This paper presents the so-called symmetric high-order microplane (SYHOM) model for the simulation of damage localization and size effect in quasi-brittle materials. Contrarily to its predecessor, the high order microplane (HOM) model, SYHOM is formulated without rotational degrees of freedom, does not require couple stresses, and solves stability issues created by the antisymmetric components of stress and high order stress tensors. Furthermore, the formulation features variable, damage-dependent localization limiter and nonlocal characteristic length that allows reproducing correctly size and shape of the fracture process zone during the entire softening process: from crack initiation to the formation of a stress-free fracture. The paper highlights the implementation of SYHOM via isogeometric analysis with quadratic shape functions and presents several numerical simulations to demonstrate SYHOM's ability to simulate damage evolution during softening. Finally, SYHOM is validated by simulating experimental data relevant to the size effect on structural strength of notched concrete samples.

中文翻译：

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准脆性材料损伤定位和尺寸效应的对称高阶微平面模型

本文提出了所谓的对称高阶微平面 (SYHOM) 模型，用于模拟准脆性材料中的损伤定位和尺寸效应。与其前身高阶微平面 (HOM) 模型相反，SYHOM 没有旋转自由度，不需要耦合应力，并解决了由应力和高阶应力张量的反对称分量产生的稳定性问题。此外，该公式具有可变的、依赖于损伤的定位限制器和非局部特征长度，允许在整个软化​​过程中正确再现断裂过程区的大小和形状：从裂纹萌生到无应力断裂的形成。本文重点介绍了 SYHOM 通过二次形状函数的等几何分析的实施，并提供了几个数值模拟来证明 SYHOM 模拟软化过程中损伤演变的能力。最后，通过模拟与缺口混凝土样品的结构强度的尺寸效应相关的实验数据来验证 SYHOM。