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Recently, there has been a surge of international interest in extraterrestrial exploration targeting the Moon, Mars, the moons of Mars, and various asteroids. This contribution discusses how current state-of-the-art Earth-based testing for designing rovers and landers for these missions currently leads to overly optimistic conclusions about the behavior of these devices upon deployment on the targeted celestial bodies. The key misconception is that gravitational offset is necessary during the \textit{terramechanics} testing of rover and lander prototypes on Earth. The body of evidence supporting our argument is tied to a small number of studies conducted during parabolic flights and insights derived from newly revised scaling laws. We argue that what has prevented the community from fully diagnosing the problem at hand is the absence of effective physics-based models capable of simulating terramechanics under low gravity conditions. We developed such a physics-based simulator and utilized it to gauge the mobility of early prototypes of the Volatiles Investigating Polar Exploration Rover (VIPER), which is slated to depart for the Moon in November 2024. This contribution discusses the results generated by this simulator, how they correlate with physical test results from the NASA-Glenn SLOPE lab, and the fallacy of the gravitational offset in rover and lander testing. The simulator developed is open sourced and made publicly available for unfettered use; it can support principled studies that extend beyond trafficability analysis to provide insights into in-situ resource utilization activities, e.g., digging, bulldozing, and berming in low gravity.

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions., Comment: 48 pages, 29 figures

In Part I of this two part series, we presented a multi-neighbor dependent contact model for adhesive elastic-plastic particles built upon the method of dimensionality reduction that is valid for the elastic and fully-plastic contact regimes. In this Part II, we complete the contact model by proposing a treatment for the bulk elastic contact regime which is characterized by a rapid stiffening in the force-displacement curve as interstitial pore spaces vanish. A simple formulation is presented for an additional bulk elastic force. A novel criterion for triggering this force (i.e. detecting the bulk elastic regime) related to the remaining free surface area of the particle is also given. This bulk elastic force is then superimposed with the force response given in Part I to achieve a contact model capable of capturing a variety of complex loadings. In this way, the methodology for treating the bulk elastic regime presented here stands independent of Part I and could be appended to any contact model. Direct comparison is made to finite element simulations showcasing bulk elastic responses, revealing the accurate predictive capabilities of the contact model. Notably, the contact model is also demonstrated to detect and evolve contacts caused purely by outward displacement of the free surface with good precision.

In this two part series, we present a contact model able to capture the response of interacting adhesive elastic-perfectly plastic particles under a variety of loadings. In Part I, we focus on elastic through fully-plastic contact with and without adhesion. For these contact regimes the model is built upon the method of dimensionality reduction which allows the problem of a 3D axisymmetric contact to be mapped to a semi-equivalent problem of a 1D rigid indenter penetrating a bed of independent Hookean springs. Plasticity is accounted for by continuously varying the 1D indenter profile subject to a constraint on the contact pressure. Unloading falls out naturally, and simply requires lifting the 1D indenter out of the springs and tracking the force. By accounting for the incompressible nature of this plastic deformation, the contact model is able to capture multi-neighbor dependent effects such as increased force and formation of new contacts. JKR type adhesion is recovered seamlessly within the method of dimensionality reduction by simply allowing the springs to stick to the 1D indenter's surface. Because of the mechanics-focused formulation of the contact model, only a few physical inputs describing the interacting particles are needed: particle radius, Young's modulus, Poisson ratio, yield stress, and effective surface energy. The contact model is validated against finite element simulations and analytic theory, including Hertz's contact law and the JKR theory of adhesion. These comparisons show that the proposed contact model is able to accurately capture plastic displacement, average contact pressure, contact area, and force as a function of displacement for contacts as well as particle volume within the elastic to fully-plastic regimes.

Detecting hidden geometrical structures from surface measurements under electromagnetic, acoustic, or mechanical loading is the goal of noninvasive imaging techniques in medical and industrial applications. Solving the inverse problem can be challenging due to the unknown topology and geometry, the sparsity of the data, and the complexity of the physical laws. Physics-informed neural networks (PINNs) have shown promise as a simple-yet-powerful tool for problem inversion, but they have yet to be applied to general problems with a priori unknown topology. Here, we introduce a topology optimization framework based on PINNs that solves geometry detection problems without prior knowledge of the number or types of shapes. We allow for arbitrary solution topology by representing the geometry using a material density field that approaches binary values thanks to a novel eikonal regularization. We validate our framework by detecting the number, locations, and shapes of hidden voids and inclusions in linear and nonlinear elastic bodies using measurements of outer surface displacement from a single mechanical loading experiment. Our methodology opens a pathway for PINNs to solve various engineering problems targeting geometry optimization., Comment: 24 pages, 16 figures including supplementary information. Added supplementary movies

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the global-scale physics are often desired to predict how external bodies interact with soft media, as occurs in diverse situations from impact and penetration problems to locomotion over natural terrains. This work proposes a systematic program to develop three-dimensional reduced-order models for soft materials from a fundamental basis using continuum symmetries and rheological principles. In particular, we derive a reduced-order technique for modeling intrusion in granular media which we term three-dimensional Resistive Force Theory (3D-RFT), which is capable of accurately and quickly predicting the resistive stress distribution on arbitrary-shaped intruding bodies. Aided by a continuum description of the granular medium, a comprehensive set of spatial symmetry constraints, and a limited amount of reference data, we develop a self-consistent and accurate 3D-RFT. We verify the model capabilities in a wide range of cases and show it can be quickly recalibrated to different media and intruder surface types. The premises leading to 3D-RFT anticipate application to other soft materials with strongly hyperlocalized intrusion behavior., Comment: 12 pages, 7 figures, 1 SI document (12 pages, 8 figures, and 4 tables)

We present a general simulation approach for incompressible fluid--structure interactions in a fully Eulerian framework using the reference map technique (RMT). The approach is suitable for modeling one or more rigid or finitely-deformable objects or soft objects with rigid components interacting with the fluid and with each other. It is also extended to control the kinematics of structures in fluids. The model is based on our previous Eulerian fluid--soft solver, and generalized to rigid structures by constraining the deformation-rate tensor in a projection framework. Several numerical examples are presented to illustrate the capability of the method.

Granular flow in a silo demonstrates multiple nonlocal rheological phenomena due to the finite size of grains. We solve the Nonlocal Granular Fluidity (NGF) continuum model in quasi-2D silo geometries and evaluate its ability to predict these nonlocal effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in arXiv:1411.5447, to produce full-field solutions. The implementation is validated against analytical results of the model in the inclined chute geometry, such as the solution for the $H_{\mathrm{stop}}$ curve for size-dependent flow arrest, and the velocity profile as a function of layer height. We then implement the model in the silo geometry and vary the apparent grain size. The model predicts a jamming criterion when the opening competes with the scale of the mean grain size, which agrees with previous experimental studies, marking the first time to our knowledge that silo jamming has been achieved with a continuum model. For larger openings, the flow within the silo obtains a diffusive characteristic whose spread depends on the model's nonlocal amplitude and the mean grain size. The numerical tests are controlled for grid effects and a comparison study of coarse vs refined numerical simulations shows agreement in the pressure field, the shape of the arch in a jammed silo configuration, and the velocity field in a flowing configuration., Comment: 30 pages, 10 figures

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition., Comment: 17 pages, 9 figures

Granular intrusion is commonly observed in natural and human-made settings. Unlike typical solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios. This multi-phase behavior increases the difficulty of accurately modeling these and other yielding (or flowable) materials. Micro-scale modeling methods, such as DEM (Discrete Element Method), capture this behavior by modeling the media at the grain scale, but there is often interest in the macro-scale characterizations of such systems. We examine the efficacy of a macro-scale continuum approach in modeling and understanding the physics of various macroscopic phenomena in a variety of granular intrusion cases using two basic frictional yielding constitutive models. We compare predicted granular force response and material flow to experimental data in four quasi-2D intrusion cases: (1) depth-dependent force response in horizontal submerged-intruder motion; (2) separation dependent drag variation in parallel-plate vertical-intrusion; (3) initial-density-dependent drag fluctuations in free surface plowing, and (4) flow zone development during vertical plate intrusions in under-compacted granular media. Our continuum modeling approach captures the flow process and drag forces while providing key meso- and macro-scopic insights. The modeling results are then compared to experimental data. Our study highlights how continuum modeling approaches provide an alternative for efficient modeling as well as a conceptual understanding of various granular intrusion phenomena., Comment: 14 pages, 8 figures, and 4 movies

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid--sediment mixtures) to dust kick-up below helicopter rotors (gas--sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g.\ the granular surface, elastic stress, etc.). Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures.

We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is obtained from a simplification of the exact solution to the continuum elasticity problem and takes the familiar form of Hertz' contact law, with the only difference being the orientation-dependence of the material-specific contact modulus. The contact law is remarkably accurate when compared with the exact solution, for a wide range of materials and surface geometries. We describe a computationally efficient implementation of the contact law into a discrete element method code, taking advantage of the precomputation of the contact modulus over all possible orientations. Finally, we showcase two application examples based on real materials where elastic anisotropy of the particles induces noticeable effects on macroscopic behavior. Notably, the second example demonstrates the ability to engineer tunable vibrational band gaps in a one-dimensional granular crystal by mere rotation of the constituent spherical particles., Comment: 27 pages, 16 figures

Granular intrusions, such as dynamic impact or wheel locomotion, are complex multiphase phenomena where the grains exhibit solid-like and fluid-like characteristics together with an ejected gas-like phase. Despite decades of modeling efforts, a unified description of the physics in such intrusions is as yet unknown. Here we show that a continuum model based on the simple notions of frictional flow and tension-free separation describes complex granular intrusions near free surfaces. This model captures dynamics in a variety of experiments including wheel locomotion, plate intrusions, and running legged robots. The model reveals that three effects (a static contribution and two dynamic ones) primarily give rise to intrusion forces in such scenarios. Identification of these effects enables the development of a further reduced-order technique (Dynamic Resistive Force Theory) for rapid modeling of granular locomotion of arbitrarily shaped intruders. The continuum-motivated strategy we propose for identifying physical mechanisms and corresponding reduced-order relations has potential use for a variety of other materials., Comment: 41 pages including supplementary document, 10 figures, and 8 video

Based on discrete element method simulations, we propose a new form of the constitution equation for granular flows independent of packing fraction. Rescaling the stress ratio $\mu$ by a power of dimensionless temperature $\Theta$ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number $I$. The basic power-law structure appears robust to varying particle properties (e.g. surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the Nonlocal Granular Fluidity model., Comment: 11 pages with 11 figures and 1 video (ancillary file)

Fine particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Recent examination of these mixtures in simple flow geometries suggests inter-granular repulsion is central to this effect --- for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas, when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to two-dimensional, steady, simple shearing flows. In this work, we introduce a predictive and general, three-dimensional continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a micro-structural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, non-uniform flow configurations where it is shown to accurately capture a variety of key behaviors: (i) the continuous shear thickening (CST) and discontinuous shear thickening (DST) behavior observed in steady flows, (ii) the time-dependent propagation of `shear jamming fronts', (iii) the time-dependent propagation of `impact activated jamming fronts', and (iv) the non-Newtonian, `running on oobleck' effect wherein fast locomotors stay afloat while slow ones sink.

Soft solids in fluids find wide range of applications in science and engineering, especially in the study of biological tissues and membranes. In this study, an Eulerian finite volume approach has been developed to simulate fully resolved incompressible hyperelastic solids immersed in a fluid. We have adopted the recently developed reference map technique (RMT) by Valkov et. al (J. Appl. Mech., 82, 2015) and assessed multiple improvements for this approach.These modifications maintain the numerical robustness of the solver and allow the simulations without any artificial viscosity in the solid regions (to stabilize the solver). This has also resulted in eliminating the striations ("wrinkles") of the fluid-solid interface that was seen before and hence obviates the need for any additional routines to achieve a smooth interface. An approximate projection method has been used to project the velocity field onto a divergence free field. Cost and accuracy improvements of the modifications on the method have also been discussed.

We analyze the capabilities of various recently developed techniques, namely Resistive Force Theory (RFT) and continuum plasticity implemented with the Material Point Method (MPM), in capturing dynamics of wheel--dry granular media interactions. We compare results to more conventionally accepted methods of modeling wheel locomotion. While RFT is an empirical force model for arbitrarily-shaped bodies moving through granular media, MPM-based continuum modeling allows the simulation of full granular flow and stress fields. RFT allows for rapid evaluation of interaction forces on arbitrary shaped intruders based on a local surface stress formulation depending on depth, orientation, and movement of surface elements. We perform forced-slip experiments for three different wheel types and three different granular materials, and results are compared with RFT, continuum modeling, and a traditional terramechanics semi-empirical method. Results show that for the range of inputs considered, RFT can be reliably used to predict rigid wheel granular media interactions with accuracy exceeding that of traditional terramechanics methodology in several circumstances. Results also indicate that plasticity-based continuum modeling provides an accurate tool for wheel-soil interaction while providing more information to study the physical processes giving rise to resistive stresses in granular media.

We present a general simulation approach for fluid-solid interactions based on the fully-Eulerian Reference Map Technique (RMT). The approach permits the modeling of one or more finitely-deformable continuum solid bodies interacting with a fluid and with each other. A key advantage of this approach is its ease of use, as the solid and fluid are discretized on the same fixed grid, which greatly simplifies the coupling between the phases. We use the method to study a number of illustrative examples involving an incompressible Navier-Stokes fluid interacting with multiple neo-Hookean solids. Our method has several useful features including the ability to model solids with sharp corners and the ability to model actuated solids. The latter permits the simulation of active media such as swimmers, which we demonstrate. The method is validated favorably in the flag-flapping geometry, for which a number of experimental, numerical, and analytical studies have been performed. We extend the flapping analysis beyond the thin-flag limit, revealing an additional destabilization mechanism to induce flapping., Comment: 28 pages, 10 figures

We present a thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes, developed from the basic balance laws for two phase-mixtures. The model can represent various limiting cases, such as pure fluid and dry grains. It is formulated to capture a number of key behaviors such as: (i) viscous inertial rheology of submerged wet grains under steady shearing flows, (ii) the critical state behavior of grains, which causes granular Reynolds dilation/contraction due to shear, (iii) the viscous thickening of the fluid response due to the presence of suspended grains, and (iv) the Darcy-like drag interaction observed in both dense and dilute mixtures, which gives rise to complex fluid-grain interactions under dilation and flow. The full constitutive model is combined with the basic equations of motion for each mixture phase and implemented in the material point method (MPM) to accurately model the coupled dynamics of the mixed system. Qualitative results show the breadth of problems which this model can address. Quantitative results demonstrate the accuracy of this model as compared with analytical limits and experimental observations of fluid and grain behaviors in inhomogeneous geometries.

Contact dynamics (CD) is a powerful method to solve the dynamics of large systems of colliding rigid bodies. CD can be computationally more efficient than classical penalty-based discrete element methods (DEM) for simulating contact between stiff materials such as rock, glass, or engineering metals. However, by idealizing bodies as perfectly rigid, contact forces computed by CD can be non-unique due to indeterminacy in the contact network, which is a common occurence in dense granular flows. We propose a CD method that is designed to identify only the unique set of contact forces that would be predicted by a soft particle method, such as DEM, in the limit of large stiffness. The method involves applying an elastic compatibility condition to the contact forces, which maintains no-penetration constraints but filters out force distributions that could not have arisen from stiff elastic contacts. The method can be used as a post-processing step that could be integrated into existing CD codes with minimal effort. We demonstrate its efficacy in a variety of indeterminate problems, including some involving multiple materials, non-spherical shapes, and nonlinear contact constitutive laws.

We investigate the initiation of cracks in vertically freestanding water-saturated colloidal pillars constructed using a direct-write technique. Paradoxically, the cracks form during drying at the free end, far from the substrate, where the particle network is unconstrained in contracting its volume as it bears compression by a uniform capillary pressure acting at its outer surface. This is explained by a dominant balance of wetting energy terms, from which follows a simple relationship between the particle size and pillar dimensions that captures the presence or absence of cracks. This relationship provides a practical guideline for fabricating crack-free colloidal structures., Comment: 11 pages, 2 figures