Hyperelastic Material Properties Research Articles

Knowledge-based self-tuning of PID control gains for continuum soft robots

In recent years, a class of soft (deformable) robots has attracted the attention of researchers due to their continuum features being advantageous over rigid robots for dexterous and safe compliant motions. These distinct advantages are obtained from the elastomer hyperelastic material properties because continuum robots are manufactured and actuated through embedded pneumatic energy fields. In this way, the continuum deformation raises novel problems in modeling and control due to its highly nonlinear behavior. That is, the deformable shape of its components varies continuously, unlike rigid robots, suggesting that the controller should compensate for its varying continuum model. Motivated by the deformable soft robot subject to parametric uncertainties and unmodeled dynamics, this paper proposes an adaptive, instead of constant, tuning of feedback gains of a model-free controller. The tuning mechanism is based on a knowledge-based scheme using a discrete wavelet neural network (DWN) by an efficient input–output identification updating its parameters and weights online, with a gradient descent algorithm driven by the identification error. At the same time, the control feedback gains are self-tuned, minimizing a convex cost function of tracking errors. Dynamic simulations show the performance of the proposed approach considering the parameters of a real soft robot mimicking a gelatin-like behavior. Finally, some discussions on the proposed scheme’s computational cost, feasibility, and viability are briefly addressed.

Driving torque model of the bionic soft arm’s hyperelastic bellows

ABSTRACT The technology of soft continuum robots represents an advance in the field of robotics to benefit a wide range of industries such as healthcare, manufacturing or environmental exploration. Soft continuum robots can be driven pneumatically by bellows as the soft continuum manipulator presented in this article. A driving torque model of the bellows considering hyperelastic material properties, friction and restoring torques is derived, whose purpose is suitability for model-based control design and subsequent trajectory generation. Hence, the driving torque model must be real-time capable. This is realized by an iterative algorithm calculating the bellows’ torque transmission by assuming a two-dimensional no-slip membrane contact. Nonlinear strain behaviours and hysteresis effects of the bellows are considered by the Ogden material model. The driving torque model’s performance is validated experimentally by measuring the external torques of the bellows.

Influence of Active-to-Passive Ratio on the Deformation in Circular Dielectric Elastomer Actuators.

To further improve the performance of dielectric elastomer actuaotrs (DEAs), the development of novel elastomers with enhanced electro-mechanical properties is focal for the advancement of the technology. Hence, reliable techniques to assess their electro-mechanical performance are necessary. Characterization of the actuator materials is often achieved by fabricating circular DEAs with the pre-stretch of the membrane fixed by a stiff frame. Because of this set-up, the electrode size relative to the carrier frame's dimension has an impact on actuator strain and displacement. To allow for comparable results across different studies, the influence of this effect needs to be quantified and taken into account. This paper presents an in-depth study of the active-to-passive ratio by proposing two simplified analytical models for circular DEA and comparing them. The first model is taking the hyperelastic material properties of the dielectric film into account while the second model is a linear elastic lumped parameter model based on the electro-mechanical analogy. Both models lie in good agreement and show a significant linear impact of the radial active-to-passive ratio on the electro-active strain and a resulting maximum of displacement around 50% radial coverage ratio. These findings are validated by experiments with actuators fabricated using silicone membranes. It is shown that the electrode size is not only an important parameter in the experimental design, but in some cases of higher significance for the accuracy of analytical models than the hyperelastic properties of the material. Furthermore, it could be shown that a radial coverage ratio of around 50% is desirable when measuring displacement as it maximizes the displacement and lowers the impact of deviations in electrode sizes due to fabrication errors.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

In-depth analysis of mechanical and electrical responses of PDMS/MWCNT micro-composite films under cyclic loading conditions

This study has comprehensively examined the variations in the mechanical and electrical properties of PDMS/MWCNT micro-composite (PMMC) films under cyclic tensile loading. While previous studies have primarily focused on the electrical performance of wearable sensors, it is essential that wearable sensors need to meet both electrical characteristics and mechanical reliability throughout their designed operational lifespan. We conducted cyclic tensile tests for PMMC films with different MWCNT mass fractions of 3-wt%, 4-wt%, and 5-wt% and obtained cyclic mechanical properties and electrical conductivity. Each PMMC film exhibited distinct stabilization trends in both mechanical and electrical responses under cyclic loading. Additionally, the stabilised cyclic hyperelastic material properties were defined from the test results to enable predicting structural behaviour of PMMC films using finite element analysis. The results of this study provide valuable insights into the material properties and mechanical/electrical responses under cyclic loads for the structural integrity assessment of wearable sensors employing PMMC films.

Fluid-structure interaction and structural simulation of high acceleration effects on surgical repaired human mitral valve biomechanics.

Mitral valve dynamics depend on force stability in the mitral leaflets, the mitral annulus, the chordae tendineae, and the papillary muscles. In chordal rupture conditions, the proper function of the valve disrupts, causing mitral regurgitation, the most prevalent valvular disease. In this study, Structural and FSI frameworks were employed to study valve dynamics in healthy, pathologic, and repaired states. Anisotropic, non-linear, hyper-elastic material properties applied to tissues of the valve while the first-order Ogden model reflected the best compatibility with the empirical data. Hemodynamic blood pressure of the cardiovascular system is applied on the leaflets as uniform loads varying by time, and exposure to high acceleration loads imposed on models. Immersed boundary method used for simulation of fluid in a cardiac cycle. In comparison between healthy and pathologic models, stress values and chordal tensions are increased, by nearly threefold and twofold, respectively. Stress concentration on leaflets is reduced by 75% after performing a successful surgical repair on the pathological model. Crash acceleration loads led to more significant stress and chordae tension on models, by 27% and 23%, respectively. It is concluded that a more sophisticated model could lead to a better understanding of human heart valve biomechanics in various conditions. If a preoperative plan is developed based on these modeling methods, the requirement for multiple successive repairs would be eliminated, operative times are shortened, and patient outcomes are improved.

Development and validation of lumbar spine finite element model.

The functional biomechanics of the lumbar spine have been better understood by finite element method (FEM) simulations. However, there are still areas where the behavior of soft tissues can be better modeled or described in a different way. The purpose of this research is to develop and validate a lumbar spine section intended for biomechanical research. A FE model of the 50th percentile adult male (AM) Total Human Model for Safety (THUMS) v6.1 was used to implement the modifications. The main modifications were to apply orthotropic material properties and nonlinear stress-strain behavior for ligaments, hyperelastic material properties for annulus fibrosus and nucleus pulposus, and the specific content of collagenous fibers in the annulus fibrosus ground substance. Additionally, a separation of the nucleus pulposus from surrounding bones and tissues was implemented. The FE model was subjected to different loading modes, in which intervertebral rotations and disc pressures were calculated. Loading modes contained different forces and moments acting on the lumbar section: axial forces (compression and tension), shear forces, pure moments, and combined loading modes of axial forces and pure moments. The obtained ranges of motion from the modified numerical model agreed with experimental data for all loading modes. Moreover, intradiscal pressure validation for the modified model presented a good agreement with the data available from the literature. This study demonstrated the modifications of the THUMS v6.1 model and validated the obtained numerical results with existing literature in the sub-injurious range. By applying the proposed changes, it is possible to better model the behavior of the human lumbar section under various loads and moments.

Numerical Simulation of PMMA Impact Based on the J–C Constitutive and Damage Models under Hydrostatic Pressure Loading

Polymethyl methacrylate (PMMA) polymer is widely used in various fields today. In order to reveal the structural impact performance of PMMA materials in underwater engineering thoroughly, this paper firstly proposed a simplified plate model for a spherical shell hull under concentrative impact loading. Then, to simulate the hyper-elastic material properties of PMMA in the impact process, the Johnson–Cook constitutive model and damage failure model were adopted. And the least squares method was used to confirm accurately the J–C constitutive and damage failure model parameters of PMMA through material test data. Moreover, the dynamic process of the steel bullet impacting the PMMA plate structure was analyzed by the finite element software ABAQUS. The calculation results show that the numerical simulation results in this paper have a good convergence, and the residual velocities at different initial velocities and thicknesses of plates are in good agreement with the experimental test data. Therefore, the feasibility and accuracy of the impact analysis of PMMA structures based on J–C constitutive and damage failure models in this paper are verified accordingly. Finally, based on the presented finite element model, the structure response and the variation of residual velocity of the bullet with the PMMA plate thickness was analyzed in depth; that is, the results show that the residual velocity of the bullet has a certain linear relationship with the thickness, even in an underwater environment, and even in an underwater environment will increase both with a thicker structure or a higher pressure.

Soft robotic finger with variable effective length enabled by an antagonistic constraint mechanism

Compared to traditional rigid robotics, soft robotics has attracted increasing attention due to its advantages in compliance, safety, and low cost. As an essential part of soft robotics, the soft robotic gripper also shows its superior while grasping objects with irregular shapes. Recent research has been conducted to improve grasping performance by adjusting the variable effective length (VEL). However, the existing VEL function achieved by mechanisms such as multi-chamber design or tunable stiffness shape memory material requires a complex pneumatic circuit design or a time-consuming phase-changing process. This work proposes a fold-based soft robotic finger with VEL function from 3D printing. It is experimentally tested and modeled by the hyperelastic material property. Mathematic and finite element modeling is conducted to study the bending behaviour of the proposed soft actuator. Most importantly, an antagonistic constraint mechanism is proposed to achieve the VEL, and the experiments demonstrate that better conformity is achieved. Finally, dual-mode grippers are designed and evaluated to demonstrate the advances of VEL on grasping performance.

FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

It is of great significance to identify the nonhomogeneous distribution of material properties in human tissues for different clinical and medical applications. This leads to the requirement of solving an inverse problem in elasticity. The Virtual Fields Method (VFM) is a rather recent inverse method with remarkable computational efficiency compared with the optimization-based methods. In this study, we aim to identify nonhomogeneous hyperelastic material properties using the VFM. We propose two novel algorithms, RE-VFM and NO-VFM. In RE-VFM, the solid is partitioned in different regions and the elastic properties of each region are determined. In NO-VFM, the distribution of elastic properties is completely reconstructed through the inverse problem without partitioning the solid. As the VFM requires to use virtual fields, we proposed an efficient way to construct them and implemented the approach in the FEniCS package. We validated the proposed methods on several examples, including a bilayer structure, a lamina cribosa (LC) model and a cube model embedded with a spherical inclusion. The numerical examples illustrate the feasibility of both RE-VFM and NO-VFM. Notably, the spatial variations of the Young's modulus distribution can be recovered accurately within only 5 iterations. The obtained results reveal the potential of the proposed methods for future clinical applications such as estimating the risk of vision loss related to glaucoma and detecting tumors.

A Method to Determine the Constitutive Parameters of Hyperelastic Films Based on Spherical Indentation

Abstract An indentation method to determine the properties of hyperelastic thin films is proposed, which is to use a spherical indenter to indent on the film with a small circular hole in the center. During this progress, there exists a maximum indentation load before penetration. Considering geometries of the film and the indenter, the specific form of relationship between the maximum indentation load and the elastic properties of the film is developed for neo-Hookean, Arruda-Boyce, and Ogden hyperelastic constitutive models. On the basis of this relationship, the initial shear modulus of the film can be directly obtained from single data of the maximum load, instead of recording and fitting to indentation curves. Furthermore, other properties of hyperelastic materials are explored from the perspective of the inverse problem. The experiments are performed with natural rubber, silicone rubber, and polydimethylsiloxane (PDMS) films to verify the feasibility of our method, and the optimal radius ratio between the indenter and the hole is concluded from the experimental results.

Convexity, polyconvexity and finite element implementation of a four-fiber anisotropic hyperelastic strain energy density—Application to the modeling of femoral, popliteal and tibial arteries

Computational analysis of the nonlinear mechanical properties of anisotropic hyperelastic materials aims at a better understanding of its physiology and pathophysiology under different loading conditions. This has an important role in biomechanics, surgical, clinical diagnostic and design of medical devices. This study investigates the modeling of arterial tissues made of a four-fiber family by using an anisotropic hyperelastic model. This model is based on the theory of polynomial invariant and was implemented in the university finite element code FER. The convex property of the strain energy function is investigated as well as the positive definite nature of the tangent stiffness matrix used within the framework of a finite element analysis. This allows us to guarantee the invertibility of the linearized problem and the uniqueness of the solution computed at each step of the Newton–Raphson scheme used to solve nonlinear problems.

Microscale Discrete Element Model for Simulating Bridging Behavior of Fractured Glass Laminates

The bridging behavior between fragments is one vital factor in the post-fracture stage of glass laminates. A particle-based discrete element model was developed in this work to simulate the bridging behavior of fractured glass laminates. The model was based on the calibration of hyperelastic PVB material properties using soft-bond model and further validated with the experimental data as well as the observations from through-crack-tensile tests. In order to investigate the bridging performance of fractured glass laminates with multiple fragments under uniaxial tension, three factors encompassing the crack aligning, fragment number and adhesion conditions were considered to perform a parametric study. The results give an exploratory application of the developed discrete element models in the estimation of the post-fracture behaviors. It is found that the smaller fragment size can diminish the tension-stiffening effect in the non-aligned case which might generate an enhancing ratio of initial modulus up to nearly 3.6. The non-aligned cracks can also lead to a very high strength if the adhesion ability can be guaranteed. However, the delamination of fragments is expected to control the post-fracture strength of fractured glass laminates with PVB interlayer.

Hyperelastic modelling of rubber with multi-walled carbon nanotubes subjected to tensile loading

This study thoroughly examined the application of inverse FE modelling and indentation tensile tests to identify nanotubes' rubber material properties. Carbon nanotubes with various percentages of multi-walled carbon nanotubes exposed to high tensile stress were used to enhance the mechanical qualities of natural rubber (NR). In this work, carbon nanotubes have been added to natural rubber. By using a solvent casting technique, toluene was used to make nanocomposites. 0.2%, 0.4%, 0.6%, 0.8%, and 1%. In this article, rubber and multi-walled carbon nanotubes interact in practical ways. Mechanical features of carbon nanotubes in NR have been researched. The results will lead to rubber products with improved mechanical qualities compared to present nanocomposite rubber containing various percentages of multi-walled carbon nanotubes exposed to large tensile test loading. The relative fitness error for significant stresses is reasonable with a second or third-order deformation model in numerical results. Non-linear finite element analysis is widely used to optimise complicated elastomeric components' design and reliability studies. However, accurate numerical results cannot be achieved without using rubber or rubber nanocomposite materials with reliable strain energy functions. The indentation tensile tests of rubber samples have been simulated and confirmed using a parametric FE model. An inverse materials parameter identification algorithm was used to calculate the hyperelastic material properties of rubber samples evaluated in uniaxial tensile. Using ABAQUS FE software, material parameters and force-displacement data may be automatically updated and extracted. The numerical data for the inverse method of material property prediction has been successfully established by developing simulation spaces for various material characteristics. The force-displacement curve can be represented using technical methods. The results demonstrate that the inverse FE modelling process might be simplified by using these curve fitting parameters and plot equations to build a mathematical link between curve coefficients and material properties. The first, second, and third-order deformation models were tested using FE simulations for the tensile test.

Properties of NBR and CR Hyperelastic Materials in a Wide Range of Both Positive and Negative Temperatures

Properties of NBR and CR Hyperelastic Materials in a Wide Range of Both Positive and Negative Temperatures

Tailoring of functionally graded hyperelastic materials via grayscale mask stereolithography 3D printing

Photopolymerization-based additive manufacturing methods like stereolithography and digital light processing only allow typically the monolithic fabrication of structures made from a single material. To overcome this limitation, grayscale digital light processing has been proposed for 3D printing of functionally graded materials. Here, this concept is extended to grayscale masked stereolithography (MSLA) printing using a LED light source and a LCD photomask to control the degree of photopolymerization of a UV-curable resin by varying grayscale pixels and thus light intensities. In this scale, tailorable hyperelastic material properties and functionally graded structures for finite deformations are realized. In this paper, the dependency of the resulting material properties on the parameters of the grayscale MSLA process is investigated and a grayscale-dependent hyperelastic material model is formulated. This parametric hyperelastic material model is fitted to the experiments and validated against experimental results for uniaxial tension and uniaxial compression tests. Then, functionally graded structures with tailored mechanical properties at finite deformations are designed and fabricated using grayscale MSLA printing. The hyperelastic material model is validated with experimental results for different geometries, showing good agreement between experimental tests and numerical calculations.

Inverse Dynamics Model-Based Shape Control of Soft Continuum Finger Robot Using Parametric Curve

Soft continuum robots are more and more used in various applications due to the multiple advantages offered by the properties of hyper-elastic soft materials, such as resilience, flexibility, etc. Despite all these essential properties that make the soft robots good candidates for some real-life needs (form enclosure grasping, obstacle-free navigation, etc.), controlling their shape remains challenging because of their hyper-redundancies. This letter investigates an inverse dynamics model-based shape control of soft continuum robots in the presence and absence of external efforts. To that end, modeling based on Pythagorean Hodograph (PH) curves with prescribed lengths is combined with Euler-Bernoulli modeling to reconstruct the robot shapes and then calculate the actuator inputs in the case of external efforts. Thus, a relationship between the actuator inputs and the PH control points is obtained. With the above strategy, the actuator inputs can be computed accordingly, and therefore, real-time shape control of the soft robots for various tasks becomes possible. The results of the proposed approach are validated both numerically and experimentally using two classes of soft continuum robots - a Fluidic Elastomeric Actuator (FEA), describing a 2D soft finger robot, with a single and multiple phalanges, and a 3D continuum manipulator, namely the Compact Bionic Handling Assistant (CBHA).

Are subject-specific models necessary to predict patellar tendon fatigue life? A finite element modelling study

Patellar tendinopathy is an overuse injury that occurs from repetitive loading of the patellar tendon in a scenario resembling that of mechanical fatigue. As such, fatigue-life estimates provide a quantifiable approach to assess tendinopathy risk and may be tabulated using nominal strain (NS) or finite element (FE) models with varied subject-specificity. We compared patellar tendon fatigue-life estimates from NS and FE models of twenty-nine athletes performing countermovement jumps with subject-specific versus generic geometry and material properties. Subject-specific patellar tendon material properties and geometry were obtained using a data collection protocol of dynamometry, ultrasound, and magnetic resonance imaging. Three FE models were created for each subject, with: subject-specific (hyperelastic) material properties and geometry, subject-specific material properties and generic geometry, and generic material properties and subject-specific geometry. Four NS models were created for each subject, with: subject-specific (linear elastic) material properties and moment arm, generic material properties and subject-specific moment arm, subject-specific material properties and generic moment arm, and generic material properties and moment arm. NS- and FE-modelled fatigue-life estimates with generic material properties were poorly correlated with their subject-specific counterparts (r2 ≤0.073), while all NS models overestimated fatigue life compared to the subject-specific FE model (r2 ≤0.223). Furthermore, FE models with generic tendon geometry were unable to accurately represent the heterogeneous strain distributions found in the subject-specific FE models or those with generic material properties. These findings illustrate the importance of incorporating subject-specific material properties and FE-modelled strain distributions into fatigue-life estimations.

Biomechanical Effects of Deep Anterior Lamellar Keratoplasty and Penetrating Keratoplasty for Keratoconus: A Finite Element Analysis.

PurposeTo theoretically compare corneal displacement and the von Mises (VM) stress distribution of deep anterior lamellar keratoplasty (DALK) and penetrating keratoplasty (PK) for keratoconus (KC) and to evaluate the effects of residual stromal thickness (RST) and intraocular pressure (IOP) on postoperative corneal biomechanics.MethodsWe performed DALK and PK simulations using Ansys by employing anisotropic nonlinear hyperelastic corneal material properties. We analyzed corneal displacement and VM stress in DALK and PK models under IOPs of 10, 15, 20, and 25 mmHg. We established two DALK models: The ideal-type DALK ensured that postoperative central corneal thickness was constant at 560 µm and the corneal graft thickness varied with RST. The clinical-type DALK ensured that corneal grafts had the same thickness (500 µm) regardless of RST. Then we analyzed the effects of RST and IOP on postoperative corneal displacement and VM stress.ResultsCorneal displacement and VM stress were lower in the DALK than in the PK model. In the ideal-type DALK model, an increase in RST was associated with increased deformation and decreased VM stress in the healing zone, except for a RST of 0 µm. In the clinical-type DALK model, deformation and VM stress in the healing zone decreased with an increase in RST, except for a RST of 0 µm.ConclusionsDALK showed more stability than PK. For the ideal-type DALK model, an increase in RST resulted in decreased postoperative corneal biomechanics in the healing zone. For the clinical-type DALK model, corneal deformation and VM stress decreased with an increase in RST, which provides numerical evidence for the design of corneal transplantation for patients with KC.Translational RelevanceIn this computational modeling study, we first theoretically compared corneal biomechanics between DALK and PK for KC. Then, the effects of RST and IOP on postoperative corneal biomechanics were investigated. Our findings provide novel insights into the optimal design for corneal transplantation for patients with KC.

A Hyper-Viscoelastic Continuum-Level Finite Element Model of the Spinal Cord Assessed for Transverse Indentation and Impact Loading.

Finite Element (FE) modelling of spinal cord response to impact can provide unique insights into the neural tissue response and injury risk potential. Yet, contemporary human body models (HBMs) used to examine injury risk and prevention across a wide range of impact scenarios often lack detailed integration of the spinal cord and surrounding tissues. The integration of a spinal cord in contemporary HBMs has been limited by the need for a continuum-level model owing to the relatively large element size required to be compatible with HBM, and the requirement for model development based on published material properties and validation using relevant non-linear material data. The goals of this study were to develop and assess non-linear material model parameters for the spinal cord parenchyma and pia mater, and incorporate these models into a continuum-level model of the spinal cord with a mesh size conducive to integration in HBM. First, hyper-viscoelastic material properties based on tissue-level mechanical test data for the spinal cord and hyperelastic material properties for the pia mater were determined. Secondly, the constitutive models were integrated in a spinal cord segment FE model validated against independent experimental data representing transverse compression of the spinal cord-pia mater complex (SCP) under quasi-static indentation and dynamic impact loading. The constitutive model parameters were fit to a quasi-linear viscoelastic model with an Ogden hyperelastic function, and then verified using single element test cases corresponding to the experimental strain rates for the spinal cord (0.32–77.22 s−1) and pia mater (0.05 s−1). Validation of the spinal cord model was then performed by re-creating, in an explicit FE code, two independent ex-vivo experimental setups: 1) transverse indentation of a porcine spinal cord-pia mater complex and 2) dynamic transverse impact of a bovine SCP. The indentation model accurately matched the experimental results up to 60% compression of the SCP, while the impact model predicted the loading phase and the maximum deformation (within 7%) of the SCP experimental data. This study quantified the important biomechanical contribution of the pia mater tissue during spinal cord deformation. The validated material models established in this study can be implemented in computational HBM.