Abstract
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.
Highlights
IntroductionThere is a large class of natural and artificial materials that, under mechanical influences, exhibit to a greater or lesser extent the property of brittleness
The main focus in this study was given to the substantiation of the damage function of a quasi-brittle material, modeling the kinetics of destruction during uniaxial compression on the example of trabecular bone tissue
New finite element method (FEM) models, which take into account the inhomogeneity of trabeculae, anisotropy and nonlinear behavior of samples of trabecular bone tissue, allow us to study the functioning of the trabecular bone in more detail [34]
Summary
There is a large class of natural and artificial materials that, under mechanical influences, exhibit to a greater or lesser extent the property of brittleness. Such quasi-brittle materials include rocks, concrete, ceramics, bones, etc. The main focus in this study was given to the substantiation of the damage function of a quasi-brittle material, modeling the kinetics of destruction during uniaxial compression on the example of trabecular bone tissue. The relevance of the topic and the practical significance of the presented work are determined by the fact that the solution of this problem is necessary sented research was to determine the speed, acceleration and jerk of the proce to a quasi-brittle material on the example of trabecular bone tissue under u pression. In addition to [8], a more detailed an damage function was carried out, which allowed us to obtain new analytica to improve the the understanding the structure and function the damage trabecular bone tissue, determining rate andofother characteristics ofofthe process of a qua which will contribute to a more accurate prediction of the risk of bone fractures [7]
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