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J. Appl. Mech. 2017;84(5):051001-051001-15. doi:10.1115/1.4036018.

Attributed to its significance in a wide range of practical applications, the post-buckling behavior of a beam with lateral constraints has drawn much attention in the last few decades. Despite the fact that, in reality, the lateral constraints are often flexible or deformable, vast majority of studies have considered fixed and rigid lateral constraints. In this paper, we make a step toward bridging this gap by studying the post-buckling behavior of a planar beam that is laterally constrained by a deformable wall. Unfortunately, the interaction with a compliant wall prevents derivation of closed-form analytical solutions. Nevertheless, careful examination of the governing equations of a simplified model reveals general properties of the solution, and let us identify the key features that govern the behavior. Specifically, we construct universal “solution maps” that do not depend on the mode number and enable simple and easy prediction of the contact conditions and of the mode-switching force (the force at which the system undergoes instantaneous transition from one equilibrium configuration (or mode) to another). The predictions of the mathematical model are validated against finite element (FE) simulations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(5):051002-051002-8. doi:10.1115/1.4036094.

A cantilever beam is subjected to both lateral force and compression under gravity. By taking into account the potential energy variation of the system, we develop a theoretical result that greatly simplifies the bending vibration frequency calculation in agreement with the experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(5):051003-051003-11. doi:10.1115/1.4036193.

Two types of tubular dielectric elastomers (DE) torsional actuators are studied in this work, which are, respectively, reinforced by a family and two families of helical inextensible fibers. When subject to a radial electric field, torsional deformation will be induced in the DE actuators due to the constraint of inextensible fibers. By conducting finite deformation analysis with the principal axis approach and adopting appropriate constitutive equations, simple analytical solutions are obtained for the considered DE actuators. Furthermore, the effects of material parameters and the fiber angles as well as externally applied axial force and twist moment on the voltage-induced torsional behaviors of the two DE actuators are discussed in order to explore their maximum torsional actuation capability. The concept design presented here provides an effective approach for achieving large torsional deformation, and the developed model and revealed results will aid the design and fabrication of soft actuators and soft robots.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(5):051004-051004-7. doi:10.1115/1.4036192.

Hydraulic fracturing (fracking) technology in gas or oil shale engineering is highly developed last decades, but the knowledge of the actual fracking process is mostly empirical and makes mechanicians and petroleum engineers wonder: why fracking works? (Bažant et al., 2014, “Why Fracking Works,” ASME J. Appl. Mech., 81(10), p. 101010) Two crucial issues should be considered in order to answer this question, which are fracture propagation condition and multiscale fracture network formation in shale. Multiple clusters of fractures initiate from the horizontal wellbore and several major fractures propagate simultaneously during one fracking stage. The simulation-based unitary fracking condition is proposed in this paper by extended finite element method (XFEM) to drive fracture clusters growing or arresting dominated by inlet fluid flux and stress intensity factors. However, there are millions of smeared fractures in the formation, which compose a multiscale fracture network beyond the computation capacity by XFEM. So, another simulation-based multiscale self-consistent fracture network model is proposed bridging the multiscale smeared fractures. The purpose of this work is to predict pressure on mouth of well or fluid flux in the wellbore based on the required minimum fracture spacing scale, reservoir pressure, and proppant size, as well as other given conditions. Examples are provided to verify the theoretic and numerical models.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(5):051005-051005-12. doi:10.1115/1.4036113.

A theoretical model of polyelectrolyte gels is presented to study continuous and discontinuous volume phase transitions induced by changing salt concentration in the external solution. Phase diagrams are constructed in terms of the polymer–solvent interaction parameters, external salt concentration, and concentration of fixed charges. Comparisons with previous experiments for an ionized acrylamide gel in mixed water–acetone solvents are made with good quantitative agreement for a monovalent salt (NaCl) but fair qualitative agreement for a divalent salt (MgCl2), using a simple set of parameters for both cases. The effective polymer–solvent interactions vary with the volume fraction of acetone in the mixed solvent, leading to either continuous or discontinuous volume transitions. The presence of divalent ions (Mg2+) in addition to monovalent ions in the external solution reduces the critical salt concentration for the discontinuous transition by several orders of magnitude. Moreover, a secondary continuous transition is predicted between two highly swollen states for the case of a divalent salt. The present model may be further extended to study volume phase transitions of polyelectrolyte gels in response to other stimuli such as temperature, pH and electrical field.

Commentary by Dr. Valentin Fuster

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