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J. Appl. Mech. 2017;84(7):071001-071001-8. doi:10.1115/1.4036475.

A solution to the problem of a hydraulic fracture driven by an incompressible Newtonian fluid at a constant injection rate in a permeable rock is presented in this paper. A set of governing equations are formed to obtain the fracture half-length, crack opening, and net fluid pressure. The solution is derived under the assumptions of plane strain, zero lag between fluid front and crack tip, followed by negligible fluid viscosity. The last assumption is related to a toughness-dominated fracture propagation regime therefore leading to a uniform fluid pressure along the crack surface. Early-time and late-time asymptotic solutions are obtained, which correspond to both regimes when the fluid contains within the crack and most of the injected fluid infiltrates into the rock, respectively. It is shown that these asymptotic solutions are in a simple form when the fracture propagation is dominated by the material toughness. The transient solution for the evolution from the early time to the late time is also obtained by a numerical method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(7):071002-071002-9. doi:10.1115/1.4036613.

Wrinkles are widely found in natural and engineering structures, ranging from skins to stretchable electronics. However, it is nontrivial to predict wrinkles, especially for complicated structures, such as multilayer or gradient structures. Here, we establish a symplectic analysis framework for the wrinkles and apply it to layered neo-Hookean structures. The symplectic structure enables us to accurately and efficiently solve the eigenvalue problems of wrinkles via the extended Wittrick–Williams (w–W) algorithm. The symplectic analysis is able to exactly predict wrinkles in bi- and triple-layer structures, compared with the benchmark results and finite element simulations. Our findings also shed light on the formation of hierarchical wrinkles

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(7):071003-071003-9. doi:10.1115/1.4036696.

The nonaxisymmetric transverse free vibrations of radially inhomogeneous circular Mindlin plates with variable thickness are governed by three coupled differential equations with variable coefficients, which are quite difficult to solve analytically in general. In this paper, we discover that if the geometrical and material properties of the plates vary in generalized power form along the radial direction, then the complicated governing differential equations can be reduced into three uncoupled second-order ordinary differential equations which are very easy to solve analytically. Most strikingly, for a class of solid circular Mindlin plates with absolutely sharp edge, the natural frequencies can be expressed explicitly in terms of elementary functions, with the corresponding mode shapes given in terms of Jacobi polynomials. These analytical expressions can serve as benchmark solutions for various numerical methods.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(7):071004-071004-10. doi:10.1115/1.4036672.

Bistable tape springs are ultrathin fiber-reinforced polymer composites, which could self-deploy through releasing stored strain energy. Strain energy relaxation is observed after long-term stowage of bistable tape springs due to viscoelastic effects and the tape springs might lose their self-deployment abilities. In order to mitigate the viscoelastic effects and thus ensure self-deployment, different tape springs were designed, manufactured, and tested. Deployment experiments show that a four-layer, [−45/0/90/45], plain weave glass fiber tape spring has a high capability to mitigate the strain energy relaxation effects to ensure self-deployment after long-term stowage in a coiled configuration. The two inner layers increase the deployment force and the outer layers are used to generate the bistability. The presented four-layer tape spring can self-deploy after more than six months of stowage at room temperature. A numerical model was used to assess the long-term stowage effects on the deployment capability of bistable tape springs. The experiments and modeling results show that the viscoelastic strain energy relaxation starts after only a few minutes after coiling. The relaxation shear stiffness decreases as the shear strain increases and is further reduced by strain energy relaxation when a constant shear strain is applied. The numerical model and experiments could be applied in design to predict the deployment force of other types of tape springs with viscoelastic and friction effects included.

Commentary by Dr. Valentin Fuster

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