利用基于变异的损伤-等塑性微机械连续模型研究颗粒材料临界状态的出现

IF 3.4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL
Nurettin Yilmaz, M. Erden Yildizdag, Francesco Fabbrocino, Luca Placidi, Anil Misra
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引用次数: 0

摘要

以摩擦晶粒相互作用为例,粒状材料的机械响应具有临界状态的特征,在这种临界状态下,当受到大的剪切变形时,材料体积或应力不会发生变化。在这项研究中,使用了基于颗粒微观力学方法(GMA)的连续体模型来研究这种临界状态的出现。连续体描述是通过基于一般晶粒对相互作用所定义的弹性能和耗散能的力学概念来构建的。半变量原理为考虑包括晶粒对接触损失和不可逆变形在内的损伤和塑性现象的演变提供了基础。因此,推导出了卡鲁什-库恩-塔克(KKT)型条件,给出了不可逆现象的演化方程。值得注意的是,在这一推导过程中,并没有引用流动规则以及经典现象学连续损伤和塑性的其他类似假设。此外,还详细阐述了皮奥拉公式,以便从运动学角度将晶粒对的颗粒微观力学与连续描述联系起来。临界状态分析的概念一直是通过现象学方法或离散数值框架来处理的,而本文则在基于微观力学的连续描述中对这一概念进行了研究。本文建立了构成模型,并对耦合损伤和塑性不可逆量进行了评估。结果表明,临界状态是在施加加载路径期间以竞争/协作方式出现的与晶粒对相关的损伤和塑性演变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Emergence of critical state in granular materials using a variationally-based damage-elasto-plastic micromechanical continuum model

The mechanical response of granular materials, exemplified by frictional grain interactions, is characterized by a critical state in which deformation occurs without change of material volume or stresses when subjected to large shear deformation. In this work, a granular micromechanics approach (GMA) based continuum model is used to investigate the emergence of such a critical state. The continuum description is constructed through mechanical concepts based upon elastic and dissipation energies defined for a generic grain-pair interaction. A hemivariational principle provides the basis for considering the evolution of damage and plasticity phenomena comprising grain-pair contact loss and irreversible deformation. As a consequence, the Karush–Kuhn–Tucker (KKT)-type conditions are derived, which give the evolution equations for the irreversible phenomena. Notably, in this derivation there is no invocation of flow rules and other similar assumptions of classical phenomenological continuum damage and plasticity. Further, Piola's ansatz is elaborated to kinematically connect granular micromechanics of grain-pair to the continuum description. While the concept of critical state analysis has been handled with either phenomenological approaches or discrete numerical frameworks, in the present paper this concept is examined within a micromechanics-based continuum description. The constitutive model is established and the coupled damage and plastic irreversible quantities are assessed. The critical state is shown to emerge as grain-pair related damage and plastic evolution in a competitive/collaborative manner during the imposed loading path.

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来源期刊
CiteScore
6.40
自引率
12.50%
发文量
160
审稿时长
9 months
期刊介绍: The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.
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