基于位错的有限元方法用于结构超材料的均质化极限域表征

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Renato Zona, Luca Esposito, Simone Palladino, Vincenzo Minutolo
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引用次数: 0

摘要

目的异质和微结构材料一直是多尺度和均质化技术的研究对象,这些技术旨在识别等效连续体的弹性特性。拟议的研究通过使用代表性体积元素(RVE)的极限分析方法分析极限强度,对异质材料结构超材料进行力学表征。为了获得所需的材料强度,我们采用了一种新颖的有限元计算方法,该方法基于通过有限元推导自平衡解来计算下限定理,并结合 Melàn 计算方法中的极限分析。利用标准有限元技术,通过对位移和应变进行有限元离散化,建立了线性算子 V,该算子将自平衡内部激励与类似位移的节点参数联系起来。弹性常数矩阵是通过对 RVE 进行数值载荷试验计算得出的,并用商用有限元计算代码进行了模拟。这一步骤显示了各向同性特性与 RVE 密度的关系,并通过齐纳理论进行了验证。材料的各向同性条件只有在体心立方(BCC)和面心立方(FCC)之间达到一定的截面比时才能实现,同时忽略节点处的挠曲效应。满足齐纳条件的密度代表了各向同性桁架的各向同性静力学。通过对残余延展性和耗散能的评估,确定了极限各向异性的测量参数。该建议的新颖之处在于同时提出了材料的线性化和非线性极限位置;因此,它为进一步对结构进行极限分析提供了起点,而结构的基本体积已通过建议的方法进行了描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dislocation-based finite element method for homogenized limit domain characterization of structured metamaterials

Purpose

Heterogeneous and micro-structured materials have been the object of multiscale and homogenization techniques aimed at recognizing the elastic properties of the equivalent continuum. The proposed investigation deals with the mechanical characterization of the heterogeneous material structured metamaterials through analyzing the ultimate strength using the limit analysis of the Representative Volume Element (RVE). To get the desired material strength, a novel finite element formulation based on the derivation of self-equilibrated solutions through the finite elements devoted to calculating the lower bound theorem has been implemented together with the limit analysis in Melàn’s formulation.

Design/methodology/approach

The finite element formulation is based on discrete mapping of Volterra dislocations in the structure using isoparametric representation. Using standard finite element techniques, the linear operator V, which relates the self-equilibrated internal solicitation to displacement-like nodal parameters, has been built through finite element discretization of displacement and strain.

Findings

The proposed work presented an elastic homogenization of the mechanical properties of an elementary cell with a geometry known in the literature, the isotropic truss. The matrix of elastic constants was calculated by subjecting the RVE to numerical load tests, simulated with a commercial FEM calculation code. This step showed the dependence of the isotropy properties, verified with Zener theory, on the density of the RVE. The isotropy condition of the material is only achieved for certain section ratios between body-centered cubic (BCC) and face-centered cubic (FCC), neglecting flexural effects at the nodes. The density that satisfies Zener’s conditions represents the isotropic geomatics of the isotropic truss.

Originality/value

For the isotropic case, the VFEM procedure was used to evaluate the isotropy of the limit domain and was compared with the Mises–Schleicher limit domain. The evaluation of residual ductility and dissipation energy allowed a measurement parameter for the limit anisotropy to be defined. The novelty of the proposal consisted in the formulation of both the linearized and the nonlinear limit locus of the material; hence, it furnished the starting point for further limit analysis of the structures whose elementary volume has been described through the proposed approach.

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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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