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1. Numerical Simulation of Fracture Initiation in Barre Granite using an Experimentally Validated XFEM Model

   Garg, P ; Hedayat, A ; Griffiths, D.V. ( June 2020 , 54th US Rock Mechanics/Geomechanics Symposium)

   null (Ed.)

   Fracturing in brittle rocks with an existing crack results in the development of a significant nonlinear region surrounding the crack tip called the fracture process zone. Various experimental and numerical studies have shown that the crack tip parameters such as the crack tip opening displacement (CTOD) and the fracture energy are critically important in characterizing the fracture process zone. In this study, numerical simulations of rock specimens with a center notch subjected to three-point bending were conducted using the extended finite element method (XFEM) along with the cohesive zone model (CZM) to account for fracture process zone. The input parameters of CZM such as the elastic and critical crack opening displacements were first estimated based on the results of three-point bending tests on the center notched Barre granite specimens. Displacements were measured using the two dimensional digital image correlation technique and used to characterize the evolution of the fracture process zone and estimate the parameters of the cohesive zone model. The results from the numerical simulations showed that CZM provided a good agreement with experimental data as it predicted all three stages of cracking from fracture process initiation to macro-crack growth. 

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2. Cyclic adaptive cohesive zone model to simulate ductile crack propagation in steel structures due to ultra‐low cycle fatigue

   https://doi.org/10.1111/ffe.13964  

   Ziccarelli, Andy ; Kanvinde, Amit ; Deierlein, Gregory ( February 2023 , Fatigue & Fracture of Engineering Materials & Structures)

   Micromechanics‐based continuum damage criteria have previously been developed to simulate the initiation of ductile fracture in structural steels under conditions with large‐scale plasticity where conventional fracture mechanics indices are invalid. Such models have been combined with methods to simulate ductile crack growth for monotonic loading. In this study, a micromechanics‐based adaptive cohesive zone model for simulating ductile crack propagation under monotonic loading is extended to handle cyclic loading. The proposed model adaptively modifies the cohesive traction–separation relationship for crack opening and closure, as the loading reverses between tension and compression. The approach is implemented into the finite element analysis platform WARP3D, and results of simulations that use the model are compared with data from coupon‐scale tests. The results demonstrate that the proposed model can accurately simulate the effect of crack propagation on specimen response, as well as other key aspects of observed behavior, including crack face closure and crack tunneling.

    

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3. A numerical study of dehydration induced fracture toughness degradation in human cortical bone

   https://doi.org/10.1016/j.jmbbm.2024.106468  

   Shin, Mihee ; Martens, Penny J. ; Siegmund, Thomas ; Kruzic, Jamie J. ; Gludovatz, Bernd ( May 2024 , Journal of the Mechanical Behavior of Biomedical Materials)

   A 2D plane strain extended finite element method (XFEM) model was developed to simulate three-point bending fracture toughness tests for human bone conducted in hydrated and dehydrated conditions. Bone microstructures and crack paths observed by micro-CT imaging were simulated using an XFEM damage model. Critical damage strains for the osteons, matrix, and cement lines were deduced for both hydrated and dehydrated conditions and it was found that dehydration decreases the critical damage strains by about 50%. Subsequent parametric studies using the various microstructural models were performed to understand the impact of individual critical damage strain variations on the fracture behavior. The study revealed the significant impact of the cement line critical damage strains on the crack paths and fracture toughness during the early stages of crack growth. Furthermore, a significant sensitivity of crack growth resistance and crack paths on critical strain values of the cement lines was found to exist for the hydrated environments where a small change in critical strain values of the cement lines can alter the crack path to give a significant reduction in fracture resistance. In contrast, in the dehydrated state where toughness is low, the sensitivity to changes in critical strain values of the cement lines is low. Overall, our XFEM model was able to provide new insights into how dehydration affects the micromechanisms of fracture in bone and this approach could be further extended to study the effects of aging, disease, and medical therapies on bone fracture. 

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4. Energy Dissipation during Crack Growth in Rubbers with Mullins Softening

   https://doi.org/10.1002/adem.202402173  

   Alzughaibi, Saleh ; Caillard, Julien ; Colombo, Davide ; Long, Rong ( January 2025 , Advanced Engineering Materials)

   The modulus and toughness of rubbers can be improved by incorporating fillers into the rubber matrix. Filled rubbers exhibit a strain‐induced softening phenomenon known as the Mullins effect. Upon deformation, filled rubbers can dissipate strain energy, which results in enhanced resistance to crack growth. An in‐depth understanding of the energy dissipation accompanying crack growth is important for the predictive modeling of rubber fracture. Herein, an experimental study on the fracture toughness of filled and unfilled rubbers with a focus on characterizing the energy dissipation caused by the Mullins effect during crack growth is presented. A particle tracking method is used to measure the nonlinear deformation fields in notched rubber specimens when subjected to monotonic tensile loading. Using the measured deformation fields and an independently calibrated constitutive model, the evolution of stress fields during crack growth is quantitatively evaluated, based on which the energy dissipation and intrinsic toughness are determined with the assumption of steady‐state crack growth. It is found that the filled rubber exhibits more energy dissipation during crack growth than the unfilled rubber. More importantly, the intrinsic toughness of the filled rubber (5000–8000 J m⁻²) is also much higher than that of the unfilled rubber (150–300 J m⁻²).

    

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5. Cohesive Zone Interpretations of Phase-Field Fracture Models

   https://doi.org/10.1115/1.4055660  

   Tran, H ; Chew, H B ( December 2022 , Journal of Applied Mechanics)

   Unlike micromechanics failure models that have a well-defined crack path, phase-field fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization length-scale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent crack-tip cohesive zone laws representing a phase-field fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I K-field loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened traction-separation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steady-state toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phase-field parameters and process zone characteristics in the material.

    

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