Multiscale modeling of diffuse damage and localized cracking in quasi-brittle materials under compression with a quadratic friction law

IF 3.4 3区 工程技术 Q1 MECHANICS International Journal of Solids and Structures Pub Date : 2024-08-22 DOI:10.1016/j.ijsolstr.2024.113038
Lun-Yang Zhao , Lu Ren , Ling-Hui Liu , Yuan-Ming Lai , Fu-Jun Niu , Tao You
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Abstract

The diffuse damage and localized cracking of quasi-brittle materials (i.e., rocks and concretes) under compression can be delineated by a matrix-microcrack system, wherein a solid matrix phase is weakened by a large number of randomly oriented and distributed microcracks, and the macroscopic cracking is formed by a progressive evolution of microcracks. Several homogenization-based multiscale models have been proposed to describe this matrix-microcrack system, but most of them are based on a linear friction law on the microcrack surface, rendering a linear strength criterion. In this paper, we propose a new quadratic friction law within the local multiscale friction-damage (LMFD) model to capture the plastic distortion due to frictional sliding along the rough microcrack surface. Following that, a macroscopic Ottosen-type nonlinear strength criterion is rationally derived with up-scaling friction-damage coupling analysis. An enhanced semi-implicit return mapping (ESRM) algorithm with a substepping scheme is then developed to integrate the complex nonlinear constitutive model. The performance of LMFD model is evaluated compared to a wide range of experimental data on plain concretes, and the robustness of ESRM algorithm is assessed through a series of numerical tests. Subsequently, to effectively describe the localized cracking process, a regularization scheme is proposed by combining the phase-field model with the established LMFD model, and the discretization independent crack localization is numerically verified.

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准脆性材料在二次摩擦律压缩条件下的弥散损伤和局部开裂的多尺度建模
准脆性材料(如岩石和混凝土)在压缩条件下的弥散破坏和局部开裂可以用基体-微裂缝体系来描述,其中固体基体相被大量随机定向分布的微裂缝削弱,宏观裂缝由微裂缝的逐渐演化形成。为描述这种基体-微裂缝体系,已经提出了几种基于均质化的多尺度模型,但大多数都是基于微裂缝表面的线性摩擦定律,从而得出线性强度准则。在本文中,我们在局部多尺度摩擦损伤(LMFD)模型中提出了一种新的二次摩擦定律,以捕捉沿粗糙微裂纹表面摩擦滑动引起的塑性变形。随后,通过放大摩擦-损伤耦合分析,合理推导出宏观奥特森型非线性强度准则。然后,开发了一种带有子步进方案的增强型半隐式返回映射(ESRM)算法,用于整合复杂的非线性构成模型。将 LMFD 模型的性能与素混凝土的大量实验数据进行了比较评估,并通过一系列数值测试评估了 ESRM 算法的稳健性。随后,为了有效描述局部开裂过程,通过将相场模型与已建立的 LMFD 模型相结合,提出了一种正则化方案,并对离散化独立裂缝局部化进行了数值验证。
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来源期刊
CiteScore
6.70
自引率
8.30%
发文量
405
审稿时长
70 days
期刊介绍: The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field. Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.
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