This special issue of the International Journal for Multiscale Computational Engineering (IJMCE) is dedicated to the minisymposium “Computational Multi-Scale Modelling and Design of New Engineering Materials,” organized within the World Congress on Computational Mechanics, WCCM 2018, in New York. The issue contains seven papers selected from those presented during this symposium. The World Congress on Computational Mechanics (WCCM) brings together our scientific communities and identifies emerging research trends and issues. Such contacts are important for establishing cooperative research activities. The objective of the “Computational Multi-Scale Modelling and Design of New Engineering Materials” minisymposium was to discuss recent progress in the design of advanced engineering materials and single-layer materials with regard to problems that consider two or more length scales, with emphasis on metamaterials and nanomaterials. The fact that many presently envisaged advances in engineering and science are based on the development of a wide range of advanced materials that are designed using various modelling techniques was the motivation for the organization of the minisymposium. The modern concept of “metamaterials,” i.e., those artificially designed materials displaying exotic mechanical, optical, electrical, acoustic, or thermal properties, among others, constitutes a paradigm of this requirement. Computational mechanics contributes to solving crucial challenges in this area by exploring the application of numerical tools to the micro/meso and nano/micro scale modelling and design of materials with morphologies and topologies at low scales satisfying preconceived optimal properties at the macro-structure scale. The nature of this kind of problem, intimately related to well-defined material length scales, suggests placing these tools around computational multiscale modelling methods and optimal design techniques. All these aspects were discussed during the objective minisymposium at the WCCM. A total of 28 papers were presented during the minisymposium, and after evaluation of the presentations, 12 authors were invited to submit extended versions of their papers to this special issue of the International Journal for Multiscale Computational Engineering. After the usual peer review procedure for IJMCE, seven articles were accepted for publication. These articles focus on topics connected with widely understood applications of multiscale methods in modelling of materials, as well as atomistic and molecular approaches. The papers also deal with the RVE approach, the homogenization-based topology optimization algorithm, various phenomenological models, the Mori-Tanaka scheme, and molecular simulations in lower dimensional scales. Subsequent papers describe selected applications of multiscale modelling techniques, including the numerical homogenization of heterogeneous materials and the design of metamaterials with periodic microarchitectures. One paper shows application of the Mori-Tanaka finite element method for numerical homogenization and modelling of composite materials. Problems of computational efficiency are addressed in the paper describing the methodology for efficient performance of multiscale modelling methods in heterogeneous hardware infrastructures. The following papers are dedicated to the modelling behaviors of particular advanced materials, including simulations of laser-assisted tube bending of Inconel 718 and the modelling of single-layered MoS 2 using energy minimization and molecular dynamics with Stillinger-Weber, REBO, and ReaxFF potentials. The last paper focuses on the mathematical aspects of the solution of a delayed differential equation describing the evolution of an internal variable in the micro scale. Analytical and numerical solutions are described, and the stability and existence of these solutions are proved in the paper. The papers also address a variety of advanced materials, including steels and nonferrous metals alloys as well as graphenelike polymorphs. The guest editors of this issue express their thanks to the authors of the papers for their contributions. Particular thanks are directed to the reviewers for their hard work in reviewing the submitted papers and for help in

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前言：新型工程材料的计算多尺度建模与设计

国际多尺度计算工程杂志 (IJMCE) 的这一特刊致力于在纽约 WCCM 2018 世界计算力学大会内组织的小型研讨会“新工程材料的计算多尺度建模和设计”。本期包含从本次研讨会上发表的论文中选出的七篇论文。世界计算力学大会 (WCCM) 汇集了我们的科学界，并确定了新兴的研究趋势和问题。这种联系对于建立合作研究活动很重要。“新型工程材料的计算多尺度建模与设计”小型研讨会的目的是针对考虑两个或更多长度尺度的问题讨论先进工程材料和单层材料设计的最新进展，重点是超材料和纳米材料。许多目前设想的工程和科学进步都基于使用各种建模技术设计的各种先进材料的开发，这是组织小型研讨会的动机。“超材料”的现代概念，即那些人工设计的材料，显示出奇特的机械、光学、电学、声学或热学特性等，构成了这一要求的范例。计算力学通过探索数值工具在微观/中观和纳米/微米尺度建模和材料设计中的应用，这些材料的低尺度形态和拓扑满足宏观结构尺度上的先入为主的最佳特性，从而有助于解决该领域的关键挑战。这类问题的性质与明确定义的材料长度尺度密切相关，建议将这些工具放在计算多尺度建模方法和优化设计技术周围。所有这些方面都在 WCCM 的客观小型研讨会上进行了讨论。小型研讨会共提交了 28 篇论文，经过评估，12 位作者受邀向本期国际多尺度计算工程杂志特刊提交他们论文的扩展版本。经过 IJMCE 的常规同行评审程序，七篇文章被接受发表。这些文章侧重于与广泛理解的多尺度方法在材料建模以及原子和分子方法中的应用相关的主题。这些论文还涉及 RVE 方法、基于均质化的拓扑优化算法、各种现象学模型、Mori-Tanaka 方案和低维尺度的分子模拟。随后的论文描述了多尺度建模技术的选定应用，包括异质材料的数值均匀化和具有周期性微结构的超材料设计。一篇论文展示了 Mori-Tanaka 有限元方法在复合材料的数值均匀化和建模中的应用。在描述异构硬件基础设施中多尺度建模方法的高效性能的方法的论文中解决了计算效率问题。以下论文致力于特定先进材料的建模行为，包括 Inconel 718 激光辅助弯管的模拟以及使用能量最小化和具有 Stillinger-Weber、REBO 和 ReaxFF 电位的分子动力学的单层 MoS 2 建模. 最后一篇论文侧重于描述微观尺度内部变量演化的延迟微分方程解的数学方面。描述了解析解和数值解，并证明了这些解的稳定性和存在性。这些论文还涉及各种先进材料，包括钢和有色金属合金以及类石墨烯多晶型物。本期特邀编辑对论文作者的贡献表示感谢。特别感谢审稿人在审阅提交的论文时的辛勤工作和帮助