Digital Image-Based Stress–Permeability Relationships of Rough Fractures Using Numerical Contact Mechanics and Stokes Equation

Flow in fractures is sensitive to their geometrical surface characteristics. The surface can undergo deformation if there is a change in stress. Natural fractures have complex geometries and rough surfaces which complicates the modelling of deformation and fluid flow. In this paper, we present a computational model that takes a digital image of a rough fracture surface and provides a stress–permeability relationship. The model is based on a first-principle contact mechanics approach at the continuum scale. Using this first principle approach, we investigate numerically the effect of fracture surface roughness and shifting of surfaces on the permeability evolution under applied stress and compare the results with laboratory experiments. A mudrock core fracture surface was digitalized using an optical microscope, and 2D cross sections through fracture surface profiles were taken for the modelling. Mechanical deformation is simulated with the contact mechanics based Virtual Element Method solver that we developed within the MATLAB Reservoir Simulation Toolbox platform. The permeability perpendicular to the fracture cross section is determined by solving the Stokes equation using the Finite Volume Method. A source of uncertainty in reproducing laboratory results is that the exact anchoring of the two opposite surfaces is difficult to determine while the stress–permeability relationship is sensitive to the exact positioning. We, therefore, investigate the sensitivity to a mismatch in two scenarios: First, we assess the stress–permeability of a fracture created using two opposing matched surfaces from the rock sample, consequently applying relative shear. Second, we assess the stress–permeability of fractures created by randomly selecting opposing surfaces from that sample. We find that a larger shift leads to a smaller drop in permeability due to applied stress, which is in line with a previous laboratory study. We also find that permeability tends to be higher in fractures with higher roughness within the investigated stress range. Finally, we provide empirical stress–permeability relationships for various relative shears and roughnesses for use in hydro-mechanical studies of fractured geological formations.

Computational contact mechanics for a medium consisting of functionally graded material coating and orthotropic substrate

This paper presents a semi-analytical method to investigate the frictionless contact mechanics between a functionally graded material (FGM) coating and an orthotropic substrate when the system is indented by a rigid flat punch. From the bottom, the orthotropic substrate is completely bonded to the rigid foundation. The body force of the orthotropic substrate is ignored in the solution, while the body force of the FGM coating is considered. An exponential function is used to define the smooth variation of the shear modulus and density of the FGM coating, and the variation of Poisson’s ratio is assumed to be negligible. The partial differential equation system for the FGM coating and the orthotropic substrate is solved analytically through Fourier transformations. After applying boundary and interface continuity conditions to the mixed boundary value problem, the contact problem is reduced to a singular integral equation. The Gauss–Chebyshev integration method is then used to convert the singular integral equation into a system of linear equations, which are solved using an appropriate iterative algorithm to calculate the contact stress under the rigid flat punch. The parametric analyses presented here demonstrate the effects of normalized punch length, material inhomogeneity, dimensionless press force, and orthotropic material type on contact stresses at interfaces, critical load factor, and initial separation distance between FGM coating and orthotropic substrate. The developed solution procedures are verified through the comparisons made to the results available in the literature. The solution methodology and numerical results presented in this paper can provide some useful guidelines for improving the design of multibody indentation systems using FGMs and anisotropic materials.

Two-Process Random Textures: Measurement, Characterization, Modeling and Tribological Impact: A Review

Two-process random textures seem to present better functional properties than one-process surfaces. There are many random two-process textures. Plateau-honed cylinder surfaces are the most popular example. Two-process surfaces are also created during the initial periods of life of machined elements. However, knowledge about two-process textures measurement, modeling, and behavior is low. Two-process surfaces are very sensitive to measurement errors. It is very difficult to model them. Special methods of their characterization were created. Their functional significance was studied in a small number of publications. In this paper, measurement, characterization, and modeling of two-process textures were presented. The functional impact of them was analyzed, the effects on contact mechanics and friction and wear were mainly studied. Finally, considerations of future challenges were addressed. The nature of two-process random textures should be taken into account during analyses of properties of machined elements. The plateau part decides about the asperity contact, and the valley portion governs the hydrodynamic lubrication.

A Tribometric Device for the Rolling Contact of Soft Elastomers

Rolling contact experimentation is a viable and instructive method for exploring the adhesive contact between surfaces. When applied to soft elastomeric or engineered surfaces, the results of such experiments can provide insights relevant to medical robotics, soft gripping applications, and reversible dry adhesives for bandages or wearable devices. We have designed and built a tribometric device to capture normal and tangential forces between a rolling indenter and substrate correlated with contact area imaging. The device was validated using an experimental setup involving a rigid, nominally smooth acrylic cylinder rolling against a flat polydimethylsiloxame (PDMS) substrate, the results of which matched favorably with accepted contact mechanics theories. The second test involved an indenter with a rigid core and thin (3 mm) smooth shell of a highly deformable, viscoelastic polyvinyl chloride (PVC) rolling on the same PDMS substrate. This test deviated significantly from analytical predictions, highlighting the effects of finite-thickness effects, viscoelasticity, and interfacial slip. This device will facilitate experimental investigations of the rolling contact mechanics between textured surfaces and soft tissue-like materials, which is an important fundamental problem in medical robotics.

A Computationally Efficient Lower Limb Finite Element Musculoskeletal Framework Directly Driven Solely by Inertial Measurement Unit Sensors

Finite element musculoskeletal (FEMS) approaches using concurrent musculoskeletal and finite element models driven by motion data such as marker-based motion trajectory can provide insight into the interactions between the knee joint secondary kinematics, contact mechanics, and muscle forces in subject-specific biomechanical investigations. However, these data-driven FEMS systems have two major disadvantages that make them challenging to apply in clinical environments: they are computationally expensive and they require expensive and inconvenient equipment for data acquisition. In this study, we developed an FEMS model of the lower limb driven solely by inertial measurement unit sensors that includes the tissue geometries of the entire knee joint and combines muscle modeling and elastic foundation theory-based contact analysis of knee into a single framework. The model requires only the angular velocities and accelerations measured by the sensors as input, and the target outputs (knee contact mechanics, secondary kinematics, and muscle forces) are predicted from the convergence results of iterative calculations of muscle force optimization and knee contact mechanics. To evaluate its accuracy, the model was compared with in vivo experimental data during gait. The maximum contact pressure (12.6 MPa) in the rigid body contact analysis occurred on the medial side of the cartilage at the maximum loading response. The proposed computationally efficient framework drastically reduced the computational time (97.5% reduction) in comparison with the conventional deformable finite element analysis. The developed framework combines measurement convenience and computational efficiency and shows promise for clinical applications.

Fundamentals and Advances in Elastohydrodynamics: The Role of Ramsey Gohar

This paper commemorates Ramsey Gohar by acknowledging his contributions to the fields of contact mechanics and elastohydrodynamic lubrication (EHL) within the context of the developments of these subjects. A historical discourse is provided on elastohydrodynamics, from its inception in the 1940s to present. We demonstrate that Ramsey Gohar was not only a pioneer in the discoveries and fundamentals of the subject, but also led or contributed significantly to continual advances in the understanding of EHL and its diverse applications.