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1. Li, B. and Hoo Fatt, M.S., “Use of a Cohesive Zone Model to Predict Dynamic Tearing of Rubber,” Tire Science and Technology, Vol. 43, No. 4, pp. 297-334, 2015.

   Li, B. and ( July 2015 , Tire science & technology)

   ABSTRACT: Tire failures, such as tread separation and sidewall zipper fracture, occur when internal flaws (cracks) nucleate and grow to a critical size as result of fatigue or cyclic loading. Sudden and catastrophic rupture takes place at this critical crack size because the strain energy release rate exceeds the tear energy of the rubber in the tire. The above-mentioned tire failures can lead to loss of vehicle stability and control, and it is important to develop predictive models and computational tools that address this problem. The objective of this article was to develop a cohesive zone model for rubber to numerically predict crack growth in a rubber component under dynamic tearing. The cohesive zone model for rubber was embedded into the material constitutive equation via a user-defined material subroutine (VUMAT) of ABAQUS. It consisted of three parts: (1) hyperviscoelastic behavior before damage, (2) damage initiation based on the critical strain energy density, and (3) hyperviscoelastic behavior after damage initiation. Crack growth in the tensile strip and pure shear specimens was simulated in ABAQUS Explicit, and good agreement was reported between finite element analysis predictions and test results
2. Modelling biological puncture: a mathematical framework for determining the energetics and scaling

   https://doi.org/10.1098/rsif.2022.0559  

   Zhang, Bingyang ; Anderson, Philip S. ( October 2022 , Journal of The Royal Society Interface)

   Biological puncture systems use a diversity of morphological tools (stingers, teeth, spines etc.) to penetrate target tissues for a variety of functions (prey capture, defence, reproduction). These systems are united by a set of underlying physical rules which dictate their mechanics. While previous studies have illustrated form–function relationships in individual systems, these underlying rules have not been formalized. We present a mathematical model for biological puncture events based on energy balance that allows for the derivation of analytical scaling relations between energy expenditure and shape, size and material response. The model identifies three necessary energy contributions during puncture: fracture creation, elastic deformation of the material and overcoming friction during penetration. The theoretical predictions are verified using finite-element analyses and experimental tests. Comparison between different scaling relationships leads to a ratio of released fracture energy and deformation energy contributions acting as a measure of puncture efficiency for a system that incorporates both tool shape and material response. The model represents a framework for exploring the diversity of biological puncture systems in a rigorous fashion and allows future work to examine how fundamental physical laws influence the evolution of these systems.
3. An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations

   https://doi.org/10.1098/rsta.2021.0365  

   Lohr, Matthew J. ; Sugerman, Gabriella P. ; Kakaletsis, Sotirios ; Lejeune, Emma ; Rausch, Manuel K. ( October 2022 , Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues’ mechanical properties for informing theoretical and computational models of biomechanical systems. Second, constitutive models can be used as a theoretical framework for extracting and comparing key quantities of interest from material characterization experiments. Over the past five decades, the Ogden model has emerged as a popular constitutive model in soft tissue biomechanics with relevance to both informing theoretical and computational models and to comparing material characterization experiments. The goal of this short review is threefold. First, we will discuss the broad relevance of the Ogden model to soft tissue biomechanics and the general characteristics of soft tissues that are suitable for approximating with the Ogden model. Second, we will highlight exemplary uses of the Ogden model in brain tissue, blood clot and other tissues. Finally, we offer a tutorial on fitting the one-term Ogden model to pure shear experimental data via both an analytical approximation of homogeneous deformation and a finite-element model of the tissue domain. Overall, we anticipate that this short review will serve as a practical introduction to the use of the Ogden model in biomechanics. This articlemore »is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.« less
4. Mechano-Triboelectric Analysis of Surface Charge Generation on Replica-Molded Elastomeric Nanodomes

   https://doi.org/10.3390/mi12121460  

   Ji, Myung ; Bazroun, Mohammed ; Cho, In ; Slafer, W. ; Biswas, Rana ; Kim, Jaeyoun ( December 2021 , Micromachines)

   Replica molding-based triboelectrification has emerged as a new and facile technique to generate nanopatterned tribocharge on elastomer surfaces. The “mechano-triboelectric charging model” has been developed to explain the mechanism of the charge formation and patterning process. However, this model has not been validated to cover the full variety of nanotexture shapes. Moreover, the experimental estimation of the tribocharge’s surface density is still challenging due to the thick and insulating nature of the elastomeric substrate. In this work, we perform experiments in combination with numerical analysis to complete the mechano-triboelectrification charging model. By utilizing Kelvin probe force microscopy (KPFM) and finite element analysis, we reveal that the mechano-triboelectric charging model works for replica molding of both recessed and protruding nanotextures. In addition, by combining KPFM with numerical electrostatic modeling, we improve the accuracy of the surface charge density estimation and cross-calibrate the result against that of electrostatic force microscopy. Overall, the regions which underwent strong interfacial friction during the replica molding exhibited high surface potential and charge density, while those suffering from weak interfacial friction exhibited low values on both. These multi-physical approaches provide useful and important tools for comprehensive analysis of triboelectrification and generation of nanopatterned tribocharge. The results willmore »widen our fundamental understanding of nanoscale triboelectricity and advance the nanopatterned charge generation process for future applications.« less
5. Damping rate measurements and predictions for gravity waves in an air–oil–water system

   https://doi.org/10.1063/5.0078160  

   Rajan, Girish Kumar ( February 2022 , Physics of Fluids)

   Dissipation of standing gravity waves of frequencies within 1–2 Hz is investigated experimentally. The waves are generated in a rectangular tank filled with water, the surface of which is covered with an oil layer of mean thickness, d. Damping rates are measured as a function of d, and compared with results from established theoretical models—in particular, with those from a recently developed three-fluid dissipation model that considers waves in a system of semi-infinitely deep fluids that lie above and below an interfacial fluid layer of finite thickness. Based on a comparison of experimental data with predictions, the oil–water interfacial elasticity, E₂, is empirically determined to be a linear function of d. The theoretical predictions include contributions from the three-fluid dissipation model, which accounts for energy losses due to shear layers at the interfaces, friction in the fluid bulk, and compression–expansion oscillations of the elastic interfaces; and from a boundary-layer dissipation model, which accounts for energy losses due to boundary layers at the tank's solid surfaces. The linear function, [Formula: see text], is used to compute the three-fluid model damping rate. An effective viscosity of the oil–water system is used to compute the boundary-layer model damping rate. The theoretical predictions are, onmore »average, within 5% of measurements for all the wave frequencies considered. The promise shown by the three-fluid model is highlighted, as are the assumptions involved in the analysis and comparisons.

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