Bistable Tape Springs Research Articles

Enhancing the Design Space of Bistable Laminates by Tailoring the Attachment Boundary Conditions

Abstract Bistable and multistable laminates are structural elements with more than one stable equilibrium configuration. The bistability makes them very interesting for the design of compliant mechanisms. However, these laminates are extremely sensitive to boundary conditions and attachment methods. It has been shown prior in the literature that restrictive boundary conditions can lead to the loss of bistability or unwanted deformation modes. This article develops attachment concepts that leverage the structural behavior changes caused by boundary conditions to expand the design space of bistable elements for structural applications. A systematic means of using the boundary conditions to improve the stability margins and load introduction of bistable tape springs is demonstrated. The stability margins and the achievable angles have been quantified using an analytical model previously developed by Guest and Pellegrino. Subsequently, high-fidelity finite element (FE) simulations are done in abaqus™ to determine the limits of the proposed method in terms of localization effects. Based on the analytical model and simulation outcomes, layup, size, and attachment points are determined, and two prototypes are fabricated, illustrating the effectiveness of the proposed method in expanding the design space of traditional bistable tape springs.

Toward thermal stimulation of shape memory polymer composite bistable tape springs

Due to their tailored thermomechanical behavior and functionality, shape memory polymer matrix composites (SMPCs) are attractive as deployable structures in aerospace applications. An analytical model based on the classical laminate theory, together with the principle of minimum potential energy is developed to capture the thermo-viscoelastic behavior of a bistable tape spring (BiTS). These tape springs are known to snap between two stable configurations by different stimulus. Here, a shape memory polymer as the matrix of a fiber-reinforced polymer BiTS is introduced to actuate the snap-back. Experimental characterization was performed to obtain the time-temperature dependent properties of a Polyurethane SMPC. The time-temperature superposition principle was employed to convert the thermal effects to a viscoelastic response. Five BiTSs were manufactured and exposed to two different thermo-viscoelastic cycles to verify the model for long-term and high-temperature behaviors. The results show that the model can estimate the coiling radius and the degree of stability of the BiTS in the coiled configuration. Analytical results, supported by experimental results, show that the temperature could initiate the snap-back in BiTS. However, time-temperature history has a significant effect on the bistability and can convert a monostable tape spring to a BiTS and vice versa.

Viscoelastic bistable tape spring behavior modeled by a two-dimensional system with rigid links, springs and dashpots

Bistable composite tape springs are often used as deployable structures in aerospace applications because of their ability to be tailored for compact size, deployed lengths and stiffness. Analytical studies of the coupling between stress-strain and moment-curvature of thin curved shells have been used to estimate the total stored strain energy in different tape spring configurations. The strain energy as function of the curvatures reveals the fundamental stability behavior of the tape springs in the different configurations. The present study investigates the minimum strain energy path between two stable equilibrium points and the passage through the unstable saddle point along this path. For a coiled fiber-reinforced composite tape spring, the strain energy level for the local minimum and the saddle points will change with respect to time due to viscoelastic effects. To explain the fundamental mechanical behavior of viscoelastic bistable tape springs, a two-dimensional (2D) model composed of rigid links, elastic springs and viscous dampers was proposed. It was shown how the 2D model can be made strain energy-equivalent to a shell model with respect to the minimum strain energy paths. The 2D model was able to capture the fundamental behavior of viscoelastic tape springs during both snap-through and snap-back paths.

Dynamics of a regularized and bistable Ericksen bar using an extended Lagrangian approach

The motivation of this work is to better understand the dynamic behaviour of bistable structures presenting an analogy with regularized Ericksen bars. The archetype of such structures is the bistable tape spring, which exhibits a particular scenario of deployment, from the stable coiled configuration to the straight stable configuration: at each time of the deployment, the geometry of the tape is similar to a two-phase bar with a coiled part and a straight part separated by a transition zone that moves along the tape. One goal of this work is to show that a regularized and bistable Ericksen bar model contains all the properties to reproduce such a dynamic behaviour. The mathematical structure of this model presents a locally non-convex potential with two minima and a dependence of higher order terms. Some similarities exist between this model and the Euler-Korteweg system with a Van der Waals equation. To study numerically the dynamic behaviour of such models, it is necessary to solve a dispersive and conditionally hyperbolic system. For this purpose, the Lagrangian of the regularized bistable Ericksen model is extended and penalized. Variable boundary conditions are deduced from Hamilton’s principle and are used to control the evolution of the system. Dispersion analysis allows to determine the numerical parameters of the model. The obtained non–homogeneous hyperbolic system can be solved by standard splitting strategy and finite-volume methods. Numerical simulations illustrate how the parameters of the model influence the width and the propagation speed of the transition zone. The effect of energy dissipation is also examined. Finally, comparisons with an exact kink wave solution indicate that the extended Lagrangian solution reproduces well the dynamics of the original Lagrangian.

Viscoelastic analysis of bistable composite shells via absolute nodal coordinate formulation

Material viscoelasticity may play a significant role in the bistable composite shells, especially after long-term stowage. This article investigates the influence of viscoelastic effects on the mechanical behaviors of bistable composite cylindrical shells in coiled state, for which a novel modeling approach for viscoelastic analysis in integral form of laminated composite shells is proposed based on the nonlinear continuum mechanics and the absolute nodal coordinate formulation. The model presented herein is also very appropriate for the dynamics analysis of deployment of bistable tape springs. Furthermore, an efficient calculation scheme of the highly nonlinear viscoelastic forces with hereditary integral is presented. By comparing the predictions of viscoelastic and elastic analyses for the radii, stresses distributions, and configurations of coiled shells, the effect of viscoelasticity on the second stable equilibrium is illustrated. The results show that relaxation behaviors of bistable composite shells at high strains are evident.

Evolution Prediction of Bistable Tape Springs' Deployed Shape While Undergoing Stowage at High Temperature

Self-deployable tape springs made of CFRP feature significant effect from relaxation, mainly happening during long time stowage in coiled configuration prior to launch. The stored strain energy contained within the structures during stowage tend to modify the polymer matrix mechanical properties. The research introduced here aims to develop an efficient numerical process capable of determining the evolution of the deployed shape, after deployment, of such structures due to viscoelastic relaxation happening during on Earth stowage. A two steps homogenization process is devised to compute the plain weave mechanical properties. The process is first based on an analytical model to determine the strand's properties, before using a finite element based numerical model for the plain weave pattern. Properties are fitted with Prony series to display the variations over a long time range. Results from this homogenization are then used in an Abaqus numerical model to predict the deployed shape evolution of the tape springs, and its recovery capabilities after full deployment. Validity of the model is checked using results from experimental stowage conducted on bistable tape springs.

Design and Analysis of Laminates for Self-Deployment of Viscoelastic Bistable Tape Springs After Long-Term Stowage

Bistable tape springs are ultrathin fiber-reinforced polymer composites, which could self-deploy through releasing stored strain energy. Strain energy relaxation is observed after long-term stowage of bistable tape springs due to viscoelastic effects and the tape springs might lose their self-deployment abilities. In order to mitigate the viscoelastic effects and thus ensure self-deployment, different tape springs were designed, manufactured, and tested. Deployment experiments show that a four-layer, [−45/0/90/45], plain weave glass fiber tape spring has a high capability to mitigate the strain energy relaxation effects to ensure self-deployment after long-term stowage in a coiled configuration. The two inner layers increase the deployment force and the outer layers are used to generate the bistability. The presented four-layer tape spring can self-deploy after more than six months of stowage at room temperature. A numerical model was used to assess the long-term stowage effects on the deployment capability of bistable tape springs. The experiments and modeling results show that the viscoelastic strain energy relaxation starts after only a few minutes after coiling. The relaxation shear stiffness decreases as the shear strain increases and is further reduced by strain energy relaxation when a constant shear strain is applied. The numerical model and experiments could be applied in design to predict the deployment force of other types of tape springs with viscoelastic and friction effects included.

Deployment of Bistable Self-Deployable Tape Spring Booms Using a Gravity Offloading System

Bistable tape springs are suitable as deployable structures thanks to their high packaging ratio, self-deployment ability, low cost, light weight, and stiffness. A deployable booms assembly compose ...

Effects of Long-Term Stowage on the Deployment of Bistable Tape Springs

In the context of strain-energy-deployed space structures, material relaxation effects play a significant role in structures that are stowed for long durations, for example, in a space vehicle prior to launch. Here, the deployment of an ultrathin carbon fiber reinforced plastic (CFRP) tape spring is studied, with the aim of understanding how long-duration stowage affects its deployment behavior. Analytical modeling and experiments show that the deployment time increases predictably with stowage time and temperature, and analytical predictions are found to compare well with experiments. For cases where stress relaxation is excessive, the structure is shown to lose its ability to deploy autonomously.

A planar rod model with flexible thin-walled cross-sections. Application to the folding of tape springs

This paper is focused on the modeling of rod-like elastic bodies that have an initially curved and thin-walled cross-section and that undergo important localized changes of the cross-section shape. The typical example is the folding of a carpenter’s tape measure for which the folds are caused by the flattening of the cross-section in some localized areas. In this context, we propose a planar rod model that accounts for large displacements and large rotations in dynamics. Starting from a classical shell model, the main additional assumption consists in introducing an elastica kinematics to describe the large changes of the cross-section shape with very few parameters. The expressions of the strain and kinetic energies are derived by performing an analytical integration over the section. The Hamilton principle is directly introduced in a suitable finite element software to solve the problem. The folding, coiling and deployment of a tape spring is studied to demonstrate the ability of the model to account for several phenomena: creation of a single fold and associated snap-through behavior, splitting of a fold into two, motion of a fold along the tape during a dynamic deployment, scenarios of coiling and uncoiling of a bistable tape spring. This 1D model may also be relevant for future applications in biomechanics, biophysics and nanomechanics.