Multiple Deformation Modes Research Articles

On the explicit dynamics implementation and validation of partitioned rate-type constitutive relation for dampers

We propose a simple 3D nonlinear rate-type constitutive relation with just three parameters for elastomeric dampers capable of emulating double-shear data in frequency and strain sweep mode. The nonlinear relation derived using two scalar functions, namely Helmholtz free energy and the rate of dissipation function [1], result in a partitioned constitutive relation: Cauchy stress tensor is described in terms of the left Cauchy-Green stretch tensor and a tensor describing instantaneous elastic response, and the evolution equation for the instantaneous elastic response is derived by maximizing the rate of dissipation function. A compressible version of this model is implemented in Abaqus® The constitutive relation and the implementation are validated by comparing with known semi-inverse solutions obtained by specializing rate-type relation to special deformations. Material parameters are obtained for dampers made of synthetic and natural rubber by fitting the predictions of the model with that of double shear data. By using the same parameters, three dimensional simulations of a cylindrical damper subjected to sinusoidal force akin to that of an unbalanced machinery predict different hysteresis curves in compression/tension and shear. To that end, we show that the non-linear 3 parameter model is one of the simple models that can be formulated within the thermodynamic framework which can predict the inherent non-linearity of the damper operating under combined harmonic loading situations. A robust implementation (VUMAT) of the developed model is included with the article. We believe that this can aid engineers in tailoring dampers for its controlled dissipation across multiple modes of deformation as well as academicians in adding more value by building and implementing sophisticated models within this framework.

An exceptional ductility of AZ31 magnesium alloy sheet achieved by consecutive multi-pass cooperative lowered-temperature rolling

In this study, a novel technique of consecutive multi-pass cooperative lowered-temperature rolling (CMCLR) was proposed for the first time, with the purpose of preparing high performance wrought magnesium alloys. Based on this, a highly ductile magnesium alloy sheet could be effectively produced from ingot. The corresponding microstructure could directly evolve from coarse dendrites to equiaxed grains with an average size of ∼5 μm, which was attributed to the intense dynamic recrystallization (DRX) during isothermal deformation. The equivalent strain gradually decreased from the surface to the interior and edge of the rolled sheet due to the anisotropic plastic deformation. Instead, the temperature of the core of the sheet was slightly higher than that of the surface due to the deformation heat effect. The basal texture in the RD-TD plane generally weakened in the form of the splitting of basal texture toward the RD and the broadening of basal plane away from the pole center due to texture randomization dominated by DRXed grains. The exceptional ductility of more than 28.7% together with acceptable ultimate tensile strength of not less than 267 MPa was ascribed to the progressive work hardening as a result of seamless switching of multiple deformation modes, i.e., basal dislocation-slip-mediated deformation was preferentially operated and then was substituted by twinning-controlled deformation and non-basal dislocation-slip-dominated deformation. The selection of {101‾2} twin variants agreed well with geometrical compatibility factor (m’) criterion instead of Schmid’s law. The activated twin variants nearly engulfed the whole parent grains for the sake of preserving compatible deformation continuity at ambient temperature, giving rise to the formation of TD-split texture. Comparatively, the {101‾2} twinning could randomize the basal texture via reorienting grain orientations which in turn facilitated the reactivation of dislocation slip systems in the case of high temperature deformation.

Cortical‐Folding‐Inspired Multifunctional Reduced Graphene Oxide Microarchitecture Arrays on Curved Substrates

AbstractAlthough controlled wrinkling is demonstrated to be a powerful tool for micro/nanofabrication, large‐area fabrication of microarchitecture arrays on curved substrates by surface wrinkling still remains challenging. Inspired by the cortical folding, a facile method for transforming graphene oxide (GO) patterns into multiscale microarchitecture arrays on curved substrates is developed. Mass production of hierarchical GO papillae arrays can be realized by homogeneous compression of patterned GO/rubber bilayers. The reduced GO (rGO) papillae arrays show superhydrophobicity with tunable adhesion to water, enabling good performance in microdroplet manipulation. Besides, the papillae are capable of regulating the formation of microcracks in the rGO films upon stretching. Similar to the mechanical sensing system of spiders, a crack‐based strain sensor with high gauge factor (≈81), good linearity (0–15%), and fast responding speed (<40 ms) is demonstrated. In addition, the strain sensor is capable of detecting and recognizing multiple deformation modes including stretching, poking, and touching. This work reveals novel cortical folding morphology and provides a simple fabrication method for multifunctional hierarchical microarchitectures on curved substrates, which may find applications in biomimetic microstructures, smart wetting surfaces, and wearable electronics.

Learning to feel better

Sensors Human-robot interfaces require sensing technologies that capture complex biomechanical motion with high fidelity. Kim et al. developed a sensing architecture that integrates optoelectronic, microfluidic, and piezoresistive sensing into a compact soft sensor to measure multiple modes of mechanical deformation. The researchers could distinguish between stretching, bending, and compressive deformation modes from the sensor signals using threshold evaluation and machine-learning algorithms. The soft sensor was integrated into a wearable controller to remotely operate various robotic devices. Sci. Robot. 5 , eabc6878 (2020).

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.

Molecular dynamics simulations of uniaxial deformation of bimodal polyethylene melts

Tensile deformation behavior of bimodal polyethylene (PE) was investigated by employing coarse-grained (CG) molecular dynamics simulations based on a united atom model. The bimodal PE was modeled by blending two linear polyethylene chains with different molecular weights. The mechanical response and corresponding conformational behaviors of the polymer melt during stretching were recorded as a function of strain under both high and low strain rates. We find that the tensile toughness was enhanced in an additive fashion by increasing the fraction of polymers with high molecular weight in bimodal PE. During elongation, the polymer chain extends and orients itself along the loading direction. Surprisingly, varying the bimodal distribution and the strain rates, the disentanglement does not synergistically follow the tendency of chain expansion and ordering along the tensile direction as the strain is gradually raised, implying that multiple deformation modes might exist during the plastic flow process. The molecular origin of this unique development of the entanglement network in bimodal PE is discussed in detail.

A near-isotropic ultrafine-grained Mg-Gd-Ag alloy with high strength-ductility synergy

It is challenging to develop Mg alloys with high strength-ductility synergy and isotropic mechanical properties. An industrial-scale ultrafine-grained (UFG) Mg-10.6Gd-2Ag wt. % alloy with excellent strength-ductility synergy and near-isotropic mechanical behavior was made by an industrial-scale rotary die equal channel angular pressing (RD-ECAP). The microstructure of the UFG alloy involves the primarily submicron α-Mg grains with an average grain size of 760.5 nm and the high-density submicron β phase (Mg5Gd) precipitates (267.8 nm). Room temperature tensile tests results reveal that the UFG alloy exhibits an over three times tensile yield strength, near two times ultimate tensile strength, and more than one and a half times elongation along three orthogonal test directions than the as-cast Mg alloy. The improvement of strength is linked to the effect of the grain boundary strengthening as well as the precipitation strengthening. The enhanced ductility is ascribed to the ultrafine grains with low dislocation density, which provide a degree of dislocation storage capacity and facilitates multiple potential deformation modes. The near-isotropic mechanical behavior stems from the weak texture and multiple deformation modes.

Magnetic Multimaterial Printing for Multimodal Shape Transformation with Tunable Properties and Shiftable Mechanical Behaviors

Magnetic soft materials (MSMs) have shown potential in soft robotics, actuators, metamaterials, and biomedical devices because they are capable of untethered, fast, and reversible shape reconfigurations as well as controllable dynamic motions under applied magnetic fields. Recently, magnetic shape memory polymers (M-SMPs) that incorporate hard magnetic particles in shape memory polymers demonstrated superior shape manipulation performance by realizing reprogrammable, untethered, fast, and reversible shape transformation and shape locking in one material system. In this work, we develop a multimaterial printing technology for the complex structural integration of MSMs and M-SMPs to explore their enhanced multimodal shape transformation and tunable properties. By cooperative thermal and magnetic actuation, we demonstrate multiple deformation modes with distinct shape configurations, which further enable active metamaterials with tunable physical properties such as sign-change Poisson's ratio. Because of the multiphysics response of the M-MSP/MSM metamaterials, one distinct feature is their capability of shifting between various global mechanical behaviors such as expansion, contraction, shear, and bending. We anticipate that the multimaterial printing technique opens new avenues for the fabrication of multifunctional magnetic materials.

How hydrogel inclusions modulate the local mechanical response in early and fully formed post-infarcted myocardium

Expansion of myocardium after myocardial infarction (MI) has long been identified as the primary mechanism that drives adverse left ventricular (LV) remodeling towards heart failure and death. Direct injection of hydrogels into the myocardium to mechanically constrain the infarct has demonstrated promise in limiting its remodeling and expansion. Despite early successes, there remain open questions in the determination of optimal hydrogel therapies, key application characteristics for which include injected polymer volume, stiffness, and spatial placement. Addressing these questions is complicated by the substantial variations in infarct type and extent, as well as limited understanding of the underlying mechanisms. Herein, we present an investigation on how hydrogel inclusions affect the effective tissue-level stiffness and strain fields in myocardium using full three-dimensional (3D) finite element simulations at early and late post-MI time points. We calibrated our simulations to triaxial mechanical and structural measurements of cuboidal LV myocardial specimens of post-infarcted myocardium, 0 and 4 weeks post-MI, injected with a dual-crosslinking hyaluronic acid-based hydrogel. Simulations included multiple deformation modes that spanned the anticipated physiological range in order to assess the effects of variations in inclusion size, location, and modulus on tissue-level myocardial mechanics. We observed significant local stiffening in the hydrogel-injected specimens that was highly dependent on the volume and mechanical properties of the injected hydrogel. Simulations revealed that the primary effect of the injections under physiological loading was a reduction in myocardial strain. This result suggests that hydrogel injections reduce infarct expansion by limiting the peak strains over the cardiac cycle. Overall, our study indicated that modulation of local effective tissue stiffness and corresponding strain reduction are governed by the volume and stiffness of the hydrogel, but relatively insensitive to its transmural placement. These findings provide important insights into mechanisms for ameliorating post-MI remodeling, as well as guidance for the future design of post-MI therapies.

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.

Visco-hyperelastic constitutive modeling of strain rate sensitive soft materials

A novel viscous dissipation potential is proposed for the visco-hyperelastic constitutive modeling of short-time memory responses of soft materials, which can capture both linear and nonlinear large deformation behaviors over a wide range of strain rates. The proposed potential is compatible with objectivity and continuum thermodynamics principles, consists of physically motivated model parameters, and adds the capability of modeling strain rate sensitivity in the small strain regime, which is currently not possible with available external state variable driven viscous dissipation potentials. By combining the proposed viscous dissipation potential with the Mooney-Rivlin strain energy density function, a visco-hyperelastic relation is formulated and fit to the rate-dependent tensile stress-strain data of human patellar tendon, which was previously modeled using an existing viscous dissipation potential. It is demonstrated that the proposed model offers improvements in fitting accuracy and prevents possible thermodynamic instabilities in quasi-static hyperelastic models from corrupting the dynamic response. In addition, the uncomplicated mathematical form of the model and the accompanying multi-step multi-start optimization procedure helps prevent numerical instabilities. Multi-deformation mode fitting of human brain gray matter under all three primary deformation modes (compression, tension and shear) is also considered using a visco-hyperelastic model based on the proposed potential and the semi-empirical Gent-Gent strain energy density function. It is shown that visco-hyperelastic models based on the proposed viscous dissipation potential capture all the essential features of the stress-strain data with unique optimal model parameters, giving reasonable accuracy in both single and multiple deformation mode cases. Further, it is demonstrated that the proposed model is stable and robust with respect to both the choice of the hyperelastic strain energy density and the availability of data from multiple deformation modes.

A CONSTITUTIVE MODEL FOR BOTH LOW AND HIGH STRAIN NONLINEARITIES IN HIGHLY FILLED ELASTOMERS AND IMPLEMENTATION WITH USER-DEFINED MATERIAL SUBROUTINES IN ABAQUS

ABSTRACT Strain energy functions (SEFs) are used to model the hyperelastic behavior of rubberlike materials. In tension, the stress–strain response of these materials often exhibits three characteristics: (i) a decreasing modulus at low strains (<20%), (ii) a constant modulus at intermediate strains, and (iii) an increasing modulus at high strains (>200%). Fitting an SEF that works in each regime is challenging when multiple or nonhomogeneous deformation modes are considered. The difficulty increases with highly filled elastomers because the small strain nonlinearity increases and finite-extensibility occurs at lower strains. One can compromise by fitting an SEF to a limited range of strain, but this is not always appropriate. For example, rubber seals in oilfield packers can exhibit low global strains but high localized strains. The Davies–De–Thomas (DDT) SEF is a good candidate for modeling such materials. Additional improvements will be shown by combining concepts from the DDT and Yeoh SEFs to construct a more versatile SEF. The SEF is implemented with user-defined material subroutines in Abaqus/Standard (UHYPER) and Abaqus/Explicit (VUMAT) for a three-dimensional general strain problem, and an approach to overcome a mathematically indeterminate stress condition in the unstrained state is derived. The complete UHYPER and VUMAT subroutines are also presented.

Symmetry and pathway analyses of the twinning modes in Ni–Ti shape memory alloys

The complex interplay of multiple deformation modes in Ni–Ti systems play a critical role in determining the mechanical properties of the shape memory alloys, e.g., superelasticity, shape memory effect and functional fatigue resistance. In particular, several different twinning modes have been observed in experiments, which include both transformation twins (generated by a phase transformation between two phases) and mechanical twins (generated in a single phase). In spite of well-established theories to treat transformation twins and mechanical twins independently, a general framework capturing the intrinsic coupling between them is still unavailable. Here we systematically analyze all the twinning modes in Ni–Ti alloys, by employing a phase transition graph approach. We show that transformation twins and mechanical twins are intrinsically coupled in symmetry-breaking processes, which results in multiple interconnected deformation pathways. By investigating those deformation pathways, we demonstrate additional characteristic twinning modes arising from the coupling, which includes both symmetric and asymmetric twins. Our work provides a theoretical foundation to investigate the coupling between transformation twins and mechanical twins from a symmetry point of view.

Caterpillar-Inspired Crawling Robot Using Both Compression and Bending Deformations

Multimodal deformations of soft materials such as compression and bending are a commonplace event on soft-bodied animals (e.g., worms) and soft-bodied robots. Usually, such deformation modes are separately analyzed or constrained to decrease the degrees of freedom when one design motion of the soft-bodied robots. This letter proposes to use multiple deformation modes and presents a highly deformable crawling robot that employs both compression and bending deformations simultaneously during the locomotion. This locomotion gait is inspired by the motion analysis experiment of a biological caterpillar, i.e., crawling gait of a silkworm Bombyx mori . Based on the biological experiment, we propose a compressive/bendable beam and develop a crawling robot using the proposed beam. The experimental results of the simulation and the prototype demonstrate that the combination of the multiple deformation modes can contribute to the locomotion speed increase. This also indicates that we can design an enormous variety of locomotion gaits by combining multiple deformation modes, which may increase the adaptability of soft-bodied robots for use in our living and natural environments. These results shed new light on how to design behavioral diversity of soft-bodied robots.

Multiresponsive polymeric microstructures with encoded predetermined and self-regulated deformability

Dynamic functions of biological organisms often rely on arrays of actively deformable microstructures undergoing a nearly unlimited repertoire of predetermined and self-regulated reconfigurations and motions, most of which are difficult or not yet possible to achieve in synthetic systems. Here, we introduce stimuli-responsive microstructures based on liquid-crystalline elastomers (LCEs) that display a broad range of hierarchical, even mechanically unfavored deformation behaviors. By polymerizing molded prepolymer in patterned magnetic fields, we encode any desired uniform mesogen orientation into the resulting LCE microstructures, which is then read out upon heating above the nematic-isotropic transition temperature (TN-I) as a specific prescribed deformation, such as twisting, in- and out-of-plane tilting, stretching, or contraction. By further introducing light-responsive moieties, we demonstrate unique multifunctionality of the LCEs capable of three actuation modes: self-regulated bending toward the light source at T < TN-I, magnetic-field-encoded predetermined deformation at T > TN-I, and direction-dependent self-regulated motion toward the light at T > TN-I We develop approaches to create patterned arrays of microstructures with encoded multiple area-specific deformation modes and show their functions in responsive release of cargo, image concealment, and light-controlled reflectivity. We foresee that this platform can be widely applied in switchable adhesion, information encryption, autonomous antennae, energy harvesting, soft robotics, and smart buildings.

Effect of Initial Microstructure on High-Temperature Dynamic Deformation of Ti-6Al-4V Alloy

One of the attractive properties of Ti-6Al-4V alloy is control of microstructure through heat treatment to vary the mechanical properties. In this study, three different microstructures, Lamellar, Widmanstatten, and Martensitic morphologies, were created through heat treatment at a post-β transus temperature followed by cooling at different rates. With faster cooling rates, the microstructures evolved finer lamellae, smaller colony sizes, and thinner grain boundary layers. High-temperature dynamic compression was conducted on these specimens at a strain rate of 1000 s−1 and temperatures in the range of 23 °C to 1045 °C. Flow stresses decreased linearly with colony size and grain boundary layer thickness, but increased with inverse square root of lamellar thickness. This strong correlation of flow stress to several microstructural feature sizes indicated multiple modes of deformation. All three microstructures showed identical thermal softening. The softening rate was intensified at elevated temperatures due to hcp → bcc allotropic phase transformation. Gangireddy modification to Johnson–Cook model could account for this augmented softening and the modified J–C model predicted the three microstructures to follow a similar thermal softening coefficient m = 0.8. The kinetics of phase transformation appear to be very rapid irrespective of the microstructural differences in the Ti-6Al-4V alloy.

Consecutive crystallographic reorientations and superplasticity in body-centered cubic niobium nanowires

Plasticity of metallic nanowires is often controlled by the activities of single deformation mode. It remains largely unclear whether multiple deformation modes can be activated in an individual metallic nanowire and how much plasticity they can contribute. In situ nanomechanical testing reveals a superior plastic deformation ability of body-centered cubic (BCC) niobium nanowires, in which a remarkable elongation of more than 269% is achieved before fracture. This superplastic deformation originates from a synergy of consecutively nucleated multiple reorientation processes that occur for more than five times via three distinct mechanisms, that is, stress-activated phase transformation, deformation twinning, and slip-induced crystal rotation. These three coupled mechanisms work concurrently, resulting in sequential reorientations and therefore superplastic deformation of Nb nanowires. Our findings reveal a superior mechanical property of BCC Nb nanowires through the close coordination of multiple deformation modes, which may have some implications in other metallic nanowire systems.

The mechanism for the different effects of texture on yield strength and hardness of Mg alloys

A study regarding the effect of texture on tensile yield strength and hardness of an extruded Mg-15Gd-0.5Zr rod was performed, with a great emphasis laid on the relevant mechanisms. A 7% pre-tension along the extrusion direction (ED) in the solid solution condition was used to transform the texture from a broad distribution of basal poles with a peak approximately 45° with respect to the ED into a texture with basal poles largely perpendicular to the ED. This texture variation enhances the yield strength of peak aged sample by approximately 103 MPa, while hardly increases the peak hardness. The analysis about the ratio of the critical resolved shear stress (CRSS) to Schmid factor shows that this texture variation results in a larger fraction of grains favoring prismatic slip with a higher activation stress under tension along the ED. In contrast, the complex stress state during hardness test initiates multiple deformation modes, which renders the value of hardness insensitive to the texture variation. This different dependence of deformation modes on texture mainly accounts for the different increments in hardness and tensile yield strength.

Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

Unusual cold rolled texture in an Mg-2.0Zn-0.8Gd sheet

The Mg-2.0Zn-0.8Gd (wt%) sheet with double peak transverse direction (TD) tilted non-basal texture was cold rolled, and obtain a new texture, named as elliptical annular texture, rather than the traditional basal texture. In addition, the maximum texture intensity of the cold rolled samples decreased with the increased accumulated reductions. The formation of this unusual texture was attributed to the initial non-basal texture and multiple deformation modes.