Deformation Path Research Articles

Geometric mechanics of kiri-origami-based bifurcated mechanical metamaterials.

We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson's ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson's ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Springback behavior after air bending of pre-strained AA 6016-T4 sheets: Influence of dislocation density and backstress on model accuracy

Predicting springback in sheets of aluminum alloys is challenging, particularly for complex strain path deformation used to form the material. This paper presents experimental and modeling results for air bending of AA 6016-T4 sheet material. Prior to bending, pre-strains were applied to the specimens in uniaxial tension, plane-strain tension, and biaxial tension. Specimens were then cut from the pre-strained material and were subjected to air bending using three different bend angles in a v-die, after which springback was measured. It was found that greater levels of pre-strain result in larger springback magnitudes, and that the biaxial pre-strained specimens generally exhibited greater springback than the others. A CPFE – EPSC model with phenomenological backstress component in the hardening law was used to predict springback magnitude across the different pre-strain paths, pre-strain levels, and imposed air bend angles. It was observed that the more significant the strain path change, as was seen in the case of biaxial tension pre-strain followed by bending, the greater the influence of backstress on model accuracy, owing to the activation of new slip systems. When backstress was excluded from the model, a 3.2 % prediction error in springback angle was observed in the worst case, versus an error of 0.8 % when backstress was included. Backstress was correlated to more rapid dislocation density development on both the tensile surface of the sheet, and also through the thickness, after the strain path change. On the other hand, for the case of plane-strain pre-strain followed by bending, dislocation density development was more gradual and the backstress impact on model prediction was less significant, with the same slip systems active during both pre-strain and bending. Therefore, it is seen that the influence of backstress on accuracy springback modeling in AA 6016-T4 varies significantly depending on the strain path. Thus, the use of a phenomenological backstress law within the CPFE-EPSC framework is seen to be an accurate and efficient approach for modeling springback after strain path changes that can occur during industrial forming applications.

Localized Manipulation of Martensite Transformation in Double-Sided Incremental Forming by Varying the Deformation Path

Localized Manipulation of Martensite Transformation in Double-Sided Incremental Forming by Varying the Deformation Path

Aneurysm growth evaluation and detection: a computer-assisted follow-up MRA analysis

Growing intracranial aneurysms pose a high risk of rupture, making the detection and quantification of the growth crucial for timely treatment strategy adoption. In this paper we propose a computer-assisted approach based on the extraction of IA shapes from associated baseline and follow-up angiographic scans and non-rigid morphing of the two shapes. From the obtained shape deformations we computed four novel features, including differential volume (dV), surface area (dSA), aneurysm-size normalized median deformation path length (dMPL), and integral of cumulative deformation distances (dICDD). An experienced neuroradiologist manually extracted the IA shape models from the baseline and follow-up MRAs and, by utilizing size change and visual assessments, classified each aneurysm into stable with morphology changes, stable or growing. We investigated the classification performance and found that three of the novel and one cross-sectional feature exhibited significantly different mean values (p-value <0.05\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$< 0.05$$\\end{document}; Tukey’s HSD test) between the stable and growing IA groups, while the mean dICDD was significantly different between all the three groups. The cross-sectional features has sensitivity to growing IAs in range 0.05–0.86, while novel features had generally higher sensitivity in range 0.81–0.90, making them promising candidates as surrogate follow-up imaging-based biomarkers for IA growth detection. These findings may offer valuable information for clinical management of patients with IAs based on follow-up imaging.

Semi-analytical framework for modelling of surface heating and its impact on nonlinear stability of nanotube reinforced doubly curved porous fiber composite panels

In elevated temperatures, the stiffness of the panel deteriorates and can lead to loss of stability of structures. Hence, the stability analysis of thin-walled structures is a critical investigation in the thermal environment. Finding such criticality, the present semi-analytical study investigated the nonlinear stability behaviour of porous doubly curved thin-walled panels subject to surface heating like dome heating and localised heating. To improve the stiffness of the panel, the matrix is reinforced with carbon nanotubes (CNTs). Improper mixing of such nanoparticles can lead to agglomeration or bundling effect, which may reduce the structure's stiffness. Still, its investigation in surface heating can be an essential aspect that is found to be untouched by researchers for porous shell panels. The effective material properties of the three-phase composite panel are determined using the Eshelby-Mori-Tanaka (E-M-T) approach and the Chamis homogenisation technique. Using the variational principle, governing equations are derived and further simplified to non-linear algebraic equations using the Galerkin technique. Gibson and Ashby foam model is used to model cell structure. It is observed that a complete agglomerated state results in higher post-buckling strength, a continuous deformation path due to biaxial compression and curved geometry, and porosity of cellular structure distribution and cell walls are the important parameters to study the stability of panel in a thermal environment are the major conclusions drawn from the current study. Current investigation can be an important contribution towards modelling aircraft structure in supersonic airflow and furnace walls of thermal power plants subjected to localised heating.

Continuous and synchronous calibration process of ovality and straightness for longitudinally submerged arc welding pipes with three rollers.

A new process of continuous and synchronous calibration process of ovality and straightness for LSAW (Longitudinally Submerged Arc Welding, LSAW) pipes with three rollers is proposed. Specifically, the process is introduced from three aspects: roller-shape, loading parameters and axial and circumferential deformation paths. The process is verified by numerical simulation and physical experiments. Further, the stress-strain in the Sections Ⅱ and Ⅳ is analyzed. The relationship between the process parameters and the residual ovality and residual straightness by experiments is discussed. The calibration scheme of LSAW pipes is put forward by using the control variable method. The results show that the shear stress is the principal stress direction in the Sections Ⅱ and Ⅳ. The residual ovality and residual straightness decrease with the increase of the radial reduction and times of reciprocating bending. The reciprocating bending process can eliminate the difference of the initial curvature, make the curvature of each section tend to be uniform. After calibration, the residual straightness is less than 0.2% and the residual ovality is less than 1%, demonstrating a good feasibility of this process.

Earmuff performance in the presence of high-level impulse from a recoilless weapon firing in a confined space.

A noise attenuation performance test was conducted on earmuffs using a recoilless weapon launch platform in a confined space, along with two acoustic test fixtures (ATFs). The overpressure at the ATF's effective tympanic membrane comprised direct sound at 185 dB sound pressure level (SPL) and reflected sound at 179 dB SPL. Wearing earmuffs reduced these peaks to 162 dB SPL and 169 dB SPL, respectively. The reflected sound from walls was defined as delayed sound. An analytical model for earmuff noise attenuation simulated their effectiveness. The simulation revealed that when the earmuffs attenuated delayed sound, the acoustic impedance of acoustic leakage and the acoustic impedance of the earmuff material decreased by 96% and 50%, respectively. The negative overpressure zone between direct and delayed sound decreased the earmuffs' fit against the ATF. Additionally, the enclosed volume between the earmuff and the ear canal decreased by 12%. After the installation of bandages on the earmuffs, the overpressure peak of delayed sound was reduced by 5 dB. Furthermore, the acoustic impedance of the earmuff's sound leakage path and the acoustic impedance of the earmuff material deformation path increased by 100% and 809%, respectively.

A hyperelastic strain energy function for isotropic rubberlike materials

A three parameter novel hyperelastic strain energy function is introduced in this paper for soft and rubber-like materials. The function integrates a non-separable exponential component with a single term Ogden-type polynomial-like function, resulting in an exponential-polynomial based strain energy function. This helps in capturing both small and large deformation (stretch) behaviours of hyperelastic materials. The structure of the model is simple and validated against several experimental datasets including rubbers, hydrogel, and soft tissues. The model is reported to capture key material behaviors, including strain stiffening and various deformation paths. Through comparative studies with well-known models like the Ogden (six parameters) and Yeoh (three parameters), the model’s effectiveness is established. Furthermore, the model successfully addresses pressure-inflation instability in thin spherical balloons. It’s applicability extends to biological materials, as evidenced by its effectiveness in characterizing porcine brain tissue and a monkey’s bladder.

Modeling of localized phase transformation in pseudoelastic shape memory alloys accounting for martensite reorientation

A reliable prediction of the pseudoelastic behavior necessitates the involvement of martensite reorientation in the model. This is important not only under non-proportional loading but in general when the phase transformation proceeds in a localized manner, which results in complex local deformation paths. In this work, an advanced model of pseudoelasticity is developed within the incremental energy minimization framework. A novel enhancement of the model over its original version lies in the formulation of a suitable rate-independent dissipation potential that incorporates the dissipation due to martensitic phase transformation and also due to martensite reorientation, thus yielding an accurate description of the inelastic transformation strain. The finite-element implementation of the model relies on the augmented Lagrangian treatment of the non-smooth incremental energy problem. Thanks to the micromorphic regularization, the related complexities are efficiently handled at the local level, leading to a robust finite-element model. Numerical studies highlight the predictive capabilities of the model. The characteristic mechanical behavior of NiTi tube under non-proportional tension–torsion and the intricate transformation evolution under pure bending are effectively captured by the model. Additionally, a detailed analysis is carried out to elucidate the important role of martensite reorientation in promoting the striations of the phase transformation front.

Balanced and Aeppli parameters for the heterotic moduli

In this paper, we fix the complex structure and explore the moduli space of the heterotic system by considering two different yet “dual” deformation paths starting from a Kähler solution. They correspond to deformation along the Bott–Chern cohomology class and the Aeppli cohomology class, respectively. Using the implicit function theorem, we prove the stability of the existence of heterotic solutions under these two deformations and hence establish an initial step in constructing local moduli coordinates around a Kähler solution.

Forming limit and failure characterization of as-received and bi-axial prestrained Cu-Cr-Zr-Ti alloy sheets in the context of multistage forming

The characterization of forming limit utilizing Cu-Cr-Zr-Ti alloy sheets during the multistage forming process is imperative for successfully fabricating thrust chamber liners used in satellite launch vehicles. Therefore, the present work studies the effect of prestrain on the forming limit and failure behaviour of this alloy under different deformation paths. A stretch-forming setup was utilized to induce 8% equi-biaxial prestrain (EBP), and subsequently, these prestrained specimens were deformed till the onset of failure using the same setup. After prestraining, a shift in the failure strains was observed in the principal strain space, whereas it was found to be absent in the polar effective plastic strain, principal stress and effective plastic strain-stress triaxiality loci. The cup height along different deformation paths was marginally decreased in the prestrained specimens because of the reduction in failure strains, and the fracture occurred in the prestrained region. Further, failure analysis revealed intergranular cracks in the specimens deformed along plane strain and uniaxial deformation paths due to the presence of micron-size Cr-rich precipitates along grain boundaries. However, intergranular and transgranular cracks were present in the prestrained specimens, which were deformed equi-biaxially similar to the as-received specimens. The presence of nano-size Cr-rich precipitates inside the grains acted as nucleation sites for voids during equi-biaxial stretching, leading to transgranular cracks. It was also observed that failure in the prestrained and as-received specimens occurred at a similar effective plastic strain value due to the combined effect of void density and void size. Based on experimental observations, it was inferred that the forming limit of Cu-Cr-Zr-Ti sheets under a two-stage forming process was primarily affected by the presence of micro and nano-size Cr-rich precipitates.

Maximum buckling load design and post-buckling compressive failure of curved grid sub-stiffened composite panels

The structural efficiency of composite stiffened panels can be substantially improved by utilizing curved stiffening components due to their exceptional mechanical performance and design flexibility. This paper aims to explore the impressive potential offered by the curved stiffening concept in the design of T-shaped stiffened composite panels featuring curved sub-stiffening components. An optimization design framework is proposed to optimize the laminates sequence of skin, ply orientation angles and distribution of the curved sub-stiffeners as well as the curvature of the sub-stiffeners of the proposed curved grid sub-stiffened composite panels to yield higher buckling performance without additional weight. Results demonstrate that introducing composite curved grid sub-stiffeners to the T-shaped stiffened composite panel leads to substantial improvements (+254.42%) in buckling performance, while maintaining equivalent weight designs. Furthermore, the introduction of composite curved grid sub-stiffeners reveals alterations to the post-buckling deformation paths of grid sub-stiffened composite panels, leading to varied collapse loads and degrees of deformation in the composite panels. This highlights the importance of utilizing the composite curved grid sub-stiffeners to improve stability and reduce the risk of failure in thin-walled structures, all while meeting lightweight design criteria.

Programmable multistable kirigami chain: Decoupling energy barrier and snapping force/displacement in a unified topology

Arraying bistable cells in a chain results in a multistable mechanical structure that is capable of sequential deformation paths and structural reconfigurability. However, to customize the multistability, for example, a prescribed energy barrier with variable snapping force/displacement, is constrained by the difficulty of decoupling energy from kinematic characteristics since they are always governed by the same geometric parameters. This paper proposes a bistable kirigami cut topology to realize decoupling. Cut parameters are classified into independent groups, corresponding to objective energy barrier or force/displacement, which are consequently independent also. On this basis, a machine learning (ML) and genetic algorithm (GA) based approach is presented to guide the inverse design of the nonlinear responses. Optimal individual kirigami cells that meet decoupled multi-objectives such as energy barrier, snapping force and stable displacement are obtained to construct kirigami chains. The conceivable deformation sequences, configurations and energy/force-displacement curves are validated by both the simulation and experimental results. The proposed mechanism decoupled strategy and inverse design framework open up new horizons for programming energy landscape and provide a general recipe for tailoring multistability in metamaterials.

Quasi-static behavior of a pair of serially-connected Kresling Origami springs

Many of the patterns seen in Origami are currently being explored as a platform for building functional engineering systems with versatile characteristics that cater to niche applications in various technological fields. One such pattern is the Kresling pattern, which can be used to construct mechanical springs with unconventional properties and rich translational-rotational restoring behavior. In this paper, we investigate, both theoretically and experimentally, the quasi-static behavior of a pair of serially-connected Kresling Origami springs under different end loading conditions. We show that, depending on the end loading of the spring, it can exhibit coupled/ decoupled motion; one, two, or three equilibria; fixed, quasi-zero, or variable stiffness; and symmetric/asymmetric restoring behavior. We also present a technique to predict the restoring behavior of the serially-connected springs by combining a simple truss model with the experimentally-identified restoring behavior of a single unit. The technique permits accurate prediction of the deformation path of any number of serially-connected springs. We believe that serially connected Kresling Origami Springs offer a pathway towards the design of axial and torsional springs with unique and versatile functionalities.

Deformation in the wrinkle–crease transformation

We investigate deformation in the wrinkle–crease transformation to reveal the missing link between the wrinkling and creasing instabilities, which occur on the surface of elastomers under compression. Plane-strain finite element (FE) analysis is performed by combining a nonlinear perturbation approach to find two bifurcated solutions for the flat surface in a metastable state. The first solution is the stable deformation path for crease evolution, and the second solution is the previously unknown unstable deformation path from wrinkling to creasing. The two deformation paths are not independent, and they are connected at the critical strain for creasing εC. The resulting deformation at εC acts as a precursive deformation to cause creasing. Although the unstable path is initiated by the wrinkling instability as a bifurcation, the creasing instability (i.e., εC) is interpreted as the singular point at which the unstable path switches to the stable path. A chain reaction model is developed to describe the mechanism and deformation of the wrinkle–crease transformation, and it shows good agreement with the FE prediction within an inevitable limitation of FEs.

Optimal computation of integrals in the Half-Space Matching method for modal simulation of SHM/NDE in 3D elastic plate

Simulating structural health monitoring (SHM) or nondestructive evaluation (NDE) methods based on elastic guided waves (GW) is very helpful to handle their complexity (co-existence of several GW modes, frequency dependence of wavespeed) and to further design optimal methods of inspection offering high sensitivity to the sought flaws. The half-space matching (HSM) method has been established for the development of a model that hybridizes local finite element (FE) computations for GW scattering by a flaw, with a modal semi-analytical model for GW radiation and propagation in flawless plate-like structures. Highly oscillatory Integral formulae appear in the HSM method that radiate the scattered field away from the FE zone as the superimposition of modal contributions, which computation can be time-consuming. The present work is concerned with their optimal computation. Integral of this form can be efficiently computed under the far-field approximation but this classical technique fails at predicting accurately wavefields at relatively short distances (small number of wavelengths). The method developed herein relies on the complexification of the integrals to be computed and on specific deformation of integration paths in the complex plane, as detailed in the paper. It allows the evaluation of the integrals without approximation other than that of numerical quadratures, ensuring high accuracy while offering high computing performances. It indifferently applies in the far-field and in the near-field. The method of computation is validated by comparing its predictions with a reference solution of GW scattering. Its computational performances are also demonstrated, compared to those of the standard computation of the HSM integral formulae.

Effect of temperature on the mechanical properties of Ni-based superalloys via molecular dynamics and crystal plasticity

Study on the influence of temperature on the mechanical properties across multiple scales has been a focus on the research of Hastelloy-X (HX) alloys for the application in high-temperature structure components. In this work, Molecular Dynamics (MD) and Crystal Plasticity (CP) are put together to solve it from atomic scale to mesoscopic scale. MD research indicates that the deformation of HX alloy occurs in two stages at temperature below 300 K: initially, as stacking fault deforms, stacking fault can transform into twinning with increasing strain. When the temperature exceeds 300 K, deformation primarily forms a stacking fault. The twinning deformation path transforms from intrinsic stacking fault to extrinsic stacking fault and then to twinning. A mesoscopic-scale CP model was developed using atomic-scale deformation mechanisms to bridge the gap between deformation mechanisms and experimental results. The CP results indicate a functional relationship between the strength of HX alloy and temperature. This relationship appears insensitive to crystal texture and grain shape. Incorporating grain morphology and texture into the model significantly impacts the strength response of calculating HX alloy. After the tensile deformation of HX alloy at 300 and 1173 K, the atomic scale deformation results characterized by transmission electron microscopy are aligned with the MD simulation results. The relationship between strength and temperature predicted by CP results has also been validated. A thorough investigation into the deformation behavior of HX alloys across different scales, employing MD and CP models, introduces a novel approach for predicting the mechanical properties of superalloys.

Determination of Limiting Deformations at Testing Cylindrical Samples for Tension

This paper proposes a method for calculating limiting deformations under conditions of localized deformation during tensile testing. The method for calculating limiting deformations was used to construct plasticity diagrams under conditions of strain localization under uniaxial tension.&#x0D; The plasticity diagram is one of the material functions that forms the technological map of the material. The plasticity diagram displays the properties of a material depending on the degree of deformation and the stress state scheme.&#x0D; According to the studies carried out in this work, it was established that the critical increase in plasticity with increasing stress state indicator is explained by the influence of three factors: the strain gradient, the history of deformation and the third invariant of the stress tensor.&#x0D; The obtained dependencies make it possible to construct plasticity diagrams for materials whose destruction is preceded by localized deformation in the form of a "neck".&#x0D; This work establishes the quantitative influence of these three factors on the magnitude of the limiting deformations of a sample stretched to the point of failure.&#x0D; Application plasticity diagrams constructed using the proposed methods for cold plastic deformation processes, depending on the type of deformation path and the features of metal rheology, clarifies the value of the used plasticity resource of the metal, which allows to reduce the number of defective products for processes whose modes are calculated according to limit deformations.

Mechanical logic gate design based on multi-stable metamaterial with multi-step deformation

Mechanical metamaterials exhibit remarkable design versatility, enabling a series of unconventional mechanical properties via structural modifications. However, it is worth noting that many existing mechanical metamaterials either possess a singular deformation path or only multi-step deformation paths without reusability. This study proposes a novel multi-step deformation metamaterial that possesses multiple stable configurations. This metamaterial produces a unique two-step deformation mode under displacement loading, where the curved beams of the unit cells undergo snap-through and the vertical beams buckling. The influence of geometrical parameters on the multistability of the structure is thoroughly examined, and a theoretical prediction model for the buckling load is formulated. To validate the accuracy of the model, experimental tests and finite element simulations are conducted on the two-step deformation mode of periodic array of the unit cell. Additionally, a bi-material design approach for the unit cell is further introduced to enhance the specific energy absorption of the structure while reinforce the negative stiffness effect. Leveraging the multistable characteristics of the structure, mechanical logic gates such as AND, OR, NOT and NAND are conceptualized and experimentally validated. Through the implementation of rational designs and combinatorial connections within the logic gate structure, more complex logic operations can be realized.

Excellent low-temperature toughness of 1 GPa grade microlaminated 5Mn steel containing retained austenite

The development of high-strength steels with excellent low-temperature toughness continues to present significant challenges. Delamination toughening and retained austenite (RA) toughening are effective methods for improving the low-temperature toughness of steels. In the present study, medium manganese steel with a microlaminated microstructure containing blocky RA is prepared by intercritical rolling (IR). A comparative steel with a microstructure containing annealed martensite and film-like and blocky RA is generated by hot rolling and intercritical annealing (HRIA). The different microstructure morphologies lead to different fracture characteristics. The IR steel plate exhibited a delaminated fracture that changes the crack propagation path, inducing large-scale and severe plastic deformation in the area below the delaminated crack in the entire temperature range (RT ∼ −196 °C). The Charpy impact V-notch absorbed energy (CVN) is as high as 450 ± 7 J at −60 °C. Moreover, the fracture behavior of the HRIA steel was similar to that of steels with equiaxed microstructures; ductile fracture takes place (above −40 °C) first, followed by brittle fracture, and the CVN is only 150 ± 83 J at −60 °C. The RA contents of the IR and HRIA steels at RT are 25.8% and 22.3%, respectively. Upon impact at −60 °C, the RA content becomes 0 and 4% in the IR and HRIA steels, respectively. Finally, a toughening mechanism is established for IR steel from the perspectives of crack propagation and microstructure evolution.