Rock masses in deep earth, deep sea, and deep space environments are often subjected to confining pressure. Considering the effects of confining pressure and friction on crack surfaces, closed-form solutions for mode I and mode II stress intensity factors and T-stress of a center-cracked Brazilian disk subjected to combined confining pressure and non-uniform pressure are presented using weight function method. The convergence of these closed-form solutions is assessed, and the recommended summation coefficients for a given truncation error are provided. Using the derived closed-form solutions, the stress intensity factors and T-stress of the center-cracked Brazilian disk under various loading conditions are calculated, and the effects of loading angle, crack length, contact angle, confining pressure, and friction coefficient on the stress intensity factors and T-stress are analyzed. Furthermore, the critical loading angle theta c for the transition of the center-cracked Brazilian disk specimen from tensile-shear fracture to compressive-shear fracture under combined confining pressure and non-uniform pressure is also given. The results indicate that confining pressure and crack-surface friction suppress both mode I and mode II fracturing of the center-cracked Brazilian disk specimen. When the loading angle is small and the contact angle is large, the influence of contact angle on stress intensity factors and T-stress should be taken into account.
This paper presents new results on the modeling of interfaces in viscoelastic media, taking into account inertial effects and damage evolution. The approach relies on an asymptotic expansion method to derive effective interface models from full three-dimensional descriptions of a stratified composite, as the thickness of the intermediate adhesive layer tends to zero. The asymptotic analysis highlights the combined influence of the viscoelastic properties of the constituent materials, inertial contributions, and damage processes. Appropriate scaling laws for the physical parameters of the adhesive layer are introduced, and the corresponding limit configurations are derived. Three distinct regimes are considered: (1) constant mass density of the adhesive, with low stiffness and very low viscosity; (2) constant mass density, with low stiffness and low viscosity; (3) very high mass density, scaling as the inverse of the layer thickness, with low stiffness and viscosity. These different regimes give rise to specific asymptotic behaviors. In the first two cases, the inertial contribution vanishes in the limit, yielding a classical equation for the damage variable at the interface, in the elastic and viscoelastic setting, respectively. In the third case, the limit configuration acquires a nonlocal character and keeps track of the dynamics in the adhesive layer.
This paper presents a numerical analysis of the vibration damping effects of an acoustic black hole on a rectangular plate supported by four three-directional nonlinear springs at its four corners, with particular attention to how the nonlinear corner supports affect the acoustic black hole-related damping performance. Here, we adopt an acoustic black hole with a two-dimensional crater-like profile, and a viscoelastic damping material is layered in the crater region. To investigate the effects of the spring constant on the damping effects of the acoustic black hole using the finite element method with the modal strain-energy method, modal loss factors, resonant frequencies, and eigenmodes were obtained under small-amplitude conditions. Subsequently, linear eigenmodes were introduced as normal coordinates, and the discretized equations including the restoring force of the nonlinear springs were transformed into nonlinear ordinary differential equations for efficient nonlinear dynamic analysis. Half-triangular wave pulses were applied to these transformed equations to obtain the impact responses. The acoustic black hole reduces nonlinear impact responses. The linear and third-order nonlinear spring stiffnesses also affect higher harmonics, fractional components, modal coupling, and peak clustering. This suggests that discrete nonlinear corner supports affect the vibration mitigation performance of acoustic black hole plates.
The peridynamic theory extends the classical continuum theory by allowing material points to interact with other material points separated by finite distances. This feature enables direct application to discontinuities, such as cracks, making the peridynamic theory particularly valuable in fracture mechanics. This work improves the bond-based peridynamic plate theory of [1], which employs a through-thickness expansion of the displacement field using the lower lateral surface as the reference plane. Whereas in the original formulation the governing equations are derived by evaluating the equation of motion at the reference and top surfaces, in this work arbitrary positions are considered along the thickness, yielding both zeroth- and first-order approximations of the displacement field. Computational results obtained from these two theories reveal numerical instabilities, motivating a further improvement by considering the midsurface of the plate as the reference plane. Because the integration of odd terms of the expansion vanishes, a second-order approximation of the displacement field is also considered. The theories together with a prototype microelastic brittle material model are then applied to formulate two fracture mechanics problems. In the first problem, the three brittle plate models yield similar results for small plate thicknesses, as expected from the peridynamic theory of membranes. For large enough thickness, however, the first two models predict very large displacements after a relatively small simulation time, and the third model predicts crack patterns that are consistent with those found for small thicknesses. In the second problem, the third brittle plate model predicts numerically stable results that are physically plausible.
To evaluate the protective performance of lightweight hybrid armors, this work investigates the ballistic characteristics of ultra-high-molecular weight polyethylene/ceramic/ultra-high-molecular weight polyethylene sandwich structures analytically and numerically. A three-stage analytical model of the ballistic characteristics of ultra-high-molecular weight polyethylene/ceramic/ultra-high-molecular weight polyethylene sandwich structures is developed, specifically incorporating a dynamic residual plug mass unloading effect to precisely characterize the evolving projectile–target momentum exchange. The finite element framework is validated against published ballistic experiments for both ultra-high-molecular weight polyethylene laminates and silicon carbide-based targets, including residual velocity, perforation/arrest behavior, and representative failure characteristics. In addition, numerical calculations for the ballistic characteristics of ultra-high-molecular weight polyethylene/ceramic/ultra-high-molecular weight polyethylene sandwich structures are conducted. The analytical results are in good agreement with the numerical results. The investigation reveals a distinct velocity-dependent transition in energy dissipation mechanisms: in the moderate-velocity regime (900–1400 m/s), the ceramic conoid facilitates effective load diffusion, activating high-efficiency global membrane stretching in the ultra-high-molecular weight polyethylene back plate (accounting for approximately 43–48% of the component-level target internal energy in the finite element analysis). Conversely, as the impact velocity increases, the failure mode shifts toward localized shear-dominated perforation driven by intensive ceramic comminution. Parametric analyses under constant areal density constraints identify a best-performing intermediate H c / H b ratio among the investigated configurations, balancing projectile attenuation with rear-plate membrane energy absorption. Furthermore, the dimensionless strength factor K is identified as a critical determinant, where high-strength ceramics exponentially suppress dynamic impact forces, facilitating a transition to high-energy-absorbing global deformation modes. This research elucidates the hierarchical failure evolution of sandwich architectures and provides a quantitative theoretical framework for the mass-efficient design of advanced composite armors.
