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To meet the requirements of effectiveness and strength in actual engineering, based on the dynamic fracture characteristics, the dynamic propagation of orthogonal anisotropic interface cracks in piezoelectric bimaterials was analyzed. By performing Laplace transformation and Fourier transformation on the governing equations, the problem was transformed into a singular integral equation. Using the Chebyshev point method and Laplace inversion, the stress and electric displacement intensity factors at the crack tip of the orthogonal anisotropic interface were obtained. The results show that the crack length affects the dimensionless function. The longer the crack, the larger the dimensionless function. Under certain conditions, the smaller the elastic parameters, the smaller the dimensionless dynamic stress intensity factor. At the same time, the impact time also affects the dynamic crack propagation. With the passage of time, the dimensionless function first increases, then reaches a peak, and finally oscillates and converges to the static value. On this basis, the response surface method was used for analysis and prediction. The R2 value of the random forest model is 0.9886, which indicates that the model has high predictive accuracy. When the optimal values of A (d1/a), B (cpt/a) and C (c44(2)/c44(1)) are 0.4045, 1.6797 and 1.9035 respectively, the stress intensity reaches its maximum value of 1.3375.

Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.

The parameters of a narrow small-scale plastic zone in an elastoplastic piece-wise homogeneous body undergoing a shear near the tip of an interfacial crack are calculated under plane strain conditions using the Wiener-Hopf method. Crack faces are in contact with friction. The plastic zone issuing out of the crack tip at an angle to a plane interface between media is modeled as the straight line of a displacement discontinuity involving two sections. Both tangential and normal displacements undergo the discontinuity at the section adjacent to the crack tip that models material destruction area. At the other section, only the tangential displacement experiences the discontinuity. The angle between the plastic zone and interface between the media is defined from the condition that the rate of energy dissipation in the zone is maximal. The sizes of the entire plastic zone, destruction zone and shear opening displacement of the crack in its tip are determined. It is studied how the friction of the crack faces, load, and the mechanical characteristics of the material influence on the parameters of the plastic zone and stress-strain state in the vicinity of the crack tip.

We developed a generalized multiphase-field modeling framework for addressing the problem of brittle fracture propagation in quartz sandstones at microscopic length scale. Within this numerical approach, the grain boundaries and crack surfaces are modeled as diffuse interfaces. The two novel aspects of the model are the formulations of (I) anisotropic crack resistance in order to account for preferential cleavage planes within each randomly oriented quartz grain and (II) reduced interfacial crack resistance for incorporating lower fracture toughness along the grain boundaries that might result in intergranular crack propagation. The presented model is capable of simulating the competition between inter- and transgranular modes of fracturing based on the nature of grain boundaries, while exhibiting preferred fracturing directions within each grain. In the full parameter space, the model can serve as a powerful tool to investigate the complicated fracturing processes in heterogeneous polycrystalline rocks comprising of grains of distinct elastic properties, cleavage planes, and grain boundary attributes. We demonstrate the performance of the model through the representative numerical examples.

The parameters of a small-scale failure zone in the bonding material of a piecewise-homogeneous body under plane strain condition are determined using the Wiener–Hopf method. The failure zone is located at the end of an interface crack with tip at the corner point of the polygonal interface of the materials. The crack faces contact according to the law of dry friction. The failure zone is modeled by discontinuity line of the normal displacement on which the normal stress is equal to the tensile strength of the bonding material. Expressions for the length of the failure zone, the opening displacement of the crack faces, and local stress field near the crack tip are derived. The starting mechanism of the initial crack is described. It is assumed that a microcrack nucleates in some part of the failure zone and coalesces with the initial crack with increasing load. The dependence of the parameters of the failure zone, the microcracks, and the limiting load on the load and the parameters of the composite are analyzed numerically.

This paper investigates the dynamic fracture problems of interfacial cracks in piezoelectric–piezomagnetic (PE–PM) bi-layered composite structures under in-plane coupled electro-magneto-mechanical impact loadings by means of the extended finite element method (X-FEM). Considering the magnetoelectrically impermeable crack-face conditions and multi-filed coupled properties in the PE–PM composites, novel and more suitable crack-tip enrichment functions for interfacial cracks in PE–PM bi-layered composite structures are newly derived and implemented in the X-FEM, where the Newmark method is applied and proved to be effective. As the fracture parameter, the J -integral is evaluated using the domain-form of the path-independent contour integral. For dynamic analysis of interfacial cracks in infinite PE–PM bi-layered composite structures, absorbing layers based on the Sarma absorbing boundary conditions are adopted and applied to avoid the unphysical wave reflections at the artificially introduced boundaries in the X-FEM meshes. In the numerical examples, the validity of the proposed scheme is verified by comparing the numerical solutions provided by the X-FEM with either analytical results obtained by solving the corresponding singular integral equations or possible stationary values obtained by introducing the corresponding absorbing layers. Finally, by the numerical examples, the effects of the applied dynamic loadings, time variable and structural geometries on the dynamic J -integral are analyzed and discussed in detail. Some important conclusions are drawn, which should be helpful for the design and applications of the PE–PM layered composite structures.

A hydrogel can be coated on various substrates to enable multiple functions. Potential applications include biomedical devices, anti-fouling surfaces and microfluidics. In practical use, hydrogel coatings are often submerged in fluids. The swell of hydrogel coating deteriorates the interfacial bonding with the substrate. This paper presents a stress analysis of a hydrogel coating on a cylindrical metal substrate. We adopt the thermodynamic theory coupling large deformation and water migration and formulate two boundary value problems for the coating–substrate system with and without an interfacial crack. The inhomogeneous stress fields in the hydrogel coating are obtained. The influences of modulus, thickness of the hydrogel coating on the maximum radial stress at the interface are analyzed. These results may guide the design of hydrogel coating to avoid interfacial failure.Graphic abstractThe swell of a hydrogel coating deteriorates the interfacial bonding with the substrate. This paper presents a stress analysis of a hydrogel coating on a cylindrical metal substrate. We adopt the thermodynamic theory coupling large deformation and water migration, formulate two boundary value problems for the coating–substrate system with and without an interfacial crack, and obtain the inhomogeneous stress fields. These results may guide the design of hydrogel coating in future applications.

The fracture of interfacial crack is the main failure type of jointed rock mass. Therefore, it is very important to study the interfacial fracture of jointed rock mass. For the similarity of jointed rock mass and composites (all are composed by two parts, intact materials and their contact interfaces), the interface fracture mechanics widely used for analysis the interface crack of the composites (bimaterials) can be applied to study the interfacial fracture of jointed rock mass. Therefore, based on the basic theories of interface fracture mechanics, the interfacial fracture of jointed rock mass was analyzed, and one new criterion of interfacial crack initiation for jointed rock mass is proposed. Moreover, based on the proposed interfacial crack initiation criterion, the effect of main influence factors on the interfacial crack initiation of jointed rock mass was analyzed comprehensively. At last, by using the triaxial compression numerical tests on a jointed rock mass specimen with interfacial crack, the theoretical studies were verified.

In this paper, we present some rigorous results for an equilibrium problem arising from the study of fiber-reinforced composites. We consider a two-dimensional homogeneous anisotropic linear elastic body containing a thin semirigid inclusion. The semirigid inclusion is an anisotropic thin structure that stretches along one direction and moves like a rigid body possessing both rotational and translatory motion along the perpendicular direction. A pre-existing interfacial crack is subject to nonlinear conditions that do not allow the opposite crack faces to penetrate each other. We focus on a variational approach to modelling the physical phenomenon of equilibrium and to demonstrate that the energy release rate associated with perturbation of the crack along the interface is well defined. A higher regularity result for the displacement field is formulated and proved. Then, taking into account this result, we deduce representations for the energy release rates associated with local translation and self-similar expansion of the crack by means of path-independent energy integrals along smooth contour surrounding one or both crack tips. Finally, some relations between the integrals obtained are discussed briefly.

The present study analyzes the fundamental properties of a rate-dependent cohesive model applied to the description of dynamic mode-II crack propagation. To make a semi-analytical treatment possible, the idealised problem of a crack along the interface between a semi-infinite elastic layer and a rigid substrate is considered. Solutions corresponding to the propagation of the crack tip at a constant speed are constructed. Using asymptotic properties of the solution far from the crack tip allows obtaining the complete solution of the boundary value problem by direct integration without iterations, using a specific form of the shooting method. By conversion of the problem to dimensionless variables, the behavior of the system for all possible crack velocities and arbitrary combinations of material and geometric parameters can be characterized. The dependence of fracture energy and other important characteristics on model parameters and the crack speed can then be analyzed. Even if the approach is applied to a specific form of damage rate dependence and motivated by the analysis of delamination propagation, the same technique could be used for other classes of interfacial cohesive rate-dependent models.