Bone encompasses a complex arrangement of materials at different length scales, which endows it with a range of mechanical, chemical, and biological capabilities. Changes in the microstructure and characteristics of the material, as well as the accumulation of microcracks, affect the bone fracture properties. In this study, two-dimensional finite element models of the microstructure of cortical bone were considered. The eXtended Finite Element Method (XFEM) developed by Abaqus software was used for the analysis of the microcrack propagation in the model as well as for local sensitivity analysis. The stress–strain behavior obtained for the different introduced models was substantially different, confirming the importance of bone tissue microstructure for its failure behavior. Considering the role of interfaces, the results highlighted the effect of cement lines on the crack deflection path and global fracture behavior of the bone microstructure. Furthermore, bone micromorphology and areal fraction of cortical bone tissue components such as osteons, cement lines, and pores affected the bone fracture behavior; specifically, pores altered the crack propagation path since increasing porosity reduced the maximum stress needed to start crack propagation. Therefore, cement line structure, mineralization, and areal fraction are important parameters in bone fracture. The parameter-wise sensitivity analysis demonstrated that areal fraction and strain energy release rate had the greatest and the lowest effect on ultimate strength, respectively. Furthermore, the component-wise sensitivity analysis revealed that for the areal fraction parameter, pores had the greatest effect on ultimate strength, whereas for the other parameters such as elastic modulus and strain energy release rate, cement lines had the most important effect on the ultimate strength. In conclusion, the finding of the current study can help to predict the fracture mechanisms in bone by taking the morphological and material properties of its microstructure into account.

To design a more efficient energy absorber, it is critical to evaluate how changing the design parameters affects its performance, and also determine each one’s order of significance. In this paper, using a new approach, the behavior and response of straight, double-tapered, and triple-tapered thin-walled tubes with rectangular cross sections under axial and dynamic loading are investigated by performing a sensitivity analysis on a support vector machine (SVM) as a surrogate machine learning model. First, a finite element model of the energy absorber is constructed and validated with available experimental and theoretical studies. Next, a design of experiments was developed using the Sobol series sampling method and an appropriate dataset was created. This information is then used to develop an SVM model to predict the initial peak load and mean load of tubes. The accuracy of the machine learning created in this study is then assessed, and it is demonstrated that the developed model can precisely predict the performance of the absorber. The machine learning model is then subjected to a Sobol sensitivity analysis, and the outcomes are compared to those of the parametric study. The results suggest that the thickness of the tube has a stronger effect on the absorber performance than other geometric parameters. Comparing the effects of different material parameters on the behavior of tubes, the results show that yield strength has the greatest impact on the response of the energy absorber. It is also observed that the tapered tubes have a much lower initial peak load compared to straight ones.

This paper studies the behavior and response of triple thin-walled tubes with rectangular cross-sections under axial and dynamic loading. First, a finite element model of the energy absorber is prepared, and the results are validated with available theoretical and experimental studies. Then the effect of different input parameters such as tube-thickness, cross-sectional ratio, slope angle, and material parameters on the performance of thin-walled energy absorbers is studied.The simulation results show that the thickness of the tube has a more significant effect on the absorber’s performance than other geometric parameters. The results also show that changing the cross-sectional ratio and the inclination angle of the tube changes the initial peak load more than the average load of the absorber. Comparing the effects of different materials on the performance of absorbers, the results show that steel alloys record the highest average loads and initial peak loads, followed by titanium alloys and then aluminum alloys. This information is then used to develop a machine learning model to predict the performance of the absorbers. Then, the performance of the machine learning developed in this study is evaluated, and it is shown that the developed machine learning can accurately predict the absorber’s performance. Finally, a Sobol sensitivity analysis is performed on the machine-learned model and the results are compared with those of parametric study.

In this paper, micromechanical simulations are employed to evaluate the performance of the Tsai–Wu and Hashin failure criteria for fiber-reinforced composites, especially in stress states whose experimental reproduction is complicated. Micromechanical responses are generated using a finite element model of a representative volume element, in which only the matrix material experiences damage and the fibers are assumed to be elastic. Micromechanical simulations of basic load cases are used to calibrate macrolevel criteria. Finally, the response of the micromodel and macromodels is compared for various load combinations. Despite a good agreement between Tsai–Wu criterion predictions and micromodel results in a wide range of stress states, some stress combinations are highlighted for which the strength is not predicted accurately. Additionally, accuracy of the Hashin criterion suffers from ignoring the influence of stress in fiber direction on matrix failure.

Micromechanical simulation of composite material failure requires a pressure-dependent failure model for the polymeric matrix. Available pressure-dependent damage formulations assume a certain shape of the stress-strain law under uniaxial loading. However, upon close inspection none of the available formulations is able to reproduce the assumed shape. This implies that input values for the fracture energy cannot be recovered exactly. In this paper, a new methodology for developing consistent pressure-dependent damage models for polymeric materials is presented. Using this method the predefined shape of the stress-strain relation of an element with localized deformation under uniaxial tension can be exactly reproduced which enables further to recover the exact amount of energy dissipation consistent with the input toughness. The methodology is demonstrated for two different softening laws, namely linear and exponential softening. These models are applied to the damage analysis of unidirectional continuous fiber-reinforced composites. The formulation is validated by simulation of a test for Mode-I fracture energy characterization and comparing the load-displacement response with that obtained with cohesive elements.