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The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate (J) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of J for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate (J) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for J that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks. [ABSTRACT FROM AUTHOR]

The single edge notch specimen (SEN) is commonly used to measure the fracture toughness, or critical energy release rate of soft elastic materials. To measure toughness, an expression for the energy release rate, J, the mechanical energy available for growing the crack per unit area, is needed. Since strains in these fracture experiments can easily exceed several hundred percent, large deformation analysis is needed to calculate J. An approximate formula for J in SEN samples subjected to moderately large deformation was given by Rivlin and Thomas in J Polym Sci 10:291–318. 10.1002/pol.1953.120100303 (1953) and Greensmith in J Appl Polymer Sci 7:993–1002. 10.1002/app.1963.070070316 (1963). However, this formula works only for small crack lengths, for stretch ratio up to two and does not match the linear elastic result in the limit of small strains. In this paper we carry out a series of finite element (FE) simulations to obtain accurate approximations that are valid for all practical crack lengths and strain levels. Our FE result shows that the small crack approximation of by Rivlin and Thomas in J Polym Sci 10:291–318. 10.1002/pol.1953.120100303 (1953) does not work well in the small strain regime, and in particular, result of Greensmith in J Appl Polymer Sci 7:993–1002. 10.1002/app.1963.070070316 (1963) underestimates the energy release rate for stretch ratios less than 1.5. [ABSTRACT FROM AUTHOR]

Motivated by the dynamics of microscale oscillators with thermo-optical feedback, a simplified third-order model capturing the key features of these oscillators is developed, where each oscillator consists of a displacement variable coupled to a temperature variable. Further, the dynamics of a pair of such oscillators coupled via a linear spring is analyzed. The analytical procedures used are the variational equation method and the two-variable expansion method. It is shown that the analytical results are in agreement with the results of numerical integration. The bifurcation structure of the system is revealed through a bifurcation diagram. [ABSTRACT FROM AUTHOR]