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1. Brittle to ductile transition during compression of glassy nanoparticles studied in molecular dynamics simulations

   https://doi.org/10.1063/5.0151127  

   Akl, Marx; Huang, Liping; Shi, Yunfeng (July 2023, Journal of Applied Physics)

   Understanding how nanoparticles deform under compression not only is of scientific importance but also has practical significance in various applications such as tribology, nanoparticle-based probes, and the dry grinding of raw materials. In this study, we conducted compression tests on model brittle glassy nanoparticles using molecular dynamics simulations. We found that during the early stages of plastic deformation, shear bands formed in a similar pattern regardless of the nanoparticle size. However, as the deformation continued, dominant cracks emerged in large nanoparticles while being suppressed in smaller ones. This size-dependent brittle-to-ductile transition can be explained by a simple model based on Griffith's theory. We also investigated the effect of the surface stress state on fracture using thermally tempered nanoparticles. We observed that the presence of compressive surface stress strengthened the nanoparticle by suppressing crack formation, even when a pre-notch was present. On the other hand, tensile surface stress had the opposite effect. Interestingly, nanoparticles with both tensile and compressive surface stress promoted shear deformation, which could potentially compromise the mechanical performance of tempered glass despite delayed crack formation. 

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2. Micromechanics based discrete damage model with multiple non-smooth yield surfaces: Theoretical formulation, numerical implementation and engineering applications

   https://doi.org/10.1177/1056789517695872  

   Jin, Wencheng; Arson, Chloé (May 2018, International Journal of Damage Mechanics)

   null (Ed.)

   The discrete damage model presented in this paper accounts for 42 non-interacting crack microplanes directions. At the scale of the representative volume element, the free enthalpy is the sum of the elastic energy stored in the non-damaged bulk material and in the displacement jumps at crack faces. Closed cracks propagate in the pure mode II, whereas open cracks propagate in the mixed mode (I/II). The elastic domain is at the intersection of the yield surfaces of the activated crack families, and thus describes a non-smooth surface. In order to solve for the 42 crack densities, a Closest Point Projection algorithm is adopted locally. The representative volume element inelastic strain is calculated iteratively using the Newton–Raphson method. The proposed damage model was rigorously calibrated for both compressive and tensile stress paths. Finite element method simulations of triaxial compression tests showed that the transition between brittle and ductile behavior at increasing confining pressure can be captured. The cracks’ density, orientation, and location predicted in the simulations are in agreement with experimental observations made during compression and tension tests, and accurately show the difference between tensile and compressive strength. Plane stress tension tests simulated for a fiber-reinforced brittle material also demonstrated that the model can be used to interpret crack patterns, design composite structures and recommend reparation techniques for structural elements subjected to multiple damage mechanisms. 

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3. Brittle and ductile deformations in uniaxial compression of Si micropillars

   https://doi.org/10.1016/j.actamat.2025.121007  

   Gu, Boyang; Li, Yang; Diaz, Adrian; Peng, Yipeng; McDowell, David L; Chen, Youping (June 2025, Acta Materialia)

   This work presents a multiscale study of the uniaxial compression of Si pillars, with diameters ranging from 50 nm to 360 nm, using the Concurrent Atomistic-Continuum (CAC) method. The simulations reproduce the brittle and ductile deformation behaviors of Si pillars observed in experiments. For defect-free Si pillars compressed by a perfectly smooth flat punch with a repulsive force field to reflect an assumed rigid indenter, dislocations are nucleated from the corner of the bottom surface for pillars with diameters of 100 nm and below, while for pillars with diameters of 220 nm and above, dislocations nucleate from the top surface; multiple slip systems are activated in all pillars except for the pillar with a diameter of 50 nm. A strong size effect is thus demonstrated with regard to the nucleation of dislocations. Another key finding is the critical role of defects on the indenter surface. For a perfectly flat indenter, all the defect-free Si pillars with diameters ranging from 50 nm to 360 nm exhibit ductile deformation. By contrast, for an indenter with surface steps, all pillars with diameters of 100 nm and above deform in a brittle manner. These surface steps cause sequential nucleation of dislocations and activation of two slip systems, leading to dislocation intersection and formation of a sessile Lomer lock. Continued pileups of dislocations against the Lomer lock lead to the initiation of a crack at the intersection. The deformation mechanism underlying the crack formation is thus demonstrated. 

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4. A modified mixed-mode Timoshenko-based peridynamics model considering shear deformation

   https://doi.org/10.1016/j.ijmecsci.2024.109802  

   Bautista, Victor; Shahbazian, Behnam; Mirsayar, Mirmilad (January 2025, International Journal of Mechanical Sciences)

   The original two-dimensional bond-based peridynamic (BBPD) framework, which only considers the pairwise forces (compression and tension) between two material points, is extended by incorporating the effect of shear deformation in the calculations and its influence on the failure of the bonds. To this end, each bond is considered as a short Timoshenko beam, and by doing so, the traditional BBPD is enhanced into a more comprehensive model known as multi-polar peridynamic (MPPD). The proposed novel approach explicitly considers the shear influence factor used in Timoshenko beams and introduces a strain-based shear deformation failure criterion. The model is then validated against two benchmark experimental tests (i.e., a standard pure mode I edge crack, and a Kalthoff-Winkler configuration) reported in the literature under in-plane dynamic loading and plane stress conditions. In most cases, the developed model is shown to be more accurate in predicting the crack paths obtained from the experimental results when compared to other theoretical methods delineated in the literature. Furthermore, a noticeable change in crack branching and crack path is observed in a study on the effects of Poisson’s ratio and the loading rate. This investigation also demonstrated that the proposed MPPD model can accommodate materials with Poisson’s ratios up to 1/3, expanding the range beyond the traditional BBPD limitations. 

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5. Molecular simulation of subcritical crack growth under dry conditions in a model brittle glass

   https://doi.org/10.1063/5.0285814  

   Deng, Binghui; Basu, Swastik; Huang, Liping; Shi, Yunfeng (September 2025, Journal of Applied Physics)

   Subcritical crack growth can occur under a constant applied load below the threshold value for catastrophic failure, also known as static fatigue. Here, we report how a crack grows under a combination of stress-intensity factor (K) and temperature in a model brittle glass using molecular dynamics simulations. The model glass is under dry conditions, thus avoiding the complexity of corrosion chemistry. The crack growth rate is shown to be inconsistent with the commonly used subcritical crack growth model rooted in the transition state theory (TST), in which the applied stress-intensity factor reduces the transition barrier. A new subcritical crack growth model is proposed with a constant barrier and a K-dependent prefactor in TST, representing the size of the region for potential bond breaking. The thermomechanical condition for subcritical crack growth is also mapped in the K-T domain, in between elastic deformation and catastrophic fracture regimes. Finally, we show substantial crack self-healing once the applied load is removed, under the thermodynamic driving force of surface energy reduction. Our findings provide new insights into the mechanochemical coupling during static fatigue and call for experimental investigation of whether the activation energy is K-dependent. 

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