Deformable Bodies Research Articles

Scalable O(log2n) Dynamics Control for Soft Exoskeletons

Robotic exoskeletons are being actively applied to support the activities of daily living (ADL) for patients with hand motion impairments. In terms of actuation, soft materials and sensors have opened new alternatives to conventional rigid body structures. In this arena, biomimetic soft systems play an important role in modeling and controlling human hand kinematics without the restrictions of rigid mechanical joints while having an entirely deformable body with limitless points of actuation. In this paper, we address the computational limitations of modeling large-scale articulated systems for soft robotic exoskeletons by integrating a parallel algorithm to compute the exoskeleton’s dynamics equations of motion (EoM), achieving a computation with O(log2n) complexity for the highly articulated n degrees of freedom (DoF) running on p processing cores. The proposed parallel algorithm achieves an exponential speedup for n=p=64 DoF while achieving a 0.96 degree of parallelism for n=p=256, which demonstrates the required scalability for controlling highly articulated soft exoskeletons in real time. However, scalability will be bounded by the n=p fraction.

Finite element simulation of knee joint pressure and surface displacement: relationship and influencing factors

Knee sleeves are widely used functional pressure garments that exert pressure on the knee, causing body surface displacement and deformation. Understanding the relationship between knee joint pressure distribution and body surface displacement, along with the factors affecting this displacement, is crucial for optimizing knee sleeves. This study established a biomechanical model of the human knee joint using three-dimensional reconstruction and finite element analysis. The study simulated the pressure distribution and body surface displacement after wearing five different knee sleeve designs. Using SPSS software, it analyzed clothing and human factors to determine the main influences on displacement, resulting in linear regression equations linking knee physiological characteristics and skin displacement. Findings indicated that skin curvature radius and the distance between skin and bone significantly affect displacement, while knee sleeve structure design shows less correlation. The study also divided the knee joint into eight sections to calculate volume shrinkage after compression, providing insights for designing knee sleeves that enhance comfort and functionality based on human physiology.

HAVEN: Haptic And Visual Environment Navigation by a Shape-Changing Mobile Robot with Multimodal Perception.

Many animals exhibit agile mobility in obstructed environments due to their ability to tune their bodies to negotiate and manipulate obstacles and apertures. Most mobile robots are rigid structures and avoid obstacles where possible. In this work, we introduce a new framework named Haptic And Visual Environment Navigation (HAVEN) Architecture to combine vision and proprioception for a deformable mobile robot to be more agile in obstructed environments. The algorithms enable the robot to be autonomously (a)predictive by analysing visual feedback from the environment and preparing its body accordingly, (b)reactive by responding to proprioceptive feedback, and (c)active by manipulating obstacles and gap sizes using its deformable body. The robot was tested approaching differently sized apertures in obstructed environments ranging from greater than its shape to smaller than its narrowest possible size. The experiments involved multiple obstacles with different physical properties. The results show higher navigation success rates and an average 32% navigation time reduction when the robot actively manipulates obstacles using its shape-changing body.

Analytical assessment of suspension bridge's 3D curved cable configuration and cable clamp pre-installation angle considering the main cable torsional and flexural stiffnesses

For a suspension bridge with a spatial cable system, the 3D curved main cable undergoes large lateral and torsional deformations during construction, which increases the difficulty of construction control. If using the traditional ideal flexible cable assumption, the torsional deformation cannot be analyzed. Therefore, incorporating the main cable's torsional and flexural stiffnesses in shape-finding analysis remains highly challenging. This study develops an analytical method for determining the target configuration of the main cable by applying the multi-segment catenary method and the Cosserat rod model. The closed-form solution of the geometrically exact force-displacement-strain relationships is derived, comprehensively considering the tension, shear, bending, and torsion of the main cable, as well as the initial curvatures and axial strains in the reference configuration. Then a two-layer shape-finding framework is established, with the first layer being recursive calculations of the cable shape and the second layer being numerical calculations of the nonlinear governing equations using the Levenberg-Marquardt method. Furthermore, a novel method for calculating the pre-deflection angle of the cable clamp in the free cable state is presented for the first time. A classic cantilever model and a suspension bridge with the spatial main cable are studied to investigate the accuracy of the proposed algorithms. Numerical results indicate that when the spatial main cable is twisted, the bottom edge of the cable cross-section moves outward along the transverse direction of the bridge. The torsion of the main cable includes both elastic deformation and rigid body displacement caused by the bidirectional bending effect. At the mid-span, the torsional angle of the main cable cross-section is 10.088°, and the pre-deflection angle of the cable clamp at the mid-span should be set to 10.851°. Moreover, the target configuration is highly sensitive to the flexural and torsional stiffnesses of the main cable while the effect of shear deformations on cable configurations can be ignored.

Active fractal networks with stochastic force monopoles and force dipoles: Application to subdiffusion of chromosomal loci.

Motivated by the well-known fractal packing of chromatin, we study the Rouse-type dynamics of elastic fractal networks with embedded, stochastically driven, active force monopoles and force dipoles that are temporally correlated. We compute, analytically-using a general theoretical framework-and via Langevin dynamics simulations, the mean square displacement (MSD) of a network bead. Following a short-time superdiffusive behavior, force monopoles yield anomalous subdiffusion with an exponent identical to that of the thermal system. In contrast, force dipoles do not induce subdiffusion, and the early superdiffusive MSD crosses over to a relatively small, system-size-independent saturation value. In addition, we find that force dipoles may lead to "crawling" rotational motion of the whole network, reminiscent of that found for triangular micro-swimmers and consistent with general theories of the rotation of deformable bodies. Moreover, force dipoles lead to network collapse beyond a critical force strength, which persists with increasing system size, signifying a true first-order dynamical phase transition. We apply our results to the motion of chromosomal loci in bacteria and yeast cells' chromatin, where anomalous sub-diffusion, MSD∼tν with ν≃0.4, was found in both normal and cells depleted of adenosine triphosphate (ATP), albeit with different apparent diffusion coefficients. We show that the combination of thermal, monopolar, and dipolar forces in chromatin is typically dominated by the active monopolar and thermal forces, explaining the observed normal cells vs the ATP-depleted cells behavior.

Deformable bodies in two dimensions and the gauge aspect of bottle flip

Abstract The water-bottle flip demonstration, that has received quite a viewership on media, involves tossing a bottle filled (up
to some fraction of its volume) with water up in the air while giving it a transverse spin in such a way that it lands
perfectly upright on its base. A mathematical description of the actual dynamics of the bottle flip is bound to be very
complicated due to the highly non-linear motion of the fluid. A model that is amenable to an analytical treatment has
been proposed in the literature. Conservation of angular momentum in the center of mass frame allows the angular
velocity of the bottle to change, and in particular it becomes very low right before the landing. This is thought to
be the essential feature needed for an upright landing of the bottle. In this paper we study a mathematical formalism
that would be useful to improve upon the analysis of this model. We point out that the proper mathematical setting to
analyze such systems is to model the content of the bottle as a deformable body. This brings out the gauge dependence
of the angular velocity and shows that it can even go to zero without violating the conservation of angular momentum.
The mechanism is well studied in literature under the heading of the falling cat problem. Indeed, from our point of
view the bottle-flip system is a two dimensional analog of the falling cat problem (modulo the self-control of the cat)

Geodesic-Based Maximal Cliques Search for Non-Rigid Human Point Cloud Registration.

Non-rigid point cloud registration holds significant importance for human body pose analysis in the fields of sports, medicine, gaming, etc. In this paper, we propose a non-rigid point cloud registration algorithm based on geodesic distance measurement, which can improve the accuracy of the registration for matching point pairs during non-rigid deformations. Firstly, a graph is constructed for two sets of point clouds using geodesic distance measurement considering that geodesic distance changes minimally during non-rigid deformation of the human body, which can preserve the point cloud matching information between corresponding points. Furthermore, a maximal clique search is employed to find combinations of matching pairs between point clouds. Finally, by driving the human body model parameters, sparse matching pairs are overlapped as much as possible to achieve non-rigid point cloud registration of the human body. The accuracy of the proposed algorithm is verified with FAUST and CAPE datasets.

Biomechanical Analysis and Modeling of Different Traction Patterns in Adolescent Idiopathic Scoliosis

Objective: Traction is a valuable treatment for Adolescent idiopathic scoliosis; however, assessing its biomechanical effects, particularly with new methods, presents challenges. This study aims to explore the biomechanics using finite element analysis, with the goal of enhancing safety and effectiveness. Methods: Based on CT images, two different boundary and loads were applied to simulate two traction methods. The effects of these two traction methods on stress and deformation of lumbar vertebral bodies and intervertebral discs were compared. Results: Under two traction methods, the stress was concentrated on the posterior side. Multi-point traction resulted in higher stress and deformation, and concentrated stress on the convex side as well. However, there is some stress concentration on the vertebral arch, which may lead to injury. Conclusion: Compared to longitudinal traction, multi-point traction can better reduce stress on the vertebral bodies and intervertebral discs, focusing the pulling force on the concave side and achieving greater deformation. Multi-point traction might better suit specific patients needing more correction and pressure relief compared to longitudinal traction.

The effect of cutting speed on the generation of bituminous coal dust: Experimental and theoretical discussion

To address the issue of an unclear mechanism for dust generation, an experiment was conducted to investigate the dust generation and migration under varying cutting speeds of a single cutting tooth. The findings indicate that coal dust production involves a rapid physical transformation process comprising four stages: coal body deformation, formation of the crushing zone, stress release, and collapse of fractured material. Increasing the cutting speed results in a continuous rise in both the total dust production rate and the respiratory dust rate. At a cutting speed of 10 mm/s, the RF coal sample exhibited a total dust production rate of 32.41 g/t, while the HP coal sample had a total dust production rate of 93.10 g/t. The moisture content of the coal samples exhibited a negative correlation with the total dust production rate, whereas the fixed carbon content and porosity showed a positive correlation with this rate. However, the size of the porosity had no significant impact on the production rates of respirable dust and PM2.5 dust. These research findings enhance the understanding of the dust production mechanism during coal and rock cutting, providing guidance for dust control at the origin.

Continuum Mechanics Applied to the Biomechanics of Motion.

Continuum Mechanics is the discipline that studies the motion and deformation of material bodies, and is at the basis of both Solid Mechanics and Fluid Mechanics. This works aims at highlighting how a basic education in modern Continuum Mechanics can be of fundamental importance not only in the Biomechanics of Tissue, but also in the Biomechanics of Movement. The latter is largely based on Rigid Body Mechanics, which can be considered as a simple particular case of the general theory of Continuum Mechanics. As an example, a straightforward methodology for the extraction of the angular velocity from motion analysis data is illustrated. The method is based on a quantity that is more primitive than the angular velocity: the spin tensor.

Landslide displacement prediction using time series InSAR with combined LSTM and TCN: application to the Xiao Andong landslide, Yunnan Province, China

AbstractResearch on landslide displacement prediction based on interferometric synthetic aperture radar (InSAR) deformation data involves two main issues. First, InSAR can provide only one-dimensional deformation data along the satellite’s line of sight (LOS), which cannot truly reflect the deformation of the landslide body in the downward direction along the slope. Second, the use of a single prediction model does not adequately account for both long-term and local changes in landslide displacement, affecting the accuracy of the predictions. To address this, in this study, Long Short-Term Memory networks (LSTM) and temporal convolutional network (TCN) models are combined to construct a method (LSTM-TCN) of landslide displacement prediction. This method can consider the long-term and localized changes in landslide displacement. The method is first based on InSAR technology to obtain surface deformation. The deformation of the landslide is subsequently computed in the downward direction along the slope to obtain the landslide displacement time series data. Next, the LSTM-TCN is used for landslide displacement prediction. Finally, the mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R2) are used to evaluate the performance of the model. The experiment is conducted on the Xiao Andong landslide in Anshi village, Fengqing County, Lincang City, Yunnan Province, China. The LSTM-TCN model achieves an R2 of 0.75, an RMSE of 0.43 cm, and an MAE of 0.36 cm. Compared with the individual LSTM and TCN models, the LSTM-TCN model exhibits the highest prediction accuracy and the smallest prediction error, which is closer to the true result that in the other models. These results demonstrate that the combined LSTM-TCN model effectively captures the complex features and long-term trends in landslide displacement data, significantly enhancing the accuracy of predictions.

From the Cosserats mechanics backgrounds to modern field theory

In the paper, yet weekly known, Cosserats’ original four concepts as follow: the four-time unification of rigid body dynamics, statics of flexible rods, statics of elastic surfaces and 3D deformable body dynamics; the intrinsic formulation based on the local, von Helmholtz symmetry group of monodromy; the invariance under the Euclidean group. The concept of a set of low-dimensional branes immersed into Euclidean space are revalorized and explained in terms of the modern gauge field theory and the extended strings theory. Additionally, some useful mathematical tools that connect the continuum mechanics and the classical field theory (for instance, the convective coordinates, von Mises’ “Motorrechnung”, the Grassmann extensions, Euclidean invariance, etc.) are involved in the historical explanation that how the ideas were developing themself.

Fast spline collision detection (FSCD) algorithm for solving multiple contacts in real-time

Collision detection has been widely studied in the last decades. While plenty of solutions exist, certain simulation scenarios are still challenging when permanent contact and deformable bodies are involved. In this paper, we introduce a novel approach based on volumetric splines that is applicable to complex deformable tubes, such as in the simulation of colonoscopy and other endoscopies. The method relies on modeling radial control points, extracting surface information from a triangle mesh, and storing the volume information around a spline path. Such information is later used to compute the intersection between the object surfaces under the assumption of spatial coherence between neighboring splines. We analyze the method’s performance in terms of both speed and accuracy, comparing it with previous works. Results show that our method solves collisions between complex meshes with over 300k triangles, generating over 1,000 collisions per frame between objects while maintaining an average time of under 1ms without compromising accuracy.

Dynamic digital image correlation method for rolling convective contact

Digital image correlation (DIC) is an increasingly popular and effective non-contact method for measuring full-field displacements and strains of deformable bodies under load. Current DIC methods applied to bodies undergoing large displacements and rotations require a large measurement area for both the reference (i.e., undeformed) image and the deformed images. This can limit the resulting resolution of the displacement and strain fields. To address this issue, we propose a two-stage dynamic DIC method capable of measuring displacements and strains under material convection with high resolution. During the first stage, the reference image is assembled from smaller, high-resolution images of the undeformed object obtained using a spatially-fixed or moving frame. Following capture, each sub-image is rigidly translated and rotated into its appropriate place, thereby producing a full, high-resolution image of the reference body. In stage two, images of the loaded and deformed body, again obtained using a small camera frame with high resolution, are aligned with matching regions of the undeformed composite image using BRISK feature detection before performing DIC. We demonstrate the method on a contact problem whereby an elastomeric roller travels along a rigid surface. In doing so, we obtain fine-resolution measurements of the state of strain of the region of the roller sidewall in contact with the substrate, even as new material convects through the region of interest. We present these measurements as a series of images and videos capturing strain evolution as the roller transitions from static loads to a fully dynamic steady-state, documenting the effectiveness of the method.

Heat transfer-deformation characteristics and fracture damage analysis during LN2 freeze-thaw process in different rank coals

Exploring the heat transfer and deformation characteristics of coal bodies of different coal ranks during the freeze-thaw process is of significant importance for analyzing the fracture mechanism under the effect of liquid nitrogen (LN2). This experiment targets lignite, bituminite, and anthracite under both saturated and dry conditions. A real-time temperature-strain monitoring system was employed to observe the heat transfer and deformation characteristics of coal samples with different ranks throughout the freeze-thaw cycle. Additionally, a nuclear magnetic resonance system was utilized to examine the characteristics of pore damage before and after fracturing. The findings reveal: (1) During the freeze-thaw process, the absolute value of the temperature evolution rate for dry coal samples shows a negative correlation with coal rank, indicating a close link between temperature diffusion and intrinsic coal properties like oxygen content and porosity. (2) For saturated coal samples, the absolute value of the temperature change rate during freezing decreases as the coal rank increases, with the opposite trend observed during thawing. The phase change effect of water in fractures during freezing can enhance internal temperature diffusion in the coal body, while it acts as an inhibitor during thawing. (3) Based on the trend of strain fluctuations, the coal body deformation process during the freeze-thaw cycle can be segmented into seven stages, summarizing the general mechanisms of deformation failure. (4) Under saturated conditions, the amplitude of elastic deformation for each sample is negatively correlated with coal rank, with the sequence for dry coal samples being bituminite > anthracite > lignite. (5) The formation of a sealed space at the beginning of freezing is identified as a necessary condition for deformation during the freeze-thaw process, with the formation and strength of the sealed space depending on the temperature diffusion rate, moisture content, and inherent properties of the coal sample.

Late mesozoic exhumation of silurian – Devonian and permian Ni-Co sulfide deposits in the East Kunlun orogenic belt: Constraints from zircon fission track ages

Ni-Co sulfide deposits of late Silurian – early Devonian and Permian ages hosted within in basic-ultrabasic rock bodies in the East Kunlun orogenic belt have been extensively investigated. Nevertheless, we have only a limited understanding of the history and dynamics of uplift, exhumation, and tectonic deformation of the basic-ultrabasic ore-bearing rock bodies of these Ni-Co sulfide deposits. We used the zircon fission track ages of seven samples obtained from basic-ultrabasic ore-bearing rocks to determine the timing of the exhumation of these Ni-Co sulfide deposits. Combining our results with published data on the timing of orogenesis, cooling events, magmatic activities, and basin infilling in adjacent areas, we conclude the following: 1) The ZFT ages obtained in this study indicate the exhumation during 169.6 ± 5.5–142.2 ± 3.2 Ma; 2) Combined with previous results, our data indicate that the exhumation during the Jurassic – Cretaceous occurred across a large area along the East Kunlun orogenic belt to the Alxa block; 3) The synchroneity of orogeny, magmatic activity, and basin infilling events suggests that the late Mesozoic exhumation was a geomorphological response to the Lhasa-Qiangtang collision driven by the breakup of Gondwanaland.

A rigid‐flexible coupled rocking structure with nonlinear stress distribution along its base: Analytical modeling, validation and parametric investigation

AbstractStructures allowing their bases to uplift and rock during an earthquake event usually experience less damage; thus, they are more resilient to seismic hazards. Accurate simulation is critical to design and seismic performance evaluation of these flexible rocking structures. Motivated from this, this article presents a new rigid‐flexible coupled rocking model for numerical evaluation of flexible rocking structures under both cyclic and dynamic loadings. The key idea in the model formulation is that the total motion of flexible rocking structure can be decomposed into a rigid‐body motion and an associated flexible deformation. The flexible deformation of the rocking body is described using displacement field of classical Timoshenko beam. Using this approach and appropriate degrees‐of‐freedom (DOFs), the governing equations‐of‐motion for flexible rocking structures are formulated using the variational principle. Multiple springs with appropriate constitutive model are distributed along rocking base to represent the inelastic behavior of rocking body. Potential post‐tensioned tendons are also considered in this model. In addition, nonlinear stress distribution along the rocking base, which cannot be considered in existing flexible rocking model, is also incorporated in the developed model. The proposed model is subsequently validated against published experimental data through quasi‐static and shake table tests, showing good accuracy when the rocking structure is relatively stockier. Finally, a parametric investigation on the effect of flexibility, nonlinear stress distribution and yield stress of rocking body on the rocking response is performed. This preliminary investigation shows that influence of flexibility and yield stress is significant while impact of nonlinear stress distribution is minor.

Multiscale contact homogenisation: A novel perspective through the method of multiscale virtual power

The interaction between deformable bodies and rigid foundations undergoing finite strains is explored in this work with the Method of Multiscale Virtual Power, unlocking novel insights into contact homogenisation theories. The focus lies in establishing the foundational kinematical links across scales and achieving seamless homogenisation of the traction vector through rigorous duality arguments. Two distinct families of contact homogenisation models are formulated: surface–surface and surface–volume models. These families emerge from the virtual power balance established between the target macroscopic surface and the corresponding microscopic contact surface or volume. They not only represent fundamental kinematical entities at each scale but also enable the replacement of the heterogeneous contact traction distribution with a smooth, homogenised version. Microscale equilibrium problems and homogenisation relations, along with the relevant macro- and microscale quantities, are derived by means of straightforward variational arguments. Furthermore, potential finite size effects are addressed in the homogenised response, enhancing the reliability and applicability of the strategy across diverse scenarios. Promising submodels have been identified within both families, broadening the understanding of multiscale contact phenomena and including existing models as particular cases. The proposed continuum-based variational families of models naturally lead to generic finite element-based frameworks for contact homogenisation of heterogeneous solids, as described in a forthcoming paper.

Development of the technology of restoration of the tail part of the body of the cutter of the road cutter

Purpose. The purpose of this work is to study the patterns of wear and develop a technology for restoring the tail part of the cutter body of the road cutter. They conducted an analysis of the wear of the cutters and found that most of them are suitable for use, since the shape of the carbide tip has not changed much and can still be used for grinding asphalt-concrete mixture. Methodology/approach. The method of restoration of the caudal part of the body of the incisors was developed and proposed. The recovery route is as follows: 1. Cleaning the incisor. 2. Heating the tail part of the cutter with a propane-oxygen flame. 3. Plastic deformation of the cutter body in the die. 4. Air cooling. 5. Control measurement of size changes. The recommended heat treatment temperature for plastic deformation depends on the concentration of carbon and alloying elements of the steel, and lies in the temperature range from 800 to 1280°С, the heating time is 1.33 min. Before distribution, the body of the cutter was heated using a propane-oxygen flame. Deposition was carried out in a closed die with the help of a special Poisson. A cutter head was placed in the matrix, on which a guide with a punch was installed. The developed technology of restoration of the tail part of the incisor by handing. Findings. According to the proposed technology, the tail part of the cutter body is distributed from 0.04 mm to 0.73 mm per side. Research limitations/implications. In this way, the cutters of the road cutters are restored to almost the dimensions of a new part, which enables repeated use.

An intelligent method for temperature load of arch dams

Temperature load significantly affects the deformation and stress of arch dams. Traditional methods for determining temperature loads may not adapt to complex environments, such as high-altitude regions with large temperature variations. This study proposes an intelligent method for temperature load of arch dams. Based on the measured data from existing dams, a physics-informed convolutional neural network is developed, enabling direct application to newly designed dams. The intelligent method delivers annual temperature boundaries on the dam surface, aiding the finite element model in predicting deformation and stress during operational phases. Validation demonstrates accurate results for dam body temperature and deformation, aligning closely with measured data, while also pinpointing critical stress areas within the dam. This method advances the AI-assisted design by predicting temperature loads during dam operation, providing strong support for determining the most unfavorable loading without measured data and ensuring the safety of the structure.