Force Propagation Research Articles

Power-Law Scaling of Early-Stage Forces during Granular Impact.

We experimentally and computationally study the early-stage forces during intruder impacts with granular beds in the regime where the impact velocity approaches the granular force propagation speed. Experiments use 2D assemblies of photoelastic disks of varying stiffness, and complimentary discrete-element simulations are performed in 2D and 3D. The peak force during the initial stages of impact and the time at which it occurs depend only on the impact speed, the intruder diameter, the stiffness of the grains, and the mass density of the grains according to power-law scaling forms that are not consistent with Poncelet models, granular shock theory, or added-mass models. The insensitivity of our results to many system details suggests that they may also apply to impacts into similar materials like foams and emulsions.

Talin Impacts Force-Induced Vinculin Activation through ‘Loosening’ the Vinculin Inactive State

Focal Adhesions (FA) are large, multi-protein complexes connecting the cytoskeleton to the extracellular matrix. Their adhesive functionality is tightly regulated by mechanical stress. A key component of FA-associated mechanosensing is vinculin. It consists of a globular head, a proline-rich neck region, and a rod-like tail domain that contains binding sites for many other cytoplasmic proteins. Vinculin can assume either a closed ("inactive") or open (“active”) conformation. The underlying activation mechanism, however, remains yet to be fully understood. Here we employ molecular dynamics (MD) simulation to demonstrate that vinculin activation is greatly facilitated by the binding of vinculin on talin's vinculin binding site. Steered MD simulations reveal that the force required for vinculin activation is drastically reduced, by more than 50%, upon formation of the vinculin-talin complex. To explore this observation further, we use dynamic network fluctuation analysis showing how force propagation through vinculin changes upon complex formation. Interestingly, after talin dissociation, vinculin returns to its native conformation on a submicrosecond time scale, with 60% of its native contacts restored. Our results suggest a rapid dynamic equilibrium between 'tight' and 'loosened' inactive vinculin, which depends on talin and determines the level of mechanical stress required for activation. Our study has important implications for our understanding of mechano-sensing mechanisms at FAs.

Developmental changes in bone mechanics from Florida manatees (Trichechus manatus latirostris), obligate swimming mammals.

Mammals living in aquatic environments load their axial skeletons differently from their terrestrial counterparts. The structure and mechanical behavior of trabecular bone can be especially indicative of varying habitual forces. Here, we investigated vertebral trabecular bone mechanical properties (yield strength, stiffness and toughness) throughout development in Florida manatees (Trichechus manatus latirostris), obligate undulatory swimmers. Thoracic, lumbar and caudal vertebrae were dissected from manatees (N=20) during necropsies. We extracted 6 mm3 samples from vertebral bodies and tested them in compression in three orientations (rostrocaudal, dorsoventral and mediolateral) at 2 mm min-1 We determined variation in mechanical properties between sexes, and among developmental stages, vertebral regions and testing orientations. We also investigated the relationships between vertebral process lengths and properties of dorsoventrally and mediolaterally tested bone. Rostrocaudally tested bone was the strongest, stiffest and toughest, suggesting that this is the principal direction of stress. Our results showed that bone from female subadults was stronger and stiffer than that of their male counterparts; based on these data, we hypothesize that hormonal shifts at sexual maturity may partially drive these differences. In calves, bone from the posterior region was stronger and tougher than that from the anterior region. We hypothesize that as animals grow rapidly throughout early development, bone in the posterior region would be the most ossified to support the rostrocaudal force propagation associated with undulatory swimming.

On the Gravitational Wave and Force Propagation Speed Impact on the GEM Decay of Circular Orbits

Subluminal values of the speed of gravitational waves (GW) were obtained that reproduce a hypothetical Hulse-Taylor binary pulsar undergoing circular orbit decay. Those values of speed were used to simulate, in the framework of gravitoelectromagnetism (GEM), the in-spiral process of 3 GW events. The calculated results show a significantly better agreement (with the results of the linear theory of relativity) than the ones obtained using the speed of light. A method was proposed to measure the speed of the GW. Constraints of 0.89c

A Novel Active Contour Model Guided by Global and Local Signed Energy-Based Pressure Force

Active contour models (ACMs) have been widely applied in the field of image segmentation. However, it is still very challenging to construct an efficient ACM to segment images with intensity inhomogeneity. In this paper, a novel ACM guided by global and local signed energy-based pressure force (GLSEPF) is proposed. First, by computing the energy difference between the inner and outer energies of the evolution curve, a global signed energy-based pressure force (GSEPF) is designed, which can improve the robustness to initial curves. Second, a local signed energy-based pressure force (LSEPF) is introduced by computing the pixel-by-pixel energy difference within local neighborhood region, which can handle images with intensity inhomogeneity and noise. Finally, the global image information and the local energy information are used for the global and local force propagation functions, respectively. The global and local variances are used to automatically balance the weights of the GSEPF and the LSEPF, which can solve the problem of setting parameters. Meanwhile, a regularization term and a penalty term are applied to avoid the re-initialization process during iterations and smooth the level set function. Experimental results on different types of images demonstrate that the proposed model is more robust than the popular region-based and mixed ACMs for segmenting images with intensity inhomogeneity and noise. The code is available at: https://github.com/HuaxiangLiu/GLSEPF/.

A Mechanistic View of Collective Filament Motion in Active Nematic Networks

Protein filament networks are structures crucial for force generation and cell shape. A central open question is how collective filament dynamics emerges from interactions between individual network constituents. To address this question, we study a minimal but generic model for a nematic network in which filament sliding is driven by the action of motor proteins. Our theoretical analysis shows how the interplay between viscous drag on filaments and motor-induced forces governs force propagation through such interconnected filament networks. We find that the ratio between these antagonistic forces establishes the range of filament interaction, which determines how the local filament velocity depends on the polarity of the surrounding network. This force-propagation mechanism implies that the polarity-independent sliding observed in Xenopus egg extracts and in vitro experiments with purified components is a consequence of a large force-propagation length. We suggest how our predictions can be tested by tangible in vitro experiments whose feasibility is assessed with the help of simulations and an accompanying theoretical analysis.

Frictional impact analysis of an elastoplastic multi-link robotic system using a multi-timescale modelling approach

Considering tangential contact compliance, material nonlinearity and contact nonlinearity, an efficient multi-timescale computational approach (MCA) is presented to analyse the contact forces and transient wave propagation generated by the frictional impact of an elastoplastic multi-link robotic system. In the formulation of the MCA, a rigid multibody dynamic equation is derived to calculate the large overall motion without a unilateral contact constraint (large timescale) and the nonlinear finite element dynamic equation, including the penalty function algorithm, is given to calculate the contact force and stress wave propagation (small timescale). An experimental test for a manipulator’s oblique impact against a rough moving plate is also introduced. The accuracy, convergence and efficiency of the MCA are validated by a comparison with the pure finite element method (FEM) solution and experimental data. The error between the MCA and pure FEM solutions for the first peak value of the normal contact force $$F_{\mathrm{n}}$$ is less than 1.5%. The total time cost of the MCA is only 0.705% of the pure FEM. The numerical results also show that the presented MCA can effectively depict the transmission and reflection of the impact-induced waves at the middle hinge. In addition, the influences of the structural compliance, the velocity of plate $$v_{\mathrm{plate}}$$ and the coefficient of friction $$\mu $$ on the transient responses are investigated. The peak value of $$F_{\mathrm{n}}$$ will increase as $$v_{\mathrm{plate}}$$ increases, which has a strong relationship with the so-called dynamic self-locking phenomenon. Due to the large structural compliance of the rod, the “succession collisions” phenomenon (i.e. multiple contacts in a very short time) can be captured during an oblique impact event, and the normal relative motion at the local contact zone may experience two transitions between compression and restitution during a single contact process. The tangential stick-slip motion occurs as a reverse phenomenon. All investigations show that the MCA has sufficient accuracy to analyse the frictional impact of flexible robotic manipulators.

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling.

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

Thermal engineering of stone increased prehistoric toolmaking skill

Intentional heat treating of toolstone has been documented to have begun at least by 70 K BP; however, the advantages of such treatment have been debated for decades. There are two schools of thought with regard to its purpose. One, is that it merely reduces the force required for flake propagation. A second is that it also alters flake morphological properties. We systematically tested these hypotheses by generating flakes from cores exposed to three different temperatures (ambient, 300 °C, and 350 °C) using automated propagation procedures that bypassed any human agency. While the force propagation magnitude is altered by heat treatment, the flakes were not. We examined these flakes according to nine measures of morphology. None differed significantly or systematically within the three categories. While our results confirm that heat treatment does reduce the force needed for flake propagation, they also demonstrate that such treatment has no significant effect on major morphological aspects of flake form.

Tensor Train Accelerated Solvers for Nonsmooth Rigid Body Dynamics

Abstract In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred a renewed interest in the discrete element method (DEM) modeling of frictional contact. Force penalty methods, while economic and widely accessible, introduce artificial stiffness, requiring small time steps to retain numerical stability. Optimization-based methods, which enforce contacts geometrically through complementarity constraints leading to a differential variational inequality problem (DVI), allow for the use of larger time steps at the expense of solving a nonlinear complementarity problem (NCP) each time-step. We review the latest efforts to produce solvers for this NCP, focusing on its relaxation to a cone complementarity problem (CCP) and solution via an equivalent quadratic optimization problem with conic constraints. We distinguish between first-order methods, which use only gradient information and are thus linearly convergent and second-order methods, which rely on a Newton type step to gain quadratic convergence and are typically more robust and problem-independent. However, they require the approximate solution of large sparse linear systems, thus losing their competitive advantages in large scale problems due to computational cost. In this work, we propose a novel acceleration for the solution of Newton step linear systems in second-order methods using low-rank compression based fast direct solvers, leveraging on recent direct solver techniques for structured linear systems arising from differential and integral equations. We employ the quantized tensor train (QTT) decomposition to produce efficient approximate representations of the system matrix and its inverse. This provides a versatile and robust framework to accelerate its solution using this inverse in a direct or a preconditioned iterative method. We demonstrate compressibility of the Newton step matrices in primal dual interior point (PDIP) methods as applied to the multibody dynamics problem. Using a number of numerical tests, we demonstrate that this approach displays sublinear scaling of precomputation costs, may be efficiently updated across Newton iterations as well as across simulation time steps, and leads to a fast, optimal complexity solution of the Newton step. This allows our method to gain an order of magnitude speedups over state-of-the-art preconditioning techniques for moderate to large-scale systems, hence mitigating the computational bottleneck of second-order methods.

Enhancement of protein mechanical stability: Correlated deformations are handcuffed by ligand binding.

As revealed by previous experiments, protein mechanical stability can be effectively regulated by ligand binding with the binding site distant from the force-bearing region. However, the mechanism for such long-range allosteric control of protein mechanics is still largely unknown. In this work, we use protein topology-based elastic network model (ENM) and all-atomic steered molecular dynamics (SMD) simulations to study the impact of ligand binding on protein mechanical stability in two systems, i.e., GB1 and CheY-binding P2-domain of CheA (CBDCheA). Both ENM and SMD results show that the ligand binding has considerable and negligible effects on the mechanical stability of these two proteins, respectively. These results are consistent with the experimental observations. A physical mechanism for the enhancement of protein mechanical stability was then proposed: the correlated deformations of the force-bearing region and the binding site are handcuffed by the binding of ligand. The handcuff effect suppresses the propagation of internal force in the force-bearing region, thus improving the resistance to the loading force. Our study indicates that ENM method can effectively identify the structure motifs allosterically related to the deformation in the force bearing region, as well as the force propagation pathway within the structure of the studied proteins. Hence, it should be helpful to understand the molecular origin of the different mechanical properties in response to ligand binding for GB1 and CBDCheA.

Tactile-Based Whole-Body Compliance With Force Propagation for Mobile Manipulators

In this paper, we propose a control method, providing mobile robots with whole-body compliance capabilities, in response to multicontact physical interactions with their environment. The external forces applied to the robot, as well as their localization on its kinematic tree, are measured using a multimodal, self-configuring, and self-calibrating artificial skin. We formulate a compliance control law in Cartesian space, as a set of quadratic optimization problems, solved in parallel for each limb involved in the interaction process. This specific formulation makes it possible to determine the torque commands required to generate the desired reactive behaviors, while taking the robot kinematic and dynamic constraints into account. When a given limb fails to produce the desired compliant behavior, the generalized force residual at the considered contact points is propagated to a parent limb in order to be adequately compensated. Hence, the robot's compliance range can be extended in a both robust and easily adjustable manner. The experiments performed on a dual-arm velocity-controlled mobile manipulator show that our methodology is robust to nullspace interactions and robot physical constraints.

Elasticity Versus Hyperelasticity Considerations in Quasistatic Modeling of a Soft Finger-Like Robotic Appendage for Real-Time Position and Force Estimation

Various methods based on hyperelastic assumptions have been developed to address the mathematical complexities of modeling motion and deformation of continuum manipulators. In this study, we propose a quasistatic approach for 3D modeling and real-time simulation of a pneumatically actuated soft continuum robotic appendage to estimate the contact force and overall pose. Our model can incorporate external load at any arbitrary point on the body and deliver positional and force propagation information along the entire backbone. In line with the proposed model, the effectiveness of elasticity versus hyperelasticity assumptions (neo-Hookean and Gent) is investigated and compared. Experiments are carried out with and without external load, and simulations are validated across a range of Young's moduli. Results show best conformity with Hooke's model for limited strains with about 6% average normalized error of position; and a mean absolute error of less than 0.08 N for force applied at the tip and on the body, demonstrating high accuracy in estimating the position and the contact force.

Mapping the Biochemical Interactions of the Mechanoresponsive Contractility Controller

Every biological process, ranging from cell migration to embryogenesis, relies on the cell's ability to adapt to changing mechanical environments. By studying the model shape change process cytokinesis in Dictyostelium, we find that the cell is a finely tuned control system, with proteins that modulate their behavior in response to mechanical and biochemical signals. Although we know many of the players involved in the contractility controller, their biochemical interactions that allow force propagation through the cortical network are still poorly defined. We use a proteomics approach to identify direct interactors of two key nodes of the control system, actin crosslinker cortexillin I and scaffolding protein IQGAP2. This analysis identifies mechanoenzyme myosin II as a biochemical interactor of both cortexillin I and IQGAP2. We use quantitative in vivo biochemical measurements, including fluorescence cross-correlation spectroscopy (FCCS) and Single Molecule Pulldown (SiMPull) to measure concentrations, apparent binding affinities, and stoichiometries of complexes. We find that the cooperative mechanoaccumulation of myosin II and cortexillin I is potentially due to their direct interaction. IQGAP1, in turn, competes with IQGAP2 to bind myosin II and cortexillin I, thus negatively regulating contractility. Our data also suggest that multi-protein complexes are pre-formed in the cytoplasm, primed for activation by chemical or mechanical stimuli to engage with the cytoskeletal network. In addition, we find a few unusual interactors by mass spectrometry analysis, such as RNP1, discoidins, and methylmalonyl semialdehyde dehydrogenase (mmsdh), which we previously identified in genetic suppressor screens, providing greater evidence for their function in the network. Using the contractility controller as a model, we are identifying a quantitative interaction map, complete with new interactions, that is uncovering new biochemistry associated with the mechanobiome.

A simulation study on the ice fracture behaviors in ice-lighthouse interaction considering initial defects in ice sheet

With the increasing marine activities in the Arctic area, the demand for reliable designs of marine structures in this area is growing. There have been many studies published regarding simulation of ice-marine structure interaction. In these studies, ice models are established without considering initial defects. However, natural ice usually contains lots of initial defects including cracks, inclusions, pores, etc. In this paper, this issue is studied by applying defect model and cohesive element method (CEM). Several ice bulk elements labeled as initial defects are deleted from the ice sheet. Then, cohesive elements are inserted in the ice sheet model that is meshed with tetrahedron elements. Collision between ice sheet and a lighthouse is simulated in full scale. Initiation and propagation of ice sheet cracks are achieved by deleting the cohesive elements that reach fracture energy. Horizontal force and failure process of ice sheet are analyzed. The results show that the initial defects can affect both the horizontal force and fracture of ice sheet. Then, a series of simulations in terms of distribution, percentage and size of ice sheet defects are performed. Effects of these factors on the horizontal force and crack propagation are discussed.

Active Contour Driven by Weighted Hybrid Signed Pressure Force for Image Segmentation

This study presents a novel active contour model (ACM) driven by weighted global and local region-based signed pressure force (SPF) to segment images in the presence of intensity inhomogeneity and noise. First, an adaptive weighted global region-based SPF (GRSPF) function as the driving centers is designed based on the global image information, which is based on the normalized global intensity to update the weights of the inner and outer regions of the curve during iterations. Second, by introducing the normalized absolute local intensity differences as the weighs of the inner and outer regions, an adaptive weighted local region-based SPF (LRSPF) function is similarly defined. Third, instead of setting a fixed force, a force propagation function is introduced to automatically balance the interior and exterior forces according to the image feature. Meanwhile, by combing the adaptive GWSPF and LWSPF functions, a weighted hybrid region-based SPF function is defined, which can improve the efficiency and accuracy of the proposed model. The experimental results on real images demonstrate that the proposed model is more robust than the popular region-based ACMs for segmenting images with intensity inhomogeneity and noise. The code is available at https://github.com/fangchj2002/WHRSPF .

Force transmission and the order parameter of shear thickening.

The origin of the abrupt shear thickening observed in some dense suspensions has been recently argued to be a transition from frictionless (lubricated) to frictional interactions between immersed particles. The Wyart-Cates rheological model, built on this scenario, introduced the concept of the fraction of frictional contacts f as the relevant order parameter for the shear thickening transition. Central to the model is the "equation-of-state" relating f to the applied stress σ, which is directly linked to the distribution of the normal components of non-hydrodynamic interparticle forces. Here, we develop a model for this force distribution, based on the so-called q-model, which we borrow from granular physics. This model explains the known f(σ) in the simple case of sphere contacts displaying only sliding friction, but also predicts strong deviation from this "usual" form when stronger kinds of constraints are applied on the relative motion. We verify these predictions in the case of contacts with rolling friction, in particular a broadening of the stress range over which shear thickening occurs. We finally discuss how a similar approach can be followed to predict f(σ) in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.

Effects of solvent quality and non-equilibrium conformations on polymer translocation.

The conformation and its relaxation of a single polymer depend on solvent quality in a polymer solution: a polymer collapses into a globule in a poor solvent, while the polymer swells in a good solvent. When one translocates a polymer through a narrow pore, a drastic conformational change occurs such that the kinetics of the translocation is expected to depend on the solvent quality. However, the effects of solvent quality on the translocation kinetics have been controversial. In this study, we employ a coarse-grained model for a polymer and perform Langevin dynamics simulations for the driven translocation of a polymer in various types of solvents. We estimate the free energy of polymer translocation using steered molecular dynamics simulations and Jarzynski's equality and find that the free energy barrier for the translocation increases as the solvent quality becomes poorer. The conformational entropy contributes most to the free energy barrier of the translocation in a good solvent, while a balance between entropy and energy matters in a poor solvent. Interestingly, contrary to what is expected from the free energy profile, the translocation kinetics is a non-monotonic function of the solvent quality. We find that for any type of solvent, the polymer conformation stays far away from the equilibrium conformation during translocation due to an external force and tension propagation. However, the degree of tension propagation differs depending on the solvent quality as well as the magnitude of the external force: the tension propagation is more significant in a good solvent than in a poor solvent. We illustrate that such differences in tension propagation and non-equilibrium conformations between good and poor solvents are responsible for the complicated non-monotonic effects of solvent quality on the translocation kinetics.

Mechanosensitive Gene Regulation by Myocardin-Related Transcription Factors Is Required for Cardiomyocyte Integrity in Load-Induced Ventricular Hypertrophy.

Hypertrophic cardiomyocyte growth and dysfunction accompany various forms of heart disease. The mechanisms responsible for transcriptional changes that affect cardiac physiology and the transition to heart failure are not well understood. The intercalated disc (ID) is a specialized intercellular junction coupling cardiomyocyte force transmission and propagation of electrical activity. The ID is gaining attention as a mechanosensitive signaling hub and hotspot for causative mutations in cardiomyopathy. Transmission electron microscopy, confocal microscopy, and single-molecule localization microscopy were used to examine changes in ID structure and protein localization in the murine and human heart. We conducted detailed cardiac functional assessment and transcriptional profiling of mice lacking myocardin-related transcription factor (MRTF)-A and MRTF-B specifically in adult cardiomyocytes to evaluate the role of mechanosensitive regulation of gene expression in load-induced ventricular remodeling. We found that MRTFs localize to IDs in the healthy human heart and accumulate in the nucleus in heart failure. Although mice lacking MRTFs in adult cardiomyocytes display normal cardiac physiology at baseline, pressure overload leads to rapid heart failure characterized by sarcomere disarray, ID disintegration, chamber dilation and wall thinning, cardiac functional decline, and partially penetrant acute lethality. Transcriptional profiling reveals a program of actin cytoskeleton and cardiomyocyte adhesion genes driven by MRTFs during pressure overload. Indeed, conspicuous remodeling of gap junctions at IDs identified by single-molecule localization microscopy may partially stem from a reduction in Mapre1 expression, which we show is a direct mechanosensitive MRTF target. Our study describes a novel paradigm in which MRTFs control an acute mechanosensitive signaling circuit that coordinates cross-talk between the actin and microtubule cytoskeleton and maintains ID integrity and cardiomyocyte homeostasis in heart disease.

Direction Matters: Monovalent Streptavidin/Biotin Complex under Load.

Novel site-specific attachment strategies combined with improvements of computational resources enable new insights into the mechanics of the monovalent biotin/streptavidin complex under load and forced us to rethink the diversity of rupture forces reported in the literature. We discovered that the mechanical stability of this complex depends strongly on the geometry in which force is applied. By atomic force microscopy-based single molecule force spectroscopy we found unbinding of biotin to occur beyond 400 pN at force loading rates of 10 nN/s when monovalent streptavidin was tethered at its C-terminus. This value is about twice as high than that for N-terminal attachment. Steered molecular dynamics simulations provided a detailed picture of the mechanics of the unbinding process in the corresponding force loading geometries. Using machine learning techniques, we connected findings from hundreds of simulations to the experimental results, identifying different force propagation pathways. Interestingly, we observed that depending on force loading geometry, partial unfolding of N-terminal region of monovalent streptavidin occurs before biotin is released from the binding pocket.