Roadmap on multiscale materials modeling van der Giessen, Erik; Schultz, Peter A; Bertin, Nicolas ...
Modelling and simulation in materials science and engineering,
06/2020, Letnik:
28, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that ...govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.
In the past decades, considerable progress had been made in bridging the mechanics of materials to other disciplines, e.g. downscaling to the field of materials science or upscaling to the field of ...structural engineering. Within this wide context, this paper reviews the state-of-the-art of a particular, yet powerful, method, i.e. computational homogenization. The paper discusses the main trends since the early developments of this approach up to the ongoing contributions and upcoming challenges in the field.
The recent decades have seen significant progress in linking the mechanical performance of materials to their underlying microstructure. This article presents an overview of some of these ...achievements, trends, and challenges. Attention is given to methods initially developed for micromechanics and their gradual evolution toward powerful multiscale methods. Various methods have been proposed for bridging scales in mechanics of materials, all aiming for efficiency and accuracy. Computational homogenization is one of these powerful approaches, now used systematically for the assessment of structure–property relations. Novel solution methods and model reduction techniques provide tools to speed up the structure–property analysis, whereby large-scale computations have been made possible. Truly fast analyses of microstructures may be expected in the near future.
This contribution presents a novel homogenization technique for modeling heterogeneous materials with micro-inertia effects such as locally resonant acoustic metamaterials. Linear elastodynamics is ...used to model the micro and macro scale problems and an extended first order Computational Homogenization framework is used to establish the coupling. Craig Bampton Mode Synthesis is then applied to solve and eliminate the microscale problem, resulting in a compact closed form description of the microdynamics that accurately captures the Local Resonance phenomena. The resulting equations represent an enriched continuum in which additional kinematic degrees of freedom emerge to account for Local Resonance effects which would otherwise be absent in a classical continuum. Such an approach retains the accuracy and robustness offered by a standard Computational Homogenization implementation, whereby the problem and the computational time are reduced to the on-line solution of one scale only.
The paper presents an in-depth analysis of solid locally resonant acoustic metamaterials (LRAMs) consisting of rubber-coated inclusions. Dispersion properties of two-dimensional LRAMs are studied by ...means of finite-element modal analysis. For an incompressible rubber, only one practically important spectral band gap is found for in-plane modes in a low-frequency range. This result is in striking contrast with the compressible coating case, previously studied in the literature. For inclusions with a circular cross-section, the lower bound of the band gap can be evaluated exactly by means of the derived analytical solution, which is also valid for compressible coatings and can therefore be used to determine lower bounds of higher band gaps as well. The influence of geometric and material parameters, filling fraction and inclusion shape on the width of the lowest band gap is investigated in detail. Based on the results of this analysis, an optimal microstructure of LRAMs yielding the widest low-frequency band gap is proposed. To achieve the band gap at the lowest possible frequencies in LRAMs suitable for practical applications, the use of the tungsten core material is advised, as a safe and economically viable alternative to commonly considered lead and gold. Two configurations of LRAM with various sizes of coated tungsten cylindrical inclusions with circular cross-section are considered. The evolution of dispersion spectra due to the presence of different inclusions is investigated, and the parameters for optimal design of LRAMs are determined.
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such ...materials, an ansatz is proposed that allows to decompose the kinematics into three parts, i.e. a smooth mean displacement field, a long-range correlated fluctuating field, and a local microfluctuation part. With this decomposition, a homogenized solution is defined by ensemble averaging the solutions obtained from a family of translated microstructural realizations. Minimizing the resulting homogenized energy, a micromorphic continuum emerges in terms of the average displacement and the amplitude of the patterning long-range microstructural fluctuation fields. Since full integration of the ensemble averaged global energy (and hence also the corresponding Euler–Lagrange equations) is computationally prohibitive, a more efficient approximative computational framework is developed. The framework relies on local energy density approximations in the neighbourhood of the considered Gauss integration points, while taking into account the smoothness properties of the effective fields and periodicity of the microfluctuation pattern. Finally, the implementation of the proposed methodology is briefly outlined and its performance is demonstrated by comparing its predictions against full scale simulations of a representative example.
On image gradients in digital image correlation Neggers, J.; Blaysat, B.; Hoefnagels, J. P. M. ...
International journal for numerical methods in biomedical engineering,
27 January 2016, Letnik:
105, Številka:
4
Journal Article
This paper presents a computational frequency-domain boundary value analysis of acoustic metamaterials and phononic crystals based on a general homogenization framework, which features a novel ...definition of the macro-scale fields based on the Floquet-Bloch average in combination with a family of characteristic projection functions leading to a generalized macro-scale continuum. Restricting to 1D elastodynamics and the frequency-domain response for the sake of compactness, the boundary value problem on the generalized macro-scale continuum is elaborated. Several challenges are identified, in particular the non-uniqueness in selection of the boundary conditions for the homogenized continuum and the presence of spurious short wave solutions. To this end, procedures for the determination of the homogenized boundary conditions and mitigation of the spurious solutions are proposed. The methodology is validated against the direct numerical simulation on an example periodic 2-phase composite structure.
PDF
