Meniscal tears are a common, painful, and debilitating knee injury with limited treatment options. Computational models that predict meniscal tears may help advance injury prevention and repair, but first these models must be validated using experimental data. Here we simulated meniscal tears with finite element analysis using continuum damage mechanics (CDM) in a transversely isotropic hyperelastic material. Finite element models were built to recreate the coupon geometry and loading conditions of forty uniaxial tensile experiments of human meniscus that were pulled to failure either parallel or perpendicular to the preferred fiber orientation. Two damage criteria were evaluated for all experiments: von Mises stress and maximum normal Lagrange strain. After we successfully fit all models to experimental force–displacement curves (grip-to-grip), we compared model predicted strains in the tear region at ultimate tensile strength to the strains measured experimentally with digital image correlation (DIC). In general, the damage models underpredicted the strains measured in the tear region, but models using von Mises stress damage criterion had better overall predictions and more accurately simulated experimental tear patterns. For the first time, this study has used DIC to expose strengths and weaknesses of using CDM to model failure behavior in soft fibrous tissue.
A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler– Pister and Willam–Warnke
An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr–Coulomb criteria—an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.
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- Award ID(s):
- 1663244
- NSF-PAR ID:
- 10170737
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 476
- Issue:
- 2238
- ISSN:
- 1364-5021
- Page Range / eLocation ID:
- 20190861
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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There are several possible mechanisms of failure of glassy polymers that can be activated by different states of stress in the material. They are reflected in the various failure criteria used to predict initiation of damage in the polymer based on the components of stress tensor. We investigated the applicability of several popular failure criteria (the von Mises, the Drucker-Prager, the parabolic stress, and the dilatational strain energy density) to predict processing-induced damage due to cooling after curing observed in 3D woven composites with high level of through-thickness reinforcement. We developed high-fidelity mesoscale finite element models of orthogonally reinforced carbon/epoxy composites and predicted their response to the uniform temperature drop from the curing to room temperature. Comparison of the simulation results with the X-ray computed microtomography indicates that matrix failure caused by the difference in thermal expansion coefficients of carbon fiber and epoxy resin is well predicted by the dilatational strain energy criterion. Initiation and propagation of this failure was numerically investigated using sequential deactivation of elements exceeding the allowable equivalent stress.more » « less
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The use of mechanical metamaterials in engineering applications is often limited because of uncertainty regarding their deformation behavior. This uncertainty necessitates large safety factors and assumptions about their behavior to be included in mechanical designs including metamaterials, which detracts from their greatest benefit, viz. their ultralight weight. In this study, a yield envelope was created for both a bending-dominated and a stretching-dominated cellular material topology to improve the understanding of the response of cellular materials under various load types and orientations. Experimental studies revealed that the shear strength of a cellular material is significantly lower than that predicted by Mohr’s criterion, necessitating a modification of the Mohr’s yield criterion for cellular materials. All topologies experienced tension–compression anisotropy and topology orientation anisotropy during loading, with the stretching-dominated topology experiencing the largest anisotropies.more » « less
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The use of mechanical metamaterials in engineering applications is often limited because of uncertainty regarding their deformation behavior. This uncertainty necessitates large safety factors and assumptions about their behavior to be included in mechanical designs including metamaterials, which detracts from their greatest benefit, viz. their ultralight weight. In this study, a yield envelope was created for both a bending-dominated and a stretching-dominated cellular material topology to improve the understanding of the response of cellular materials under various load types and orientations. Experimental studies revealed that the shear strength of a cellular material is significantly lower than that predicted by Mohr’s criterion, necessitating a modification of the Mohr’s yield criterion for cellular materials. All topologies experienced tension–compression anisotropy and topology orientation anisotropy during loading, with the stretching-dominated topology experiencing the largest anisotropies.more » « less
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We present a double-yield-surface plasticity theory for transversely isotropic rocks that distinguishes between plastic deformation through the solid matrix and localized plasticity along the weak bedding planes. A recently developed anisotropic modified Cam-Clay model is adopted to model the plastic response of the solid matrix, while the Mohr-Coulomb friction law is used to represent the sliding mechanism along the weak bedding planes. For its numerical implementation, we derive an implicit return mapping algorithm for both the semi-plastic and fully plastic loading processes, as well as the corresponding algorithmic tangent operator for finite element problems. We validate the model with triaxial compression test data for three different transversely isotropic rocks and reproduce the undulatory variation of rock strength with bedding plane orientation. We also implement the proposed model in a finite element setting and investigate the deformation of rock surrounding a borehole subjected to fluid injection. We compare the results of simulations using the proposed double-yield-surface model with those generated using each single yield criterion to highlight the features of the proposed theory.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2019.0861
