Single Deformation Mode Research Articles

NUMERICAL INVESTIGATION OF A OMNIDIRECTIONAL BENDING ACTUATOR FOR CLIMBING ANALYSIS

With its good flexibility and adaptability to the environment, soft robot has been attached great importance by the majority of researchers in recent years, and is widely used in rehabilitation treatment, flexible grasping and other fields. However, the existing actuators have disadvantages such as single deformation mode, poor flexibility and insufficient environmental adaptability. The reason is that the actuator structure is too simple to meet the complex application scenarios. In this paper, an omnidirectional bending multi-segment soft actuator is proposed, and the parameter analysis and dynamic analysis models are given. Meanwhile, the prestressed modal analysis of the proposed model is carried out to better characterize the dynamic behavior. A numerical study of a climbing motion verifies the novelty and validity of the proposed structure.

Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials

AbstractA novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress–strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II

In Part I of this study, it was shown that all the three known types of monohedral hexagonal tessellations of the plane, those composed of equal irregular hexagons, have just a single deformation mode when tiles are considered as rigid bodies hinged to each other along the edges. A gallery of tessellated plates was simulated numerically to demonstrate the range of achievable deformed shapes. In Part II, the displacement field was first derived and a continuous interpolant for each type of tessellated plate. It turns out that all corresponding metasurfaces are described by quadrics. Afterwards, a parametric analysis was carried out to determine the effect of varying angles and edge lengths on the curvature, and the values of the geometric Poisson ratio of the plates. Finally, a method of fabrication is proposed based on the additive manufacturing of stiff tiles of negligible deformability and flexible connectors. Using this modular technique, it is possible to join together different monohedral tessellated plates able to deform into piece-wise quadrics. The nodal positions in the deformed configuration of the realized plates are measured after enforcing one principal curvature to assume a chosen value. The estimate of the other principal curvature confirms the analytical predictions. The presented tessellated plates permit to realize doubly curved shape-morphing metasurfaces with assorted shapes, which also can feature a certain surface roughness, and they can be employed in all applications demanding high surface accuracy and few actuators or just one.

Structural design and crashworthiness analysis of expanding-splitting circular tubes

The use of expanding-splitting circular tubes was proposed to improve crashworthiness and overcome their deficiencies in terms of low energy absorption and poor stroke efficiency in a single deformation mode. Quasi-static experiments and finite element simulations were conducted to study the force–displacement response of circular tubes under combined deformation modes. A theoretical model of the circular tube during expanding-splitting deformation was established to reveal the coupled expanding-splitting deformation and energy-absorbing mechanism of the circular tube. Furthermore, the factors influencing key parameters were analyzed using the finite element model. The results showed that the behavior changed smoothly from splitting deformation to curling deformation when adding preformed notches to the circular tube, and the final platform force of the circular tube decreased when increasing the transitional radius. Compared with the traditional expansive structure, the combined energy absorber offers better energy absorption with a 78% increase in platform force.

Droplet oscillations in a turbulent flow

The oscillations of an initially unperturbed spherical droplet immersed in a homogeneous and isotropic turbulent background flow are investigated through spherical harmonic decomposition. As suggested in the literature, the shape oscillations under turbulent conditions are related to the frequency of droplets oscillating in a fluid without background flow. A series of direct numerical simulations (DNS) of droplets with single deformation modes in a fluid at rest are first performed. The frequency and damping rate are compared with weakly viscous linear theory. Then, a database of 220 droplets deformed under turbulent conditions for a single Weber and Reynolds number is generated with an identical numerical set-up. Each spherical harmonic coefficient shows an oscillatory motion with comparable frequency to the single deformation mode simulations. The power spectrum of the coefficients provides the amount of surface of each mode. After a transient regime, the surface area reaches a stationary saturation level. The saturation level of each mode is linked to the turbulence and the energy stored at the interface. Droplets after a high deformation are studied with and without background flow. As expected, the physics of relaxation is driven by capillary forces.

Experimental and numerical study on the crashworthiness performance of a hybrid energy absorber with expanding–splitting–bending process

The single deformation mode of splitting tube significantly restricts its energy absorption capability. To address this limitation, in this paper we propose a new hybrid absorber with an external die added to the outside of the expanding–splitting tube, thus the circular tube undergoes sequential expanding, splitting, and bending deformations. We fabricate samples and perform quasi-static compressive experiments on the splitting tube, expanding–splitting tube, and proposed hybrid splitting tube. Experimental results show that the hybrid tube deforms in a controlled and ordered way as designed. Remarkably, the steady crushing force of the hybrid tube is 52.1% and 221.6% higher in comparison to that of the same tube with splitting mode, and expanding–splitting mode, respectively. The crushing force responses and deformation processes are well captured by finite element simulations. The relative errors of the steady crushing forces and energy absorption are within 5.0%. A parametric analysis is performed. We show that the structure parameters play an important role in the crashworthiness performance. In particular, the tube with thicker walls has a larger crushing force and a higher specific energy absorption. The small cracking number and spacing between the inner and outer die can trigger unstable deformation. Our results can advance the engineering application of splitting tubes and the lightweight design of energy absorbers.

Modelling energy dissipation and hysteresis of woven fabrics with large deformation under single loading-unloading cycle

Based on energy decomposition according to main mesoscopic deformation mechanisms of woven fabrics, a piecewise total-strain model for characterizing their dissipation and hysteresis with finite strain under single loading–unloading cycle is presented. In the piecewise model for single deformation mode, a loading–unloading hysteresis cycle is decomposed into four deformation states to characterize according to main mesoscopic mechanisms. Strongly non-linear unloading curve is characterized by constructing energetic relation with loading curve. Dissipation is characterized in a total-strain form and history-dependence is characterized by internal variables, namely dissipation ratio factors. The model is implemented with UMAT in ABAQUS. Three experiments namely trellising, bias extension and uniaxial tension in the literature are simulated for model validation. Excellent consistency between simulation results and experimental data is obtained for each test.

Performance Assessment of an Energy–Based Approximation Method for the Dynamic Capacity of RC Frames Subjected to Sudden Column Removal Scenarios

The alternative load path method is widely used to assess the progressive collapse performance of reinforced concrete structures. As an alternative to an accurate non–linear dynamic analysis, an energy–based method (EBM) can also be adopted to approximately calculate the dynamic load–bearing capacity curve or the dynamic resistance based on a static capacity curve. However, dynamic effects cannot be explicitly taken into account in the EBM. The model uncertainty associated with the use of the EBM for evaluating the dynamic ultimate capacity of structural frames has not yet been quantified. Knowledge of this model uncertainty is however necessary when applying EBM as part of reliability calculations, for example, in relation to structural robustness quantification. Hence, this article focuses on the evaluation of the performance of the EBM and the quantification of its model uncertainty in the context of reliability–based assessments of progressive or disproportionate collapse. The influences of damping effects and different column removal scenarios are investigated. As a result, it is found that damping effects have a limited influence on the performance of the EBM. In the case of an external column removal scenario, the performance of the EBM is lower as the response is not a single deformation mode according to the results in the frequency domain. However, a good performance is found in the case of an internal column removal scenario in which the assumption of a single deformation mode is found to be sufficiently adequate. Probabilistic models for the model uncertainties related to the use of the EBM compared to direct dynamic analyses are proposed in relation to both the resistances and the associated displacements. Overall, the EBM shows to be an adequate approximation, resulting in a small bias and small standard deviation for its associated model uncertainty.

Heterogeneous sensing in a multifunctional soft sensor for human-robot interfaces.

Soft sensors have been playing a crucial role in detecting different types of physical stimuli to part or the entire body of a robot, analogous to mechanoreceptors or proprioceptors in biology. Most of the currently available soft sensors with compact form factors can detect only a single deformation mode at a time due to the limitation in combining multiple sensing mechanisms in a limited space. However, realizing multiple modalities in a soft sensor without increasing its original form factor is beneficial, because even a single input stimulus to a robot may induce a combination of multiple modes of deformation. Here, we report a multifunctional soft sensor capable of decoupling combined deformation modes of stretching, bending, and compression, as well as detecting individual deformation modes, in a compact form factor. The key enabling design feature of the proposed sensor is a combination of heterogeneous sensing mechanisms: optical, microfluidic, and piezoresistive sensing. We characterize the performance on both detection and decoupling of deformation modes, by implementing both a simple algorithm of threshold evaluation and a machine learning technique based on an artificial neural network. The proposed soft sensor is able to estimate eight different deformation modes with accuracies higher than 95%. We lastly demonstrate the potential of the proposed sensor as a method of human-robot interfaces with several application examples highlighting its multifunctionality.

Multi-step deformation mechanical metamaterials

Mechanical metamaterials have gained increasing interest owing to its unique properties and promising applications. However, most developed mechanical metamaterials feature a single-step pathway and/or a single deformation mode, which limits their multi-task applications. In this paper, a multi-step metamaterial (MSM) is introduced. Under compression, the MSM can translate global loading into multiple pathways of deformation, giving rise to multi-stress plateaus in the stress-strain curves. The underlying mechanism is the combination of sequential snap-through and Euler buckling at microscopic unit cell level. Theoretical models are developed to quantify the multi-step deformation feature of the MSM and are validated by experiments and finite element simulations. By varying the geometric parameters of the constituent components of the MSM, its deformation can be programmed. The concept of the developed MSM provides a new perspective for designing metamaterials with multiple tasks, e.g., an energy absorber suitable for both light and heavy impacts, logic gates for manipulating mechanical signals in mechanical computing, among others.

Hyperelastic constitutive modeling of hydrogels based on primary deformation modes and validation under 3D stress states

In isotropic linear elasticity, a constitutive model calibrated using a single deformation mode (e.g., compression or tension or shear) is sufficient to describe a complex three-dimensional (3D) stress state. Such an approach, however, is likely inadequate for modeling hydrogels, which exhibit a nonlinear stress-strain response that varies significantly between deformation modes and is also sensitive to microstructure via gel concentration. In this study, a combined experimental and constitutive modeling framework is proposed for the development and validation of concentration-dependent 3D hyperelastic models for hydrogels. Agarose hydrogel in a concentration range of 0.4–4% w/v is chosen as the model material. Uniaxial compression, uniaxial tension, and simple shear (three primary deformation modes) experiments are conducted. The small strain elastic modulus-gel concentration relationships obtained from experiments are compared with those predicted by the molecular theory of rigid polymer networks (Jones-Marques theory) to identify the concentration range in which entropic elastic (hyperelastic) response dominates. In this range (1.5–4% w/v), four hyperelastic constitutive models are fit to the combined compression-tension-shear stress-strain data: Mooney-Rivlin, three-parameter generalized Rivlin, Gent, and Gent-Gent models. It is demonstrated that the generalized Rivlin model offers the best overall accuracy, and the variation of its model parameters with gel concentration is consistent with the Jones-Marques theory. The resulting concentration-dependent Extended Generalized Rivlin model is employed in finite element simulations of the non-homogeneous 3D stress state of wedge indentation. Simulated load versus depth and strain field predictions show very good agreement with experimental wedge indentation results. Finally, it is shown that a hyperelastic model calibrated using only a single deformation mode yields poor results for other primary and 3D deformations, and thus multiple primary deformation modes (preferably all three) should be considered.

Nanoindentation Induced Deformation and Pop-in Events in a Silicon Crystal: Molecular Dynamics Simulation and Experiment

Silicon has such versatile characteristics that the mechanical behavior and deformation mechanism under contact load are still unclear and hence are interesting and challenging issues. Based on combined study using molecular dynamics simulations and experiments of nanoindentation on Si(100), the versatile deformation modes, including high pressure phase transformation (HPPT), dislocation, median crack and surface crack, were found, and occurrence of multiple pop-in events in the load-indentation strain curves was reported. HPPTs are regard as the dominant deformation mode and even becomes the single deformation mode at a small indentation strain (0.107 in simulations), suggesting the presence of a defect-free region. Moreover, the one-to-one relationship between the pop-in events and the deformation modes is established. Three distinct mechanisms are identified to be responsible for the occurrence of multiple pop-in events in sequence. In the first mechanism, HPPTs from Si-I to Si-II and Si-I to bct5 induce the first pop-in event. The formation and extrusion of α-Si outside the indentation cavity are responsible for the subsequent pop-in event. And the major cracks on the surface induces the pop-in event at extreme high load. The observed dislocation burst and median crack beneath the transformation region produce no detectable pop-in events.

Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids

Control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials, in particular those with negative Poisson’s ratio. This article sheds light on the old question of the relationship between geometric microstructure and mechanical response, by comparison of the deformation properties of bar-and-joint-frameworks with those of their realisation as a cellular solid made from linear-elastic material. For ordered planar tessellation models, we find a classification in terms of the number of degrees of freedom of the framework model: first, in cases where the geometry uniquely prescribes a single deformation mode of the framework model, the mechanical deformation and Poisson’s ratio of the linearly-elastic cellular solid closely follow those of the unique deformation mode; the result is a bending-dominated deformation with negligible dependence of the effective Poisson’s ratio on the underlying material’s Poisson’s ratio and small values of the effective Young’s modulus. Second, in the case of rigid structures or when geometric degeneracy prevents the bending-dominated deformation mode, the effective Poisson’s ratio is material-dependent and the Young’s modulus E˜cs large. All analysed structures of this type have positive values of the Poisson’s ratio and large values of E˜cs. Third, in the case, where the framework has multiple deformation modes, geometry alone does not suffice to determine the mechanical deformation. These results clarify the relationship between mechanical properties of a linear-elastic cellular solid and its corresponding bar-and-joint framework abstraction. They also raise the question if, in essence, auxetic behaviour is restricted to the geometry-guided class of bending-dominated structures corresponding to unique mechanisms, with inherently low values of the Young’s modulus.

A multiaxial elastic potential with error-minimizing approximation to rubberlike elasticity

This study is concerned with a new, explicit approach by means of which forms of the large strain elastic potential for multiaxial rubberlike elasticity may be obtained based on data for a single deformation mode. As a departure from usual studies, here for the first time errors may be estimated and rendered minimal for all possible deformation modes and, furthermore, failure behavior may be incorporated. Numerical examples presented are in accurate agreement with Treloar’s well-known data.

Distortional buckling modes of semi-discretized thin-walled columns

This paper presents distorting buckling solutions for semi-discretized thin-walled columns using the coupled differential equations of a generalized beam theory (GBT). In two related papers recently published by the authors a novel semi-discretization approach to GBT has been presented. The cross section is discretized and analytical solutions are sought for the variation along the beam. With this new approach the general GBT equations for identification of a full set of deformation modes corresponding to both homogeneous and non-homogenous equations are formulated and solved. Thereby giving the (complex) deformation modes of GBT which decouple the state space equations corresponding to the reduced order differential equations. In this paper the developed semi-discretization approach to generalized beam theory (GBT) is extended to include the geometrical stiffness terms, which are needed for column buckling analysis and identification of buckling modes. The extension is based on an initial stress approach by addition of the related potential energy terms. The potential energy of a single deformation mode is formulated based on a discretization of the cross section. Through variations in the potential energy and the introduction of the constraints related to beam theory this leads to a modified set of coupled homogeneous differential equations of GBT with initial stress for identification of distortional displacement modes. In this paper we seek instability solutions using these GBT initial stress equations for simply supported columns with constrained transverse displacements at the end sections and a constant axial initial stress. Based on the known boundary conditions the reduced order differential equations are solved by using the trigonometric solution functions and solving the related eigenvalue problem. This gives the buckling mode shapes and the associated eigenvalues corresponding to the bifurcation load factors. Thus the buckling modes are found directly by the analytical solution of the coupled GBT-equations without modal decomposition. Illustrative examples showing global column buckling, distortional buckling and local buckling are given and it is shown how the novel approach may be used to develop signature curves and elastic buckling curves. In order to assess the accuracy of the method some of the results are compared to results found using the commercial FE program Abaqus as well as the conventional GBT and FSM methods using the software packages GBTUL and CUFSM.

Rheo-dielectric effect in liquid suspensions

A rheo-dielectric effect, dielectrostriction, relates the polarizability of a material to its deformation. Stress, strain, strain rate or some combination of these parameters could be the state variables for a given material. The description of the dielectrostriction in isotropic materials involves two material coefficients. A key advantage of the presented experimental technique is the utilization of a single deformation mode, shear deformation, for two independent measurements of the material coefficients in liquid suspensions. The study is conducted with micro- and nano-sized alumina oxide (Al2O3) particles dispersed either in silicone oil (Newtonian fluid) or in liquid silicone elastomer (viscoelastic fluid). The dielectrostriction response of each suspension is compared with those of the corresponding base liquids. The selection of strain or stress as the state variable of deformation is discussed. Material coefficients for both the strain- and stress-based descriptions are presented for each system.

Resonant vibrational excitation and electron induced dissociation processes in HREELS studies of trimethylindium chemisorbed on GaAs(100)

Vibrational high resolution electron energy loss spectroscopy (HREELS) has been used to monitor the wide variety of electron induced processes involving excited electronic states for trimethylindium ((CH 3 ) 3 In) chemisorbed on GaAs(100). The vibrational modes of the adsorbed CH 3 groups undergo strong resonant vibrational excitation at 10 eV. HREEL spectra of the adsorbed layer, recorded with beam energies greater than 8 eV, indicate the formation of a surface CH 2 species characterised by a single deformation mode (δ(CH 2 )) at 1340 cm −1 . The conversion of CH 3 to CH 2 rises dramatically at the resonance energy of 10 eV and reaches a broad maximum between 20 and 30 eV. The implication is that the incident HREELS beam leads to decomposition of adsorbed CH 3 groups. It is suggested that resonant dissociative electron attachment and dipolar dissociation processes are responsible for the conversion of CH 3 to CH 2 at the surface.

Resonant vibrational excitation and electron induced dissociation processes in HREELS studies of trimethylindium chemisorbed on GaAs(100)

Vibrational high resolution electron energy loss spectroscopy (HREELS) has been used to monitor the wide variety of electron induced processes involving excited electronic states for trimethylindium ((CH 3) 3In) chemisorbed on GaAs(100). The vibrational modes of the adsorbed CH 3 groups undergo strong resonant vibrational excitation at 10 eV. HREEL spectra of the adsorbed layer, recorded with beam energies greater than 8 eV, indicate the formation of a surface CH 2 species characterised by a single deformation mode (δ(CH 2)) at 1340 cm −1. The conversion of CH 3 to CH 2 rises dramatically at the resonance energy of 10 eV and reaches a broad maximum between 20 and 30 eV. The implication is that the incident HREELS beam leads to decomposition of adsorbed CH 3 groups. It is suggested that resonant dissociative electron attachment and dipolar dissociation processes are responsible for the conversion of CH 3 to CH 2 at the surface.

Post‐Yield Analysis of Rigid‐Plastic Beams with Variable Restraints

A theoretical study is undertaken in this paper to investigate the influence of finite deflections on transversely loaded rigid‐perfectly plastic beams. The support conditions are specified through both variable rotational and axial restraint factors. Quasi‐static loading conditions and a small strain assumption are adopted throughout. The analysis, based on continuing the initial deformation mode, leads to a determination of the load‐deflection relationship, thereby highlighting the significant influence of both geometry changes and support conditions. In particular, it is found that the load‐carrying capacity of the structure can be increased considerably, even for moderate support restraints. For the case of distributed loading, the method is only approximate in view of its assumption of a single deformation mode that leads to a violation of the yield conditions. However, reasonable results, as evidenced by comparisons with existing exact solutions, are obtained. It is also shown that further simplific...