0

IN THIS ISSUE

### Research Papers

J. Appl. Mech. 2018;85(10):101001-101001-11. doi:10.1115/1.4040408.

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as $K∼G∼p1/3$. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following $kn∼Fnm$ and $m∈[1/3, 1]$, with $m=1/3$ for Hertzian contact, $m=1/2$ soft thin-coating contact, $m=2/3$ for incompressible soft thin-coating, and $m=1$ for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to $pm$ with $m∈[1/3, 1]$.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101002-101002-9. doi:10.1115/1.4040538.

Many natural materials, such as shell and bone, exhibit extraordinary damping properties under dynamic outside excitations. To explore the underlying mechanism of these excellent performances, we carry out the shear-lag analysis on the unit cell in staggered composites. Accordingly, the viscoelastic properties of the composites, including the loss modulus, storage modulus, and loss factor, are derived. The damping properties (particularly, the loss modulus and loss factor) show an optimization with respect to the constituents' properties and morphology. The optimal scheme demands a proper selection of four key factors: the modulus ratio, the characteristic frequency of matrix, aspect ratios of tablets, and matrix. The optimal loss modulus is pointed out to saturate to an upper bound that is proportional to the elastic modulus of tablets when the viscosity of matrix increases. Furthermore, a loss factor even greater than one is achievable through microstructure design. Without the assumption of a uniform shear stress distribution in the matrix, the analysis and formulae reported herein are applicable for a wide range of reinforcement aspect ratios. Further, for low-frequency loading, we give practical formulae of the three indexes of damping properties. The model is verified by finite element analysis (FEA) and gives novel ideas for manufacturing high damping composites.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101003-101003-6. doi:10.1115/1.4040478.

Harnessing reversible snap-through of a dielectric elastomer (DE), which is a mechanism for large deformation provided by an electromechanical instability, for large-volume pumping has proven to be feasible. However, the output volume of snap-through pumping is drastically reduced by adverse pressure gradient, and large-volume pumping under high adverse pressure gradient by a DE pump has not been realized. In this paper, we propose a new mechanism of DE fluid pumping that can address this shortcoming by connecting DE pumps of different membrane stiffnesses serially in a pumping circuit and by harnessing synergistic interactions between neighboring pump units. We build a simple serial DE pump to verify the concept, which consists of two DE membranes. By adjusting the membrane stiffness appropriately, a synergistic effect is observed, where the snap-through of membrane 1 triggers the snap-through of membrane 2, ensuring that a large volume (over 70 ml/cycle) can be achieved over a wide range of large adverse pressure gradients. In comparison, the conventional single DE pump's pumping volume rapidly decreased beyond a low adverse pressure gradient of 0.196 kPa. At the pressure difference of 0.98 kPa, the serial DE pump's pumping volume is 4185.1% larger than that of the conventional DE pump. This pumping mechanism is customizable for various pressure ranges and enables a new approach to design DE-based soft pumping devices such as a DE total artificial heart, which requires large-volume pumping over a wide range of pressure difference.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101004-101004-7. doi:10.1115/1.4040477.

The deformation of microfluidic channels in a soft elastic medium has a central role in the operation of lab-on-a-chip devices, fluidic soft robots, liquid metal (LM) electronics, and other emerging soft-matter technologies. Understanding the influence of mechanical load on changes in channel cross section is essential for designing systems that either avoid channel collapse or exploit such collapse to control fluid flow and connectivity. In this paper, we examine the deformation of microchannel cross sections under far-field compressive stress and derive a “gauge factor” that relates externally applied pressure with change in cross-sectional area. We treat the surrounding elastomer as a Hookean solid and use two-dimensional plane strain elasticity, which has previously been shown to predict microchannel deformations that are in good agreement with experimental measurements. Numerical solutions to the governing Lamé (Navier) equations are found to match both the analytic solutions obtained from a complex stress function and closed-form algebraic approximations based on linear superposition. The application of this theory to soft microfluidics is demonstrated for several representative channel geometries.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101005-101005-16. doi:10.1115/1.4040406.

Any casing with perfect integrity within a complex oil and gas development scenario is subject to formation extrusion resulting in ellipticity. This paper proposes a novel casing wear prediction model, which encompasses ellipticity, geometric structural relationships, and the energy dissipation law at work in the casing. Composite structural wear models are also utilized to determine the influence of different drill pipe combinations on casing wear predictions. The casing wear position is predicted based on casing ellipticity. The proposed model yields more accurate casing wear predictions than previous models which do not properly account for casing ellipticity; to this effect, it may more effectively minimize the cost of drilling engineering and safeguard against accidents. The proposed method also outperformed other methods in a case study on a shale gas development project in Fuling, China. The inversion method is applicable to wells with similar structure to the drilled well, where casing wear position can be evaluated very accurately according to caliper logging system measurements. The proposed method facilitates sound decision-making while guaranteeing secure and reliable oil and gas well-drilling with complex structures.

Topics: Wear , Drilling
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101006-101006-11. doi:10.1115/1.4040479.

Microseismic imaging of the hydraulic fracturing operation in the naturally fractured rocks confirms the existence of a stimulated volume (SV) of enhanced permeability. The simulation and characterization of the SV evolution is uniquely challenging given the uncertainty in the nature of the rock mass fabrics as well as the complex fracturing behavior of shear and tensile nature, irreversible plastic deformation and damage. In this paper, the simulation of the SV evolution is achieved using a nonlocal poromechanical plasticity model. Effects of the natural fracture network are incorporated via a nonlocal plasticity characteristic length, . A nonlocal Drucker–Prager failure model is implemented in the framework of Biot's theory using a new implicit C0 finite element method. First, the behavior of the SV for a two-dimensional (2D) geomechanical injection problem is simulated and the resulting SV is assessed. It is shown that breakdown pressure and stable fracturing pressure are the natural outcomes of the model and both depend upon . Next, the post-shut-in behavior of the SV is analyzed using the pressure and pressure derivative plots. A bilinear flow regime is observed and it is used to estimate the flow capacity of the SV. The results show that the flow capacity of the SV increases as decreases (i.e., as the SV behaves more like a single hydraulic fracture); however, for $0.1m≤ℓ≤1m$, the calculated flow capacity indicates that the conductivity of the SV is finite. Finally, it is observed that as tends to zero, the flow capacity of the SV tends to infinity and the SV behaves like a single infinitely conducting fracture.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101007-101007-9. doi:10.1115/1.4040537.

The current work aims to develop two extended Greenwood–Williamson (GW) models for spherical particles with surface roughness which can be incorporated into the discrete element modeling (DEM) framework. The defects of the classic GW model when directly adopted in DEM are fully addressed and illustrated by both theoretical and numerical results. The first model, the extended elastic GW (E-GW) model, which evaluates the elastic deformation of the asperities and the bulk substrate separately is developed to consider the positive overlap involved in the contact problem. The capability of incorporating the extended elastic model into the DEM is illustrated by the comparison between the classic and extended models. The second model, the extended elasto–plastic GW (EP-GW) model, is further developed to consider the plastic deformation of the asperities which reduces the pressure increased by the surface roughness. Numerical comparisons between the E-GW and EP-GW models are also conducted to demonstrate the effect of the plastic deformation on the pressure and deformation distributions in the contact region.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101008-101008-9. doi:10.1115/1.4040598.

In this paper, the theoretical analysis and the inversion of the contact stress on the finite thickness rubber contact surface with the friction effect are investigated. First, an explicit expression of deformation and stress on the surface of rubber under a rigid spherical indenter is developed by means of theoretical model, dimensional analysis, and nonlinear finite element simulation. Second, the inverse approach for obtaining the contact stress on the finite thickness rubber contact surface is presented and verified theoretically. Also, the displacement, the stress field, and the friction coefficient are obtained by means of three-dimensional digital image correlation (3D DIC) method. Finally, the applicability to other hyperelastic models, general boundary conditions, and loading modes are discussed. The results will provide an important theoretical and experimental basis for evaluating the contact stress on the finite thickness rubber layer.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101009-101009-7. doi:10.1115/1.4040599.

As a versatile yet simple technique, transfer printing has been widely explored for the heterogeneous integration of materials/structures, particularly important for the application in stretchable and transient electronics. The key steps of transfer printing involve pickup of the materials/structures from a donor and printing of them onto a receiver substrate. The modulation of the interfacial adhesion is critically important to control the adhesion/delamination at different material–structural interfaces. Here, we present a magnetic-assisted transfer printing technique that exploits a unique structural design, where a liquid chamber filled with incompressible liquid is stacked on top of a compressible gas chamber. The top liquid chamber wall uses a magnetic-responsive thin film that can be actuated by the external magnetic field. Due to the incompressible liquid, the actuation of the magnetic-responsive thin film induces the pressure change in the bottom gas chamber that is in contact with the material/structure to be transfer printed, leading to effective modulation of the interfacial adhesion. The decreased (increased) pressure in the bottom gas chamber facilitates the pickup (printing) step. An analytical model is also established to study the displacement profile of the top thin film of the gas chamber and the pressure change in the gas chamber upon magnetic actuation. The analytical model, validated by finite element analysis, provides a comprehensive design guideline for the magnetic-assisted transfer printing.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101010-101010-13. doi:10.1115/1.4040539.

Stress concentration in porous materials is one of the most crucial culprits of mechanical failure. This paper focuses on planar porous materials with porosity less than 5%. We present a stress-prediction model of an arbitrarily rotated elliptical hole in a rhombus shaped representative volume element (RVE) that can represent a class of generic planar tessellations, including rectangular, triangular, hexagonal, Kagome, and other patterns. The theoretical model allows the determination of peak stress and distribution of stress generated near the edge of elliptical holes for any arbitrary tiling under displacement loading and periodic boundary conditions. The results show that the alignment of the void with the principal directions minimizes stress concentration. Numerical simulations support the theoretical findings and suggest the observations remain valid for porosity as large as 5%. This work provides a fundamental understanding of stress concentration in low-porosity planar materials with insight that not only complements classical theories on the subject but also provides a practical reference for material design in mechanical, aerospace, and other industry.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101011-101011-7. doi:10.1115/1.4040334.

Stepwise crack propagation is evidently observed in experiments both in geomaterials and in hydrogels. Pizzocolo et al. (2012, “Mode I Crack Propagation in Hydrogels is Step Wise,” Eng. Fract. Mech., 97(1), pp. 72–79) show experimental evidence that mode I crack propagation in hydrogel is stepwise. The pattern of the intermittent crack growth is influenced by many factors, such as porosity of the material, the permeability of the fluid, the stiffness of the material, etc. The pause duration time is negatively correlated with the stiffness of the material, while the average propagation length per step is positively correlated. In this paper, we integrate extended finite element method (XFEM) and enhanced local pressure (ELP) method, and incorporate cohesive relation to reproduce the experiments of Pizzocolo et al. in the finite deformation regime. We investigate the stepwise phenomenon in air and in water, respectively, under mode I fracture. Our simulations show that despite the homogeneous material properties, the crack growth under mode I fracture is stepwise, and this pattern is influenced by the hydraulic permeability and the porosity of the material. Simulated pause duration is negatively correlated with stiffness, and the average propagating length is positively correlated with stiffness. In order to eliminate the numerical artifacts, we also take different time increments into consideration. The staccato propagation does not disappear with smaller time increments, and the pattern is approximately insensitive to the time increment. However, we do not observe stepwise crack growth scheme when we simulate fracture in homogeneous rocks.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(10):101012-101012-8. doi:10.1115/1.4040692.

In this paper, we present an experimental study on strain hardening of amorphous thermosets. A series of amorphous polymers is synthesized with similar glass transition regions and different network densities. Uniaxial compression tests are then performed at two different strain rates spanning the glass transition region. The results show that a more pronounced hardening response can be observed as decreasing temperature and increasing strain rate and network density. We also use the Neo-Hookean model and Arruda–Boyce model to fit strain hardening responses. The Neo-Hookean model can only describe strain hardening of the lightly cross-linked polymers, while the Arruda–Boyce model can well describe hardening behaviors of all amorphous networks. The locking stretch of the Arruda–Boyce model decreases significantly with increasing network density. However, for each amorphous network, the locking stretch is the same regardless of the deformation temperature and rate. The hardening modulus exhibits a sharp transition with temperature. The transition behaviors of hardening modulus also vary with the network density. For lightly crosslinked networks, the hardening modulus changes 60 times with temperature. In contrast, for heavily crosslinked polymers, the hardening modulus in the glassy state is only 2 times of that in the rubbery state. Different from the results from molecular dynamic simulation in literatures, the hardening modulus of polymers in the glassy state does not necessarily increase with network density. Rather, the more significant hardening behaviors in more heavily crosslinked polymers are attributed to a lower value of the stretch limit.

Commentary by Dr. Valentin Fuster