Contact Normal Directions Research Articles

Breakage effect of calcareous sand on pile tip resistance and the surrounding soil stress

Due to the irregular shape, high porosity and fragility of calcareous sand particles, the construction of reef engineering is seriously affected, and the application of pile foundation engineering technology in calcareous sand stratum is also faced with great challenges. Based on the discrete element method (DEM), the pile installation process in the fractured calcareous sand stratum and non-fractured silica sand stratum are simulated, respectively, and the influence of particle breakage of calcareous sand on soil stress around the pile and pile tip resistance are discussed. The results show that the particle contact has no obvious dominant direction, and the particle breakage has little contribution on the variation of the particle contact normal directions while has great influence on the number of contact normals and the magnitude of contact normal force which is more uniform after particle breakage. The vertical and horizontal stresses in calcareous sand stratum are obviously lower than that in siliceous sand stratum. With the increase of the pile penetration depth, the number of crushing particles increases gradually. The particle breakage only can be found within the range of 3 times of pile diameter at the bottom of the pile and also within the range of 1 time of pile diameter around the pile. The effect of particle breakage on pile tip resistance is mainly reflected in the later stage of pile sinking. In calcareous sand, when the pile tip resistance increases to a certain extent, particle breakage occurs and the stresses in the soil cannot continually increase. Therefore, the pile tip resistance fluctuates around a stable value (∼0.3MPa). This is the reason that the pile tip resistance in calcareous sand is far less than that in siliceous sand, which is prone to pile foundation failure.

The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles

AbstractA unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this article. This overlap is based on the concept of the Minkowski difference of two shapes, and particularly on the equivalence between the contact state of the two shapes and the location of the origin relative to their Minkowski difference. The Minkowski contact features of a contact, including the overlap, normal direction, and contact points, are also defined for convex shapes. In particular, an important property of the Minkowski overlap is introduced which lays the solid theoretical foundation for proposing a Minkowski overlap based energy‐conserving contact model in the current work. The energy‐conserving property for cases where the contact normal direction and point may be subject to discrete changes is also rigorously proved. For convex particles, the computational procedures combining both GJK and EPA algorithms are outlined, and uniqueness and ambiguity issues associated with some special cases are clarified and resolved. The elastic energy conservation of the proposed contact model for convex shapes in elastic impact is further verified using two numerical examples, and two more examples involving more convex particles with different sizes and shapes are also conducted to demonstrate the robustness and applicability of the proposed Minkowski overlap contact model and the computational procedures.

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

The first paper of this series establishes a unified theoretical framework that lays a solid foundation for developing energy-conserving normal contact models for arbitrarily shaped bodies in the discrete element method. It is derived based solely on the requirement that the potential energy must be conserved for an elastic impact of two shapes under any condition. The resulting general energy-conserving contact model states that the normal force as a vector must be the gradient of a contact potential field. When such a contact potential or energy function is specified, a complete normal contact model for a pair of arbitrarily shaped particles, including the contact normal direction, contact point/line and force magnitude, will be automatically followed without introducing any additional assumptions. In this framework, the contact geometry and contact force are indispensably related and are evaluated in a consistent manner. Due to the paramount role that the energy function plays in the current theory, its fundamental properties are discussed, which serve as general guidance for choosing a valid energy function. In addition, both single and multiple contacts and their evolution can be handled in a seamless way. Some symmetric properties of particle shapes can also be utilised to simplify the contact models. Within the proposed theoretical framework, different choices or combinations of geometric features as variables for the contact energy function can give rise to unique types of energy-conserving contact models with distinct characteristics and features. Two such functions using only one primary feature, which lead to two specialised energy-conserving contact models, will be presented in the subsequent papers of this series.

Jamming-Free Immobilizing Grasps Using Dual-Friction Robotic Fingertips

Successful grasping of objects with robotic hands is still considered a difficult task. One aspect of the grasping problem is the physical contact interaction between the robotic fingertips and the object. Friction at the fingertip contacts can improve grasp robustness, but frictional fingertips may be difficult to precisely place on the object's perimeter. This paper describes a novel fingertip design that can switch from frictionless to frictional modes. The transformation from frictionless to frictional contact is achieved passively by the finger force exerted on the object at the target grasp. A novel swivel mechanism ensures that the force magnitude required to switch friction states is independent on the grasped object's contact normal direction, thus ensuring robustness. Analysis of the displacement and eventual sliding of the fingertip contacts in response to external torque is presented, taking into account the amount of friction and the compliant behavior of the fingertip mechanism. Experiments validate the analytic model and demonstrate the fingertip's ability to change friction modes by the applied force magnitude irrespective of the contact normal direction. In line with the analytic model predictions, the experiments show that when converted to frictional contacts, the fingertips provide a more robust and hence secure grasp in the presence of external disturbances. The robustness of the fingertips is further validated by real-world demonstrations shown in an external video referenced in the paper.

Modeling and prototyping of a soft closed-chain modular gripper

PurposeThis paper aims to present a soft closed-chain modular gripper for robotic pick-and-place applications. The proposed biomimetic gripper design is inspired by the Fin Ray effect, derived from fish fins physiology. It is composed of three axisymmetric fingers, actuated with a single actuator. Each finger has a modular under-actuated closed-chain structure. The finger structure is compliant in contact normal direction, with stiff crossbeams reorienting to help the finger structure conform around objects.Design/methodology/approachStarting with the design and development of the proposed gripper, a consequent mathematical representation consisting of closed-chain forward and inverse kinematics is detailed. The proposed mathematical framework is validated through the finite element modeling simulations. Additionally, a set of experiments was conducted to compare the simulated and prototype finger trajectories, as well as to assess qualitative grasping ability.FindingsKey Findings are the presented mathematical model for closed-loop chain mechanisms, as well as design and optimization guidelines to develop controlled closed-chain grippers.Research limitations/implicationsThe proposed methodology and mathematical model could be taken as a fundamental modular base block to explore similar distributed degrees of freedom (DOF) closed-chain manipulators and grippers. The enhanced kinematic model contributes to optimized dynamics and control of soft closed-chain grasping mechanisms.Practical implicationsThe approach is aimed to improve the development of soft grippers that are required to grasp complex objects found in human–robot cooperation and collaborative robot (cobot) applications.Originality/valueThe proposed closed-chain mathematical framework is based on distributed DOFs instead of the conventional lumped joint approach. This is to better optimize and understand the kinematics of soft robotic mechanisms.

Correlation of fabric tensors for granular materials using 2D DEM

Soil fabric anisotropy can be quantitatively assessed by means of fabric tensors introduced as internal variables in constitutive models and defined by unit vectors along the directions of different orientation microstructural entities such as particle long axes, inter-particle contact normal vectors and void vectors. The most common choice is a fabric tensor based on contact normal directions. However, contact normal directions are more difficult to determine experimentally, due to difficulties associated with accurate measurement of tangent contact planes. The main scope in this study is to seek for possible correlations for fabric tensors defined using different fabric entities, i.e., contact normal, void and particle orientation vector directions, and based on this correlation to suggest the two latter instead of the first one because of the easiness of their measurements. The void fabric is defined using a very recent contribution of the authors concerning a modified and a novel approach of the scan line method for the determination of appropriate void vectors by means of 2D discrete element method analysis. In this very recent work of the authors, a first qualitative correlation was detected between contact normal and void fabric for both the void fabric tensors used therein. Given that this observation concerned only one 2D test, the current work aims at presenting an extended parametric analysis on the correlation of fabric tenors for all the above-mentioned fabric entities.

SynGrasp: A MATLAB Toolbox for Underactuated and Compliant Hands

SynGrasp is a MATLAB toolbox for grasp analysis of fully or underactuated robotic hands with compliance. Compliance can be modeled at contact points in the joints or in the actuation system, including transmission. It is possible to use a graphical user interface (GUI) or directly assemble and modify the available functions to exploit all of the toolbox features. Grasps can be described either using the provided grasp planner or by directly defining contact points on the hand with the respective contact normal directions. Several analysis functions have been developed to investigate the main grasp properties: 1) controllable forces and object displacement, 2) manipulability analysis, and 3) grasp stiffness and quality measures. The functions for the graphical representation of the hand and object as well as the main analysis results are provided. The toolbox is freely available at http://syngrasp.dii.unisi.it.

Load assessment and analysis of impacts in multibody systems

The evaluation of contact forces during an impact requires the use of continuous force-based methods. An accurate prediction of the impact force demands the identification of the contact parameters on a case-by-case basis. In this paper, the preimpact effective kinetic energy (Formula presented.) is put forward as an indicator of the intensity of the impact force along the contact normal direction. This represents a part of the total kinetic energy of the system that is associated with the subspace of constrained motion defined by the impact constraints at the moment of contact onset. Its value depends only on the mechanical parameters and the configuration of the system. We illustrate in this paper that this indicator can be used to characterize the impact force intensity. The suitability of this indicator is confirmed by numerical simulations and experiments

Discrete element simulation of mechanical characteristics of sands under principal stress axes rotation

The mechanical behavior of sands and other granular materials subjected to rotation of principal stress axes is significantly dependent on the micro fabric properties and their evolution. The discrete element simulation for sands under cyclic rotation of principal stress axes was validated by comparing the numerical simulation and laboratory test results on the development of two normal strains,the relationship between shear stress and shear strain,the evolution of the volumetric strain,and the effects of initial void ratio and stress ratio. Four variables characterized by the spatial distribution features of particle major axis orientation and interparticle contact normal directions were used to describe the fabric properties of granular materials. The evolution of the four fabric variables in a single cycle was studied for granular materials subjected to cyclic rotation of principal stress axes. The effects of initial void ratio and stress ratio on the evolution of fabric variables were also investigated in detail.

Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials

Fabric tensors are commonly used in the study of granular materials as internal variables to quantify anisotropic fabrics. Fabric tensors can be constructed based on different microstructural entities in the material, such as particle long axis orientations, inter-particle contact normal directions, and orientations of void shapes. The current study explores the relationship between these different fabric tensors. Using two-dimensional discrete element method (DEM) simulations, we discover a simple and strong linear correlation between contact normal- and void vector-based fabric tensors for granular materials composed of non-elongated particles. This correlation holds true independent of the variations of all parameters and conditions exhaustively considered in this study, including the material’s packing density, stress state, inter-particle friction angle, particle size distribution, and particle shape. We also perform a preliminary and exploratory study of materials consisting of significantly elongated particles. The limited results show that the change of void vector-based fabric tensor appears to be affected by the corresponding components of the particle orientation-based fabric tensor and contact normal-based fabric tensor. Meanwhile, the normal component of the particle orientation-based fabric tensor and the corresponding component of contact normal-based fabric tensor are negatively correlated.

On the stress–force–fabric relationship for granular materials

This paper employed the theory of directional statistics to study the stress state of granular materials from the particle scale. The work was inspired by the stress–force–fabric relationship proposed by Rothenburg and Bathurst (1989), which represents a fundamental effort to establish analytical macro–micro relationship in granular mechanics. The micro-structural expression of the stress tensor σij=1V∑c∈Vvicfjc, where fic is the contact force and vic is the contact vector, was transformed into directional integration by grouping the terms with respect to their contact normal directions. The directional statistical theory was then employed to investigate the statistical features of contact vectors and contact forces. By approximating the directional distributions of contact normal density, mean contact force and mean contact vector with polynomial expansions in unit direction vector n, the directional dependences were characterized by the coefficients of the polynomial functions, i.e., the direction tensors. With such approximations, the directional integration was achieved by means of tensor multiplication, leading to an explicit expression of the stress tensor in terms of the direction tensors. Following the terminology used in Rothenburg and Bathurst (1989), the expression was referred to as the stress–force–fabric (SFF) relationship.Directional statistical analyses were carried out based on the particle-scale information obtained from discrete element simulations. The result demonstrated a small but isotropic statistical dependence between contact forces and contact vectors. It has also been shown that the directional distributions of contact normal density, mean contact forces and mean contact vectors can be approximated sufficiently by polynomial expansions in direction n up to 2nd, 3rd and 1st ranks, respectively. By incorporating these observations and revoking the symmetry of the Cauchy stress tensor, the stress–force–fabric relationship was further simplified, while its capacity of providing nearly identical predictions of the stresses was maintained. The derived SFF relationship predicts the complete stress information, including the mean normal stress, the deviatoric stress ratio as well as the principal stress directions.The main benefits of deriving the stress–force–fabric relationship based on the directional statistical theory are: (1) the method does not involve space subdivision and does not require a large number of directional data; (2) the statistical and directional characteristics of particle-scale directional data can be systematically investigated; (3) the directional integration can be converted into and achieved by tensor multiplication, an attractive feature to conduct computer program aided analyses.