Elastic Instability Research Articles

Elastic instabilities of soft laminates with stiffening behavior

This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications.

Elasto-visco-plastic flows in benchmark geometries: I. 4 to 1 planar contraction

We present predictions for the flow of elastoviscoplastic (EVP) fluids in the 4 to 1 planar contraction geometry. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method with the OpenFOAM software. Both the constitutive model and the solution method require using transient simulations. In this benchmark geometry, whereas viscoelastic fluids may exhibit two vortices, referred to as lip and corner vortices, we find that EVP materials are unyielded in the concave corners. They are also unyielded along the mid-plane of both channels, but not around the contraction area where all stress components are larger. The unyielded areas using this EVP model are qualitatively similar to those using the standard viscoplastic models, when the Bingham or the Weissenberg numbers are lower than critical values, and then, a steady state is reached. When these two dimensionless numbers increase while they remain below the respective critical values, which are interdependent, (a) the unyielded regions expand and shift in the flow direction, and (b) the maximum velocity increases at the entrance of the contraction. Increasing material elasticity collaborates with increasing the yield stress, which expands the unyielded areas, because it deforms the material more prior to yielding compared to stiffer materials. Above the critical Weissenberg number, transient variations appear for longer times in all variables, including the yield surface, instead of a monotonic approach to the steady state. They may lead to oscillations which are damped or of constant amplitude or approach a flow with rather smooth path lines but complex stress field without a plane of symmetry, under creeping conditions. These patterns arise near the entrance of the narrow channel, where the curvature of the path lines is highest and its coupling with the increased elasticity triggers a purely elastic instability. Similarly, a critical value of the yield stress exists above which such phenomena are predicted.

Intrinsically Multistable Soft Actuator Driven by Mixed-Mode Snap-Through Instabilities.

Actuators utilizing snap-through instabilities are widely investigated for high-performance fast actuators and shape reconfigurable structures owing to their rapid response and limited reliance on continuous energy input. However, prevailing approaches typically involve a combination of multiple bistable actuator units and achieving multistability within a single actuator unit still remains an open challenge. Here, a soft actuator is presented that uses shape memory alloy (SMA) and mixed-mode elastic instabilities to achieve intrinsically multistable shape reconfiguration. The multistable actuator unit consists of six stable states, including two pure bendingstates and four bend-twist states. The actuator is composed of a pre-stretched elastic membrane placed between two elastomeric frames embedded with SMA coils. By controlling the sequence and duration of SMA activation, the actuator is capable of rapid transition between all six stable states within hundreds of milliseconds. Principles of energy minimization are used to identify actuation sequences for various types of stable state transitions. Bendingand twisting angles corresponding to various prestretch ratios are recorded based on parameterizations of the actuator's geometry. To demonstrate its application in practical conditions, the multistable actuator is used to perform visual inspection in a confined space, light source tracking during photovoltaic energy harvesting, and agilecrawling.

Assessing nozzle flow dynamics in fused filament fabrication through the parametric map α−λ

Polymer rheology profoundly influences the intricate dynamics of material extrusion in fused filament fabrication (FFF). This numerical study, which uses the Giesekus model fed with a full rheometric experimental dataset, meticulously examines the molten flow patterns inside the printing nozzle in FFF. Our findings reveal new insight into the interplay between elastic stresses and complex flow patterns, highlighting their substantial role in forming upstream vortices. The parametric map α–λ from the Giesekus model allowed us to sort the materials and connect the polymer rheology with the FFF nozzle flow dynamics. The identification of elastic instabilities, the characterization of flow types, and the correlation between fluid rheology and pressure drop variations mark significant advancements in understanding FFF processes. These insights pave the way for tailored nozzle designs, promising enhanced efficiency and reliability in FFF-based additive manufacturing.

Investigating the Influence of the Improved Multibody Rope Approach on the Structural Behavior of Dakar Mosque Gridshell Structure

Gridshell structures are characterized by an impressive strength-to-weight ratio, allowing their application in large-span roofing structures. However, their complex construction process and maintenance limited their widespread application. In recent years, the development of parametric and computational design tools has rekindled interest in this type of structure. Among these techniques, the Multibody Rope Approach (MRA) is a form-finding method based on the dynamic equilibrium of a system of masses (nodes) connected by ropes, which allows optimizing the structural shape starting from the dual geometry of the funicular network. To optimize the construction process, an improved version of the MRA, i-MRA, has been recently developed by the authors with the goal of uniforming the size of the structural components. To investigate the impact of the i-MRA method on the structural behavior of gridshell structures, the practical case of the design of a mosque roof is here analyzed. The comparison is carried out in terms of structural performance with respect to permanent and equivalent quasi-static loads. In addition, free-vibration natural-frequency shift is obtained by performing linear modal analysis. Finally, the global behavior with respect to buckling and elastic instability is assessed solving the relevant eigenvalue problem. The results demonstrate that for the roofing of the Dakar mosque, the structural configuration obtained through i-MRA is superior in terms of both construction efficiency and structural performance. The achieved shape exhibits a more uniform distribution of stresses induced by the applied loads together with very limited structural element typologies.

Mechanical response of a novel square dome shell with bistable behavior: Improved analytical method and empirical model

In this study, a novel square dome-shaped shell with a fascinating bistable behavior is proposed, which is able to quickly switch to a new stable configuration within its elastic range under a certain load, due to its elastic instability. Compared to most circular shells currently studied, it is easier to arrange multiple structures in three-dimensional space to obtain multistable responses. Numerical and experimental methods were adopted for the study of the mechanical response of the square shell, and main influence parameters were also investigated. In addition, an improved piecewise fitting method is introduced to establish an empirical formula for predicting the mechanical response of bistable shells, which can be used to guide the design of bistable shells. Finally, two types of metamaterials, uniaxial compressible metamaterials and triaxial compressible metamaterials, are successfully designed according to the above theory, the typical behaviors of which are studied via simulations. This novel structure presented in this paper has broad application prospects in the fields of energy absorption and programmable deformation structures.

Elastic instability in a family of rectilinear viscoelastic channel flows devoid of centerline symmetry

Elastic instability in a family of rectilinear viscoelastic channel flows devoid of centerline symmetry

Research on stability of CLT wall under uniform compression based on orthotropic plate buckling theory

Cross-laminated timber (CLT) has been widely used in the construction of multi-story timber structures, but a method for determining the buckling capability of CLT walls has not been obtained yet. Based on the plate buckling theory and lateral restraints of CLT walls, a method for calculating the uniform-compression buckling capability of CLT walls in cases of elasto-plastic instability and elastic instability is derived in this paper. In addition, equations for determining the boundary between the elasto-plastic instability and elastic instability is also proposed. A numerical model of the CLT wall under uniform compression was established on the basis of previous experiments. The theoretical results were compared with the results of numerical simulations, and the overall error was found to be small. The proposed equations can provide good predictions for the buckling capability of uniformly compressed CLT walls to provide a basis for the design and engineering application of timber structures.

Designing necks and wrinkles in inflated auxetic membranes

This article presents the potentiality of inflatable, functionally-graded auxetic membranes to produce wrinkles and necks. We obtain elastic instabilities at desired locations in axisymmetric membranes and with prescribed patterns in square membranes. First, we use an analytical approach to obtain a series of universal results providing insights into the formation of wrinkles and necks in inflated, axisymmetric membranes. For example, we prove analytically that necks and wrinkles may never overlap in pressurized, axially symmetric membranes. Second, we implement the relaxed strain energy of tension field theory into a Finite Element solver (COMSOL). By tuning spatial inhomogeneities of the material moduli, we corroborate our universal results, describe the onset of wrinkling in an averaged way, and also generate non-trivial instabilities at desired locations. This study on membranes with morphing or corrugation on demand has potential applications in Braille reading and haptics.

Tunable sequential pathways through spatial partitioning and frustration tuning in soft metamaterials.

Elastic instabilities have been leveraged in soft metamaterials to attain novel functionalities such as mechanical memory and sequential pathways. Pathways have been realized in complex media or within a collection of hysteretic elements. However, much less has been explored in frustrated and partitioned soft metamaterials. In this work, we introduce spatial partitioning as a method to localize deformation in sub-regions of a large and soft metamaterial. The partitioning is achieved through the strategic arrangement of soft inclusions in a soft lattice, which form distinct regions behaving as mechanical units. We examine two partitions: an equally spaced layer partition with mechanical units connected in series, and a cross partition, represented by interconnected series of mechanical units in parallel. Sequential pathways are obtained by frustrating the partitioned metamaterial post-manufacture and are characterized by tracking the polarization change in each partition region. Through a combination of experiments and simulations, we demonstrate that partitioning enables tuning the pathway from longitudinal with weak interactions to a pathway exhibiting strong interactions rising from geometric incompatibility and central domain rotation. We show that tuning the level of uniform lateral pre-strain provides a wide range of tunability from disabling to modifying the sequential pathway. We also show that imposing a nonuniform confinement and altering the tilting of one or two of the domain edges enables to program the pathway, access a larger set of states, and tune the level of interaction between the regions.

Rigidity sensing by blood-borne leukocytes: Is it independent of internal signaling?

<abstract> <p>Atherosclerosis is a chronic inflammatory disease that results in the formation of lipid-rich lesions and stiffening of arterial walls. An increasing body of evidence suggests that nearly all members of the leukocyte family accumulate within atherosclerosis-prone arteries and participate in various stages of disease progression. Recently, it has been proposed that progressive changes of the elastic modulus of the arterial wall during plaque development may directly influence the kinematics of leukocyte rolling. In the present study, we propose that rigidity sensing of rolling leukocytes may occur spontaneously due to the stiffness-dependent elastic instability of reversible bonds between rolling leukocytes and the arterial walls. This effect is mechanistic in nature and operates independently of cell biochemical signaling. To partially test this hypothesis, we measured the rolling velocities of functionalized microparticles, comparable in size to leukocytes, interacting with E-selectin coated substrates of controlled stiffness. The kinematic analysis of the particles' motion reveals a larger rolling velocity on softer substrates, aligning with previous reports regarding monocytes. A simple kinetic model for a cluster of reversible bonds formed between a cell and the underlying substrate demonstrates that the critical forces needed for bond disassembly decrease as substrate stiffness decreases. Consequently, bonds are more likely to break on softer substrates, resulting in enhanced cell mobility.</p> </abstract>

Rheological effects on purely-elastic flow asymmetries in the cross-slot geometry.

Viscoelastic flows in the cross-slot geometry can undergo a transition from a steady symmetric to a steady asymmetric flow state, ostensibly due to purely-elastic effects arising beyond a critical flow rate, or Weissenberg number Wi. However, some reports suggest that shear thinning of the fluid's viscosity may also play an important role in this transition. We employ a series of polymer solutions of varying rheological properties to investigate in detail how the interplay between fluid elasticity and shear thinning affects the onset and development of asymmetric flows in the cross-slot. Flow velocimetry is performed on each of the polymer solutions, and is used to assess the degree of flow asymmetry I in the cross-slot as a function of both Wi and a dimensionless parameter S quantifying the flow-rate-dependent extent of shear thinning. Typically, the flow field breaks symmetry as Wi is increased beyond a critical value, but the magnitude of I is found to also be dependent on S. For a few specific polymer solutions, the flow field recovers symmetry above a second, higher critical Wi as S becomes small. The experimental results are summarized in a flow state diagram in Wi-S space, showing the relationship between flow asymmetry and fluid rheology. Finally, to gain a deeper understanding of the effects of shear thinning, numerical simulations are performed using the linear simplified Phan-Thien-Tanner model. We demonstrate that the degree of both shear thinning and elasticity of the fluid, and their interplay, are important factors controlling elastic instabilities in the cross-slot geometry.

Elasto-inertial instabilities in the merging flow of viscoelastic fluids.

Many engineering and natural phenomena involve the merging of two fluid streams through a T-junction. Previous studies of such merging flows have been focused primarily upon Newtonian fluids. We observed in our recent experiment with five different polymer solutions a direct change from an undisturbed to either a steady vortical or unsteady three-dimensional flow at the T-junction with increasing inertia. The transition state(s) in between these two types of merging flow patterns is, however, yet to be known. We present here a systematic experimental study of the merging flow of polyethylene oxide (PEO) solutions with varying polymer concentrations and molecular weights. Two new paths of flow development are identified with the increase of Reynolds number: one is the transition in very weakly viscoelastic fluids first to steady vortical flow and then to a juxtaposition state with an unsteady elastic eddy zone in the middle and a steady inertial vortex on each side, and the other is the transition in weakly viscoelastic fluids first to a steady vortical and/or a juxtaposition state and then to a fully unsteady flow. Interestingly, the threshold Reynolds number for the onset of elastic instabilities in the merging flow is not a monotonic function of the elasticity number, but instead follows a power-law dependence on the polymer concentration relative to its overlap value. Such a dependence turns out qualitatively consistent with the prediction of the McKinley-Pakdel criterion.

Parallel governing criteria for non-Newtonian droplet rebound suppression on superhydrophobic surfaces

Non-Newtonian droplets are known to suppress rebound on superhydrophobic (SH) surfaces. Our previous work (Dhar et al., Phys Rev Fluids, 2019, vol 4 [1]) showed that the polymer concentration and impact velocity must exceed a certain threshold to initiate the onset of rebound suppression. Analogous to drag reduction or elastic instabilities, we proposed that rebound suppression occurs only when the Weissenberg number exceeds unity (i.e., Wi >1) at the onset of retraction. In this study, we explore four different types of SH surfaces to examine the universality of the previous observation (the importance of Wi >1 for rebound suppression). We observed that rebound suppression does not occur on all types of SH surfaces. The surfaces where rebound suppression was observed are categorized as ‘Type-I’, while the remaining as ‘Type-II’. The non-uniformity in the rebound suppression phenomena is explained by the role of Cassie to Wenzel transformation (CWT) or impalement. We showed that for ‘Type-I’ surfaces, when the ratio of dynamic pressure (PD) to minimum capillary pressure (PC) exceeds unity (i.e., PD/PC > 1), the rebound is suppressed. The ‘Type-II’ surfaces have characteristic spacing in the order of nanometers, which is three orders of magnitude lower than the microtextured ‘Type-I’ surfaces. Thereby, the minimum capillary pressure is significantly higher for ‘Type-II’ surfaces. The dynamic pressure could not surpass the minimum capillary pressure for the impact velocities and polymer concentrations studied for the ‘Type-II’ surfaces. As PD/PC remained < 1, for ‘Type-II’ surfaces, rebound suppression was not observed. It must be noted that for the same values of PD/PC > 1 values, water droplets didn’t show rebound suppression on ‘Type-I’ surfaces. The non-Newtonian droplets are known to slow down the retraction dynamics due to normal stress, extensional viscosity and higher adsorption at the substrate. We have demonstrated the role of extensional viscosity in this study, particularly how strain stiffening of radial filaments emanating from the droplet aids in dissipating energy, which further aids in arresting drop rebound. Therefore, the existence of two parallel mechanisms: the role of fluid elasticity (manifested through Wi > 1), and the role of CWT or impalement (manifested through PD/PC> 1), are necessary conditions for non-Newtonian drop rebound suppression on superhydrophobic surfaces.

Rayleigh-Taylor Instability in Soft Viscoelastic Solids.

We present an experimental characterization of the gravity-driven Rayleigh-Taylor instability in viscoelastic solids. The instability creates periodic patterns on the free surface of the soft solids that are distinct from the previously studied elastic Rayleigh-Taylor instability. The experimental results are supported by the linear stability analysis reported here. We identify the dependence of the steady-state pattern of deformations on the gel's geometry, complex shear modulus, and surface tension. This study provides quantitative measures applicable to the design of tunable surface textures, soft machines, and 3D structures.

Exploring multi-stability in three-dimensional viscoelastic flow around a free stagnation point

Fluid elements passing near a stagnation point experience finite strain rates over long persistence times, and thus accumulate large strains. By the numerical optimization of a microfluidic 6-arm cross-slot geometry, recent works have harnessed this flow type as a tool for performing uniaxial and biaxial extensional rheometry (Haward et al., 2023 [5,6]). Here we use the microfluidic ‘Optimized-shape Uniaxial and Biaxial Extensional Rheometer’ (OUBER) geometry to probe an elastic flow instability which is sensitive to the alignment of the extensional flow. A three-dimensional symmetry-breaking instability occurring for flow of a dilute polymer solution in the OUBER geometry is studied experimentally by leveraging tomographic particle image velocimetry. Above a critical Weissenberg number, flow in uniaxial extension undergoes a supercritical pitchfork bifurcation to a multi-stable state. However, for biaxial extension (which is simply the kinematic inverse of uniaxial extension) the instability is strongly suppressed. In uniaxial extension, the multiple stable states align in an apparently random orientation as flow joining from four neighbouring inlet channels passes to one of the two opposing outlets; thus forming a mirrored asymmetry about the stagnation point. We relate the suppression of the instability in biaxial extension to the kinematic history of flow under the context of breaking the time-reversibility assumption.

The role of elastic instability on the self-assembly of particle chains in simple shear flow

Flow-induced self-assembly (FISA) is the phenomena of particle chaining in viscoelastic fluids while experiencing shear flow. FISA has a large number of applications across many fields including materials science, food processing, and biomedical engineering. Nonetheless, this phenomena is currently not fully understood and little has been done in literature so far to investigate the possible effects of the shear-induced elastic instability. In this work, a bespoke cone and plate shear cell is used to provide new insights on the FISA dynamics. In particular, we have fine-tuned the applied shear rates to investigate the chaining phenomenon of micrometer-sized spherical particles suspended into a viscoelastic fluid characterized by a distinct onset of elastic instability. This has allowed us to reveal three phenomena never reported in literature before, i.e.,: (I) the onset of the elastic instability is strongly correlated with an enhancement of FISA; (II) particle chains break apart when a constant shear is applied for “sufficiently” long-time (i.e., much longer than the fluids' longest relaxation time). This latter point correlates well with the outcomes of parallel superposition shear measurements, which (III) reveal a fading of the elastic component of the suspending fluid during continuous shear flows.

Energy harvesting using an inverted piezohydroelastic flag with resistor–inductor–capacitor circuit

We develop a high-fidelity multi-physics model and, by using it, study the energy conversion process of a piezohydroelastic flag. Instead of a regular flag with a clamped upstream leading edge, we use an inverted flag so as to make the best of fluid elastic instability for energy harvesting. Moreover, different from many previous studies where a resistor–capacitor (RC) circuit is usually used, we adopt a resistor–inductor–capacitor (RLC) circuit for electricity generation. The influences of several key parameters associated with fluid, structure and electric dynamics are studied. Significantly different response modes are identified, among which the symmetric- and asymmetric-flutter modes are most suitable for sustainable energy harvesting, both emerging with moderate bending stiffness. If only deploying the RC circuit, increasing the resistance makes the flag more stable. By adding an inductor to turn the RC circuit into an RLC one, we observe the occurrence of ‘lock-in’ between the flag frequency and the circuit frequency as first reported on a regular flag by Xia et al. (Phys. Rev. Appl., vol. 3, 2015, 014009). This phenomenon can significantly enhance the energy output, but it only happens when the circuit resistance is sufficiently large. From a derivation based on dynamic mode decomposition analysis, we further identify an optimal condition for maximizing the energy output, which can serve as a guideline to determine whether deploying an inductor can boost the performance, and, if yes, the required inductance. The findings from this study can better guide the design of flow-induced-vibration-based piezoelectric energy harvesters for microelectronic devices.

Viscoelastic flow asymmetries in a helical static mixer and their impact on mixing performance

Helical static mixers are often used during the processing of formulated products with complex rheological properties, such as viscoelasticity. Previous experimental studies have highlighted that increasing the viscoelasticity of the flow hinders the mixing performance in the laminar flow regime. In this study, we use computational fluid dynamics to investigate the flow of a FENE-CR model fluid in a helical static mixer. The numerical results show clearly that the reduced mixing performance is caused by flow distribution asymmetries which develop at the mixer element intersections. The results allow us to quantify the degree of asymmetry for the range of conditions studied, which is correlated with the quantified mixing performance for each simulation. The mixing is quantified using a Lagrangian particle tracking technique, and a new mixing index is defined based on the mean nearest distance between the two sets of tracked particles. The results show that the asymmetry parameter does not follow a pitchfork bifurcation, as it typically does for elastic instabilities in symmetrical geometries such as the cross-slot. For low values of the extensibility parameter, L2, the flow remained (Eulerian) steady for all Reynolds Re and Weissenberg Wi numbers studied. At fixed Re and Wi, increasing L2 causes the flow to become transient and greatly increases the magnitude of the asymmetry. The results presented in this study help us to understand the effects that viscoelasticity can cause in mixing processes.

Sim2Real Neural Controllers for Physics-Based Robotic Deployment of Deformable Linear Objects

Deformable linear objects (DLOs), such as rods, cables, and ropes, play important roles in daily life. However, manipulation of DLOs is challenging as large geometrically nonlinear deformations may occur during the manipulation process. This problem is made even more difficult as the different deformation modes (e.g., stretching, bending, and twisting) may result in elastic instabilities during manipulation. In this paper, we formulate a physics-guided data-driven method to solve a challenging manipulation task—accurately deploying a DLO (an elastic rod) onto a rigid substrate along various prescribed patterns. Our framework combines machine learning, scaling analysis, and physical simulations to develop a physics-based neural controller for deployment. We explore the complex interplay between the gravitational and elastic energies of the manipulated DLO and obtain a control method for DLO deployment that is robust against friction and material properties. Out of the numerous geometrical and material properties of the rod and substrate, we show that only three non-dimensional parameters are needed to describe the deployment process with physical analysis. Therefore, the essence of the controlling law for the manipulation task can be constructed with a low-dimensional model, drastically increasing the computation speed. The effectiveness of our optimal control scheme is shown through a comprehensive robotic case study comparing against a heuristic control method for deploying rods for a wide variety of patterns. In addition to this, we also showcase the practicality of our control scheme by having a robot accomplish challenging high-level tasks such as mimicking human handwriting, cable placement, and tying knots.