Morphogenesis in plasticity: gradients, dislocation patterns & deformation bands - in recognition of Nasr Ghoniem’s research contributions

Elias C. Aifantis
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Abstract

A personal, but quite general viewpoint on current morphogenic plasticity developments is given by elaborating on dislocation patterning and deformation bands with an eye on Nasr Ghoniem’s pioneering contributions to material instabilities. It is based on the gradient approach advocated by the author in the early 1980s and subsequently pursued by him and his co-workers, as well as other leading scientists, including Ghoniem himself. Since the physical origin of plastic flow in metals is due to the existence of dislocations, a brief discussion on the removal of classical elasticity singularities for this type of line defects is provided based on a gradient modification of Hooke’s law and its extension to also include fractional and fractal effects. The article will thus first briefly revisit early efforts on pattern-forming instabilities in plasticity and then discuss the need for combined gradient-stochastic models to capture plastic heterogeneity phenomena at small scales. It will continue with listing easy-to-use fractional/fractal dislocation solutions for potential implementation to respective dislocation-based computer simulations and conclude with a few remarks on possible extensions of the Laplacian-based gradient approach described herein to other multiscale/multiphysics phenomena. The last topic is an open issue that has not been pursued as yet in the material physics and mechanics community. Even though some of our new unpublished results are preliminary and sporadically shared with the community in conference presentations available at the internet, it is hoped that they can still inspire a much-needed collective collaboration and more elaborate interdisciplinary studies in the near future.

塑性中的形态发生:梯度、位错模式和变形带——表彰Nasr Ghoniem的研究贡献
通过详细阐述位错模式和变形带,并着眼于Nasr Ghoniem对材料不稳定性的开创性贡献,给出了对当前形态形成塑性发展的个人但相当普遍的观点。它基于作者在20世纪80年代初倡导的梯度方法,随后被他和他的同事以及包括高尼姆本人在内的其他主要科学家所采用。由于金属中塑性流动的物理起源是由于位错的存在,因此基于胡克定律的梯度修正及其扩展,对这类线缺陷的经典弹性奇点的去除进行了简要讨论,以包括分数和分形效应。因此,本文将首先简要回顾早期对塑性模式形成不稳定性的研究,然后讨论在小尺度上采用梯度-随机组合模型来捕捉塑性非均质现象的必要性。本文将继续列出易于使用的分数/分形位错解决方案,用于各自基于位错的计算机模拟,并对本文描述的基于拉普拉斯的梯度方法可能扩展到其他多尺度/多物理场现象进行一些评论。最后一个主题是一个尚未在材料物理和力学界进行研究的开放性问题。尽管我们的一些新的未发表的结果是初步的,并且偶尔会在互联网上的会议报告中与社区分享,但希望它们仍然可以在不久的将来激发急需的集体合作和更详细的跨学科研究。
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期刊介绍: Journal of Materials Science: Materials Theory publishes all areas of theoretical materials science and related computational methods. The scope covers mechanical, physical and chemical problems in metals and alloys, ceramics, polymers, functional and biological materials at all scales and addresses the structure, synthesis and properties of materials. Proposing novel theoretical concepts, models, and/or mathematical and computational formalisms to advance state-of-the-art technology is critical for submission to the Journal of Materials Science: Materials Theory. The journal highly encourages contributions focusing on data-driven research, materials informatics, and the integration of theory and data analysis as new ways to predict, design, and conceptualize materials behavior.
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