient of AlGaX (X = P, As, Sb) in rocksalt phase, are calculated using full
potential linearized augmented plane wave (FP-LAPW) method. All optical parameters are calculated in
the incident photon energy range 0–25 eV. The maximum value of optical conductivity observed is 15
000 S. Index of refraction has a maximum value of 4.6. A decrease in the absorption coefficient and optical
conductivity is observed when X is replaced by P, As and Sb. The extinction coefficient increases when P
is replaced by As and Sb. The high value (n = 4.6) of the index of refraction shows that AlGaX is a suitable
alloy to be used in making advanced optical devices.

The objective of this study was to assess the effect of silica nano-filler particle diameters in a computer-aided design/manufacturing (CAD/CAM) composite resin (CR) block on physical properties at the multi-scale in silico. CAD/CAM CR blocks were modeled, consisting of silica nano-filler particles (20, 40, 60, 80, and 100 nm) and matrix (Bis-GMA/TEGDMA), with filler volume contents of 55.161%. Calculation of Young's moduli and Poisson's ratios for the block at macro-scale were analyzed by homogenization. Macro-scale CAD/CAM CR blocks (3 × 3 × 3 mm) were modeled and compressive strengths were defined when the fracture loads exceeded 6075 N. MPS values of the nano-scale models were compared by localization analysis. As the filler size decreased, Young's moduli and compressive strength increased, while Poisson's ratios and MPS decreased. All parameters were significantly correlated with the diameters of the filler particles (Pearson's correlation test, r = -0.949, 0.943, -0.951, 0.976, p < 0.05). The in silico multi-scale model established in this study demonstrates that the Young's moduli, Poisson's ratios, and compressive strengths of CAD/CAM CR blocks can be enhanced by loading silica nanofiller particles of smaller diameter. CAD/CAM CR blocks by using smaller silica nano-filler particles have a potential to increase fracture resistance.

A common reductionist assumption is that macro-scale behaviors can be described "bottom-up" if only sufficient details about lower-scale processes are available. The view that an "ideal" or "fundamental" physics would be sufficient to explain all macro-scale phenomena has been met with criticism from philosophers of biology. Specifically, scholars have pointed to the impossibility of deducing biological explanations from physical ones, and to the irreducible nature of distinctively biological processes such as gene regulation and evolution. This paper takes a step back in asking whether bottom-up modeling is feasible even when modeling simple physical systems across scales. By comparing examples of multi-scale modeling in physics and biology, we argue that the " tyranny of scales " problem presents a challenge to reductive explanations in both physics and biology. The problem refers to the scale-dependency of physical and biological behaviors that forces researchers to combine different models relying on different scale-specific mathematical strategies and boundary conditions. Analyzing the ways in which different models are combined in multi-scale modeling also has implications for the relation between physics and biology. Contrary to the assumption that physical science approaches provide reductive explanations in biology, we exemplify how inputs from physics often reveal the importance of macro-scale models and explanations. We illustrate this through an examination of the role of biomechanics modeling in developmental biology. In such contexts, the relation between models at different scales and from different disciplines is neither reductive nor completely autonomous, but interdependent.

Ge growth on high-indexed Si (1110) is shown to result in the spontaneous formation of a perfectly
f105g faceted one-dimensional nanoripple structure. This evolution differs from the usual Stranski-
Krastanow growth mode because from initial ripple seeds a faceted Ge layer is formed that extends
down to the heterointerface. Ab initio calculations reveal that ripple formation is mainly driven by
lowering of surface energy rather than by elastic strain relief and the onset is governed by the edge energy
of the ripple facets. Wavelike ripple replication is identified as an effective kinetic pathway for the
transformation process.

The Darss–Zingst peninsula at the southern Baltic Sea is a typical wave-dominated barrier island system which includes an outer barrier island and an inner lagoon. The formation of the Darss–Zingst peninsula dates back to the Littorina Transgression onset about 8,000 cal BP. It originated from several discrete islands, has been reshaped by littoral currents, wind-induced waves during the last 8,000 years and

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large deformations generally occur in the vicinity of a crack, the numerical framework of the chosen SGP theory is developed for allowing large strains and rotations. The material model is implemented in a commercial finite element (FE) code by a user subroutine, and crack-tip fields are evaluated thoroughly for both infinitesimal and finite deformation theories by a boundary-layer formulation. An extensive parametric study is conducted and differences in the stress distributions ahead of the crack tip, as compared with conventional plasticity, are quantified. As a consequence of the strain-gradient contribution to the work hardening of the material, FE results show a significant increase in the magnitude and the extent of the differences between the stress fields of SGP and conventional plasticity theories when finite strains are considered. Since the distance from the crack tip at which the strain gradient significantly alters the stress field could be one order of magnitude higher when large strains are
considered, results reveal that the plastic size effect could have important implications in the modelization of several damage mechanisms where its influence has not yet been considered in the literature.

This paper develops a two-way (bottom-up or hierarchical and top-down) multi-scale modeling framework for predicting fatigue crack nucleation in structural components of Titanium alloys, e.g. Ti-7Al. Pure micromechanical analyses are deficient in this regard. A parametrically homogenized constitutive model (PHCM) and a parametrically homogenized crack nucleation model (PHCNM) are developed from computational homogenization of crystal plasticity finite element (CPFE) simulation results performed on microstructural statistically equivalent RVEs or M-SERVEs. Image-based CPFE of the M-SERVEs predict time-dependent plastic deformation, as well as location and time-dependent fatigue crack nucleation in the microstructure. Micromechanical analysis data is utilized by a machine learning code to derive functional forms of PHCM and PHCNM coefficients. Macroscopic FE models for Ti-7Al test specimens are created next, by matching correlation functions of the micro-texture and other microstructural variabilities in EBSD scans. Macroscopic simulations of dwell and cyclic loading are performed and nucleation hotspots are identified by PHCNM. Top-down simulations of the local M-SERVEs are then used to probe microstructural fatigue crack nucleation sites and cycles. The multi-scale simulations predict sub-surface nucleation for a majority of dwell cracks, which is corroborated by fractography images. The computed nucleation cycles and spatial distributions across a range of loading conditions follow experimentally observed characteristics of dwell effect in Ti alloys.

The Mode I and Mode II fracture of steel fibre-reinforced self-consolidating concrete is investigated experimentally at two scales of observation, namely at the scale of a single fibre (Micro-scale) and at the scale of a single localised crack (Meso-scale). The Meso-scale data is used to calibrate and validate a material model implemented in a numerical procedure via a user material (UMAT) in the commercial finite element package Abaqus. An empirical model reconciles the fibre component characterised via a single fibre transverse pull-out test with the composite Iosipescu shear test.

The concept of numerically solving the rate theory equations was used in determining hydrogen retention to carbon, oxygen and argon impurities in bulk tungsten. In the simulations, a hydrogen pulse with low energy and low fluence was subjected to tungsten with varying impurity concentrations. Retention and release of hydrogen atoms from impurities and intrinsic high-energy traps was monitored during and after the pulse. At 500 K the detrapping of hydrogen and diffusion to the W surface was found to take place in long timescales after the pulse shutdown.