A diversity of quasi-brittle materials can be observed in various engineering structures and natural objects (rocks, frozen soil, concrete, ceramics, bones, etc.). In order to predict the condition and safety of these objects, a large number of studies aimed at analyzing the strength of quasi-brittle materials has been conducted and presented in publications. However, at the modeling level, the problem of estimating the rate and acceleration of destruction of a quasi-brittle material under loading remains relevant. The purpose of the study was to substantiate the function of damage to a quasi-brittle material under uniaxial compression, determine the rate, acceleration and jerk of the damage process, and also to apply the results obtained to predicting the destruction of trabecular bone tissue. In accordance with the purpose of the study, the basic concepts of fracture mechanics and standard methods of mathematical modeling were used. The proposed model is based on the application of the previously obtained differentiable damage function without parameters. The results of the study are presented in the form of plots and analytical relations for computing the rate, acceleration and jerk of the damage process. Examples are given. The predicted peak of the combined effect of rate, acceleration and jerk of the damage process are found to be of practical interest as an additional criterion for destruction. The simulation results agree with the experimental data known from the available literature.

中文翻译：

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单轴压缩过程中准脆性材料的损伤函数、损伤率、加速度和加加速度：小梁骨组织破坏分析的模型及应用

在各种工程结构和自然物体（岩石、冻土、混凝土、陶瓷、骨骼等）中可以观察到多种准脆性材料。为了预测这些物体的状况和安全性，已经进行了大量旨在分析准脆性材料强度的研究，并在出版物中进行了介绍。然而，在建模级别，估计加载下准脆性材料的破坏速率和加速度的问题仍然具有相关性。该研究的目的是证实在单轴压缩下对准脆性材料的损伤作用，确定损伤过程的速率、加速度和急动度，并将获得的结果应用于预测骨小梁组织的破坏。根据研究目的，使用了断裂力学的基本概念和数学建模的标准方法。所提出的模型基于先前获得的无参数可微损伤函数的应用。研究结果以绘图和分析关系的形式呈现，用于计算损坏过程的速率、加速度和加加速度。给出了例子。发现损坏过程的速率、加速度和急动的组合效应的预测峰值作为破坏的附加标准具有实际意义。模拟结果与现有文献中已知的实验数据一致。所提出的模型基于先前获得的无参数可微损伤函数的应用。研究结果以绘图和分析关系的形式呈现，用于计算损坏过程的速率、加速度和加加速度。给出了例子。发现损坏过程的速率、加速度和急动的组合效应的预测峰值作为破坏的附加标准具有实际意义。模拟结果与现有文献中已知的实验数据一致。所提出的模型基于先前获得的无参数可微损伤函数的应用。研究结果以绘图和分析关系的形式呈现，用于计算损坏过程的速率、加速度和加加速度。给出了例子。发现损坏过程的速率、加速度和急动的组合效应的预测峰值作为破坏的附加标准具有实际意义。模拟结果与现有文献中已知的实验数据一致。发现损坏过程的加速度和急动度作为破坏的附加标准具有实际意义。模拟结果与现有文献中已知的实验数据一致。发现损坏过程的加速度和急动度作为破坏的附加标准具有实际意义。模拟结果与现有文献中已知的实验数据一致。