Accepted Manuscripts

Jiazhen Leng, Gerard Reynolds, Megan Schaenzer, Minh Quan Pham, Genevieve Bourgeois, Ali Shanian and Damiano Pasini
J. Appl. Mech   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.
TOPICS: Stress concentration, Porosity, Stress, Porous materials, Computer simulation, Aerospace industry, Design, Boundary-value problems, Displacement, Failure
Junjie Liu, Xusheng Hai, Wenqing Zhu and Xiaoding Wei
J. Appl. Mech   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 in 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 and gives novel ideas for manufacturing high damping composites.
TOPICS: Composite materials, Optimization, Damping, Design, Finite element analysis, Elastic moduli, Shells, Storage, Excitation, Shear stress, Viscosity, Manufacturing, Viscoelasticity, Shear (Mechanics), Bone
Tingting Zhao and Y. T. Feng
J. Appl. Mech   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 modelling (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.
TOPICS: Surface roughness, Deformation, Discrete element methods, Pressure, Particulate matter, Contact mechanics, Modeling
Leichuan Tan and Deli Gao
J. Appl. Mech   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, Energy dissipation, Accidents, Pipes, China, Decision making, Shales, Wells, Composite materials, Drills (Tools), Extruding
Erfan Sarvaramini, Maurice Dusseault and Robert Gracie
J. Appl. Mech   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 article, the simulation of the SV evolution is achieved using a non-local poro-mechanical plasticity model. Effects of the natural fracture network are incorporated via a non-local plasticity characteristic length, l. A non-local Drucker-Prager failure model is implemented in the framework of the Biot's theory using a new implicit C^{0} finite element method. First, the behavior of a representative injection scenario is simulated and resulting SV is assessed. Next, the post-shut-in behavior of the SV is analyzed using the pressure and pressure derivative plots. A bi-linear 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 l 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. Lastly, it is observed that as l tends to zero, the flow capacity of the SV tends to infinity and the SV behaves like a single infinitely conducting fracture.
TOPICS: Reservoirs, Pressure, Fracture (Process), Flow (Dynamics), Plasticity, Simulation, Rocks, Imaging, Uncertainty, Damage, Hydraulic fracturing, Failure, Electrical conductivity, Shear (Mechanics), Finite element methods, Thermal conductivity, Deformation, Permeability, Textiles
Yingxi Wang, Zhe Li, Lei Qin, George Caddy, Choon Hwai Yap and Jian Zhu
J. Appl. Mech   doi: 10.1115/1.4040478
Harnessing reversible snap-through of a dielectric elastomer (DE), which is a mechanism for large deformation provided by an electro-mechanical 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 letter, we propose a new mechanism of DE fluid pumping that can address this shortcoming, by connecting DE pumps of different membrane stiffness serially in a pumping circuit, and by harnessing synergistic interactions between neighbouring 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 0.98kPa, the serial DE pump's pumping volume is 4185.1% larger than that of the conventional DE pump.
TOPICS: Fluids, Elastomers, High pressure (Physics), Pumps, Membranes, Pressure gradient, Stiffness, Pressure, Deformation, Circuits, Cycles
VIvek Ramachandran and Carmel Majidi
J. Appl. Mech   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 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 manuscript, 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 2D 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 Lam\'e (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.
TOPICS: Deformation, Microchannels, Microfluidics, Collapse, Stress, Cross section (Physics), Pressure, Fluid dynamics, Elasticity, Matter, Robots, Elastomers, Liquid metals, Compressive stress, Plane strain, Electronics, Design, Approximation, Algebra
Xiongfei Lv, Liwu Liu, Yanju Liu and Jinsong Leng
J. Appl. Mech   doi: 10.1115/1.4040405
Dielectric elastomer (DE) is a promising electroactive polymer. As DE material, rubbers are often filled with functional particles to improve their electromechanical coupling performance. However, the filled particles also bring stress softening, which is known as Mullins effect. In this paper, we prepared the carbon nanotube filled silicone elastomer as dielectric elastomer composite, and used the pseudo-elastic theory to model its Mullins effect. Then the thermodynamics and pseudo-elastic theory were combined to predict the idealized electromechanical softening behavior. Two cases are considered: linear dielectric and saturated dielectric. For linear dielectric with an initial force, the voltage-controlled unloading remains "residual strain" after every cycle and reloading may eliminate instability. For saturated dielectric, we assume it is all linear before polarization saturation. After saturation, the material response changes a lot, which also affects the following softening behavior. At last, viscoelasticity was further incorporated to account for rate-dependent softening deformation, and we also carried out some simply electromechanical experiments on VHB 4910 to explore its softening behavior. This work may lead to a better understanding of the softening behavior in dielectric elastomers undergoing electromechanical coupling situations.
TOPICS: Elastomers, Modeling, Particulate matter, Carbon nanotubes, Cycles, Silicones, Conducting polymers, Polarization (Electricity), Stress, Viscoelasticity, Polarization (Light), Deformation, Thermodynamics, Polarization (Waves), Composite materials
Shunhua Zhou, Peijun Guo and Dieter. F. E. Stolle
J. Appl. Mech   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~p^(1/3) . 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 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~Fn^m and m=[1/3,1], with m=1/3 for Hertzian contact, m=1/3 for 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 p^m with m=[1/3,1].
TOPICS: Particulate matter, Granular materials, Coating processes, Coatings, Elastic moduli, Stiffness, Gravel, Packing (Shipments), Surface roughness, Packings (Cushioning), Scaling laws (Mathematical physics), Contact mechanics, Pressure, Sands, Binders (Materials), Asphalt, Manufacturing, Asphalt concrete
Jingqian Ding, Ernst W. Remij, Joris J.C. Remmers and Jacques M. Huyghe
J. Appl. Mech   doi: 10.1115/1.4040334
Stepwise crack propagation is evidently observed in experiments both in geomaterials and in hydrogels. Pizzocolo et al. 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 Method (ELP), and incorporate cohesive relation to reproduce Pizzocolo et al.'s experiments 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 artefacts, we also take different time increments into consideration. The staccato propagation does not disappear with smaller time increments, 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.
TOPICS: Crack propagation, Hydrogels, Fracture (Materials), Stiffness, Porosity, Permeability, Simulation, Finite element methods, Pressure, Deformation, Fluids, Rocks, Water, Materials properties, Engineering simulation

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