基于异质微尺度的微形态连续体建模

IF 2.8 3区 工程技术 Q2 MECHANICS
Pamela D.N. Reges, Roque L.S. Pitangueira, Leandro L. Silva
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引用次数: 0

摘要

传统连续介质力学在全面描述微观结构影响不容忽视的材料行为方面存在局限性,而广义连续介质理论则有望解决这一问题。例如,准脆性材料的宏观响应与其异质微观结构密切相关,而经典理论的简化假设不足以解决所有相关现象。通过加入与微观尺度相关的长度尺度,广义连续体可以处理以弹性降解介质表示的准脆性材料中的局部化问题。极大限制此类广义模型适用性的一个重要缺点是众多弹性参数的定义。考虑到微形态理论,描述各向同性介质需要 18 个常数。本文详细介绍了一种确定微形态构成关系的数值方法,该方法以前仅适用于均质介质,现在则基于异质微尺度的均质化。由聚集体和基质形成的微观结构在较细尺度下通过取放算法生成,其行为由经典连续体描述。本文进行了分析,以了解细尺度的不同特征(如网格、微连续尺寸和异质性分布)对所产生的宏观微观形态构成关系的影响。随后,介绍了一种模拟,其中检测了局部化现象,并采用了专门针对微观连续体提出的损伤模型。这项工作可以在广义连续介质理论的框架内建立能够捕捉微观结构影响的模型,而微观结构的影响在建立准脆性介质模型时往往被忽视,同时还能解决定义弹性参数的难题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modeling of micromorphic continuum based on a heterogeneous microscale

Generalized continuum theories have emerged as a promising solution for the limitations of traditional continuum mechanics in fully describing the behavior of materials in which the influence of the microstructure is not negligible. The macroscopic response of quasi-brittle material, for example, is closely tied to its heterogeneous microstructure and the simplifying hypothesis of classical theory is insufficient to address all the phenomena involved. By incorporating a length scale associated to the microscale, generalized continua can handle localization issues in quasi-brittle materials represented as elastic-degrading media. An important drawback that greatly limits the applicability of such generalized models is the definition of the numerous elastic parameters. Taking into account the micromorphic theory, 18 constants are required for the description of an isotropic medium. In this paper, a numerical approach for determining the micromorphic constitutive relations, previously applied only for a homogeneous medium, is detailed based on the homogenization of a heterogeneous microscale. The microstructure formed by aggregates and matrix considered in the finer-scale is generated by the take-and-place algorithm and its behavior is described by a classical continuum. An analysis is here conducted in order to understand the effect of different characteristics of the finer-scale, as mesh, microcontinuum size, and heterogeneity distribution, on the resulting macroscopic micromorphic constitutive relations. Afterwards, a simulation is presented wherein the localization phenomenon is detected and a damage model specifically proposed for the micromorphic continuum is employed. This work could lead to models that are able to capture the microstructure influence, often disregarded when modeling quasi-brittle media, within the framework of generalized continuum theory, while also addressing the challenge of defining the elastic parameters.

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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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