The fracture properties of pre-cracked monocrystalline/polycrystalline graphene were investigated via a finite element method based on molecular structure mechanics, and the mode I critical stress intensity factor (SIF) was calculated by the Griffith criterion in classical fracture mechanics. For monocrystalline graphene, the size effects of mode I fracture toughness and the influence of crack width on the mode I fracture toughness were investigated. Moreover, it was found that the ratio of crack length to graphene width has a significant influence on the mode I fracture toughness. For polycrystalline graphene, the strain energy per unit area at different positions was calculated, and the initial fracture site (near grain boundary) was deduced from the variation tendency of the strain energy per unit area. In addition, the effects of misorientation angle of the grain boundary (GB) and the distance between the crack tip and GB on mode I fracture toughness were also analyzed. It was found that the mode I fracture toughness increases with increasing misorientation angle. As the distance between the crack tip and GB increases, the mode I fracture toughness first decreases and then tends to stabilize.

A novel auxetic honeycomb (RSSHR) is developed by introducing the arc-shaped structure into the re-entrant star-shaped honeycomb (RSSH). Based on theoretical models and finite element methods, the dynamic crushing responses of RSSH and RSSHR plate (RSSH_P and RSSHR_P) structures are investigated to elucidate the dependence of plateau stress, negative Poisson’s ratio (NPR), deformed shape and specific energy absorption (SEA) on crushing velocity. The stress–strain curves of two types of structures are calculated to analyze configuration–mechanical property relationships. The results exhibit that the plateau stress and SEA of the RSSH_P and RSSHR_P structures increase as the crushing velocity increases. Owing to the stress-mitigating effect of the arc-shaped structure, the RSSHR_P structure exhibits a stronger NPR effect. And the SEA of the RSSHR_P structure is higher than that of the RSSH_P structure. In addition, it is also found that at low crushing velocity, the stress–strain curves of the two structures exhibit three distinct stages: the elastic stage (I), the stress plateau stage (II) and the densification stage (III). During the crushing process, there are three deformed shapes. They are the global deformed shape, the local deformed shape and the layer-by-layer deformed shape.

Compression packers are widely used in oil and gas well operations for zonal isolation, yet the large-deformation mechanical behavior of their rubber sealing elements lacks a closed-form analytical solution. This paper presents a complete theoretical analysis of the axisymmetric compression of an annular rubber cylinder based on the incompressible Mooney–Rivlin hyper-elastic model. The deformation process is divided into three successive stages: free expansion, casing-constrained deformation, and fully constrained deformation. Analytical expressions for the principal stretches, stress fields, and axial force are derived for each stage by integrating the radial equilibrium equation with proper treatment of the Lagrange multiplier. The frictionless analytical results are validated against axisymmetric finite element simulations, showing excellent agreement for all stress components. The applicability of the frictionless theory to frictional conditions is then examined. Results show that although friction introduces non-uniform axial deformation and end bulging, the average contact pressure on the rubber–mandrel interface agrees closely with the theoretical prediction, especially at higher axial forces (150–250 kN). A linear relationship between the average contact pressure and the axial force is confirmed, providing a simple design tool. The theoretical solution offers a computationally efficient alternative to finite element analysis for preliminary packer design and parametric studies.

The rubber cylinder is the core sealing element of a compression packer, and its structural stability directly determines downhole sealing reliability. The rubber cylinder is made of HNBR, while the central tube, support rings, and casing are made of 35 CrMo steel. During axial compression, the rubber cylinder may undergo localized creasing instability characterized by sharp self-contacting folds, inducing severe stress concentration and degrading sealing performance. This paper presents a systematic finite element investigation of creasing behavior in rubber cylinders, focusing on meshing strategy, interfacial friction, and geometric parameters. A refined meshing strategy is proposed that captures creasing and self-contact, demonstrating that a mesh size less than 0.5 mm is required. A zone-specific friction model distinguishes the tribological roles of different interfaces: increasing friction at the support ring suppresses shoulder protrusion, while increasing friction at the central tube reduces contact stress. For the packer geometries and operating conditions investigated, the critical expansion ratio at which the crease initiates is approximately 1.13. Increasing rubber cylinder length and reducing radial clearance are identified as effective measures to suppress creasing. The logarithmic strain at crease nucleation is approximately −0.66, which is more negative than the Biot linear bifurcation threshold (−0.61). This deeper strain is mechanically attributed to bulging-induced curvature and superimposed bending compression, confirming the crease as a nonlinear instability. This work provides numerical references for the anti-creasing design of packer rubber cylinders under quasi-static setting.