Bent Shape Research Articles

Investigation of scalable chiral metamaterial beams for combined stiffness and supplemental energy dissipation

Abstract Metamaterials have gained important interest in the research community attributable to advances in additive manufacturing enabling their fabrication at reasonable costs. The vast majority of their applications and demonstrations are at micro- and nano-scales, and challenges remained regarding the larger scale applications. In this paper, we are interested by the scalability of metamaterials, targeting structural engineering applications. To do so, we explore mechanisms capable of providing both bending stiffness and high-performance energy dissipation. Our study includes beams constructed with chiral topologies of different structural hierarchy orders, and we also explore three new topologies that we termed chiral friction, chiral-rectangular and chiral-hexagonal design to engineer the beams and the use of friction rods with tunable post-stress that inserted longitudinally through the beams to provide enhanced friction. The mechanical performance of the metamaterial beams is characterized through a series three-point bending tests. Of interest is to evaluate the bending stiffness, shape recoverability, and energy dissipation capabilities. We find that the chiral-hexagonal topology equipped with a non-stressed friction rod exhibit excellent energy dissipation capabilities, showing an improved loss factor by 11.9 times compared to the control beam using 68% of its materials density. Moreover, the use of the post-stress mechanism shows that it is possible to augment both its shape recovery and bending stiffness up to 99.3% and 47.1%, respectively. Overall, our investigation shows that it is possible to engineer scalable metamaterial beams targeting structural engineering applications, and that the use of topology optimization and strategically designed post-tensioning mechanism can allow tuning of mechanical performance.

Structural response of glass fiber-polymer composite bending-active elastica beam under long-term loading conditions

Bending-active elastica beams represent structural members which are initially installed as straight beams and then bent into arched shapes by applying horizontal displacements to one support. Designing such members for permanent structures made of fiber-polymer composites involves complex viscoelastic responses, which have not yet been thoroughly investigated. An experimental investigation of medium-scale bending-active elastica beams, consisting of pultruded glass fiber-polymer composite profiles, was thus conducted to investigate the long-term structural behavior of such members under imposed sustained bending and axial compression. The results revealed that viscoelastic responses are based on an interaction of stress relaxation and creep with their effects increased with increasing bending degree and time of exposure to sustained strains and stresses. The imposed horizontal displacement to one of the supports to maintain the bent beam shape induced sustained bending stresses in the beam. Beneficial relaxation of these stresses occurred with relaxation predicted to reach 12 % during a targeted 50-year design service life. Furthermore, the likelihood of the curved beam exhibiting in-plane deformations under sustained stresses enabled creep to occur simultaneously, with associated in-plane creep deformations and strength reduction. While creep deformations remained insignificant, progressive creep rupture occurred at highest bending degrees, exhibiting sequential creep rupture in the outer combined mat layers, delamination, crack opening and final fiber failure. Creep rupture can be prevented by postponing crack initiation in the combined mat layer beyond the targeted design service life. This can be achieved by limiting the bending degree to 50 % of the bending degree at which short-term crack initiation occurs.

Numerical analysis of energy dissipation due to eddy currents in a vibrating beam

Vibration attenuation is a key aspect of mechanical engineering. One method to achieve this is through eddy currents, which can be generated in a vibrating system when a magnetic field is present, creating forces that oppose motion. This study examines a mechanical system consisting of a thin cantilever beam vibrating in a uniform and time-invariant magnetic field under steady-state conditions to understand the nature of energy dissipation and the relationship between motion, eddy currents, and damping forces. The calculation of eddy currents generally requires the use of complex numerical procedures. However, for systems with simple geometry, such as a cantilever beam, a recent numerical procedure based on the finite difference method, known for its simplicity in implementation, has been adapted and expanded to determine eddy currents under motional induction. A numerical application has been developed in which the vibration of a specific beam is characterised by its bending or torsional mode shapes, and the nature of the corresponding dissipative forces is analysed. Results indicate that the eddy currents are an effective means of dissipating energy at lower-order modes. Additionally, the direction of the applied magnetic field can induce coupling between bending and torsional vibrations.

Omnidirectional optic fiber shape sensor for submarine landslide monitoring

In-situ submarine landslide monitoring is imperative for ensuring the safety of ocean infrastructures, although it poses greater challenges compared to conventional landslide monitoring methods. In response to this need, we developed an omnidirectional optic fiber shape sensor (OFSS) and a self-contained submarine landslide monitoring system. Wavelength division multiplexing (WDM) and space division multiplexing (SDM) are used to build 10 omnidirectional curvature sensors with 3 fiber Bragg gating (FBG) arrays. Difference curvature demodulation algorithm is introduced to eliminate bending-irrelative effects. The omnidirectional curvature transmission matrix (OCTM) is obtained through calibration process with standard curvature molds. Frenet algorithm is used to recovery the shape. Laboratory experiments demonstrate OFSS’s ability to monitor 3D shape in real time, achieving the deflection error of 0.23 % and the bending direction error of 0.06 rad in the simple bending shape recovery experiment. In the S-shape recovery experiment, the OFSS’s deflection error is 0.77 % and the bending direction error is 0.04 rad. Subsequently, the system underwent testing in shallow water within a ship dock. In this experiment, the OFSS is successfully penetrated into the seabed and remained embedded in the soil for 90 min. The maximal shift observed at the end of the OFSS is 4.61×10-3m with the standard deviation of 9.95×10-4m, while the bending direction exhibited a maximal shift of 3×10-3 rad with the standard deviation of 7.51×10-4rad over the course of the 90-minute duration. These results validate the system’s effectiveness in providing accurate and reliable in-situ monitoring of submarine landslide.

Prediction of the Upwarp Buckling Critical Temperature Rise for Longitudinally Connected Slab Track Under Joint Damage State

The joint of longitudinally connected slab track is vulnerable to damage from environmental impacts and repeated train loads. Under high temperature environments, the joint becomes a high risk area for track slab upwarp, which significantly affects the upwarp stability of the track slab and the safe operation of trains. This study employs the arc length approach and a finite element model to investigate the upwarp equilibrium development path of the track slab, the upwarp evolution process of the track slab under the joint damage is further analyzed. Then, the influence of different initial defects on the vertical stability of the track slab is studied. Utilizing dimensional analysis, a general formula for calculating the critical temperature rise of the track slab is proposed. The results are as follows: (1) The entire upwarp process of track slab under joint damage can be divided into three stages: stability, upwarping development, and instability. (2) A nonlinear correlation exists between the upwarp critical temperature rise of the track slab and three types of initial defects. Height defects in narrow joints exert the most significant impact on the critical temperature rise, followed by initial Out-of-straight (initial OOS), with the initial bending shape having the least effect. The complete defect of the narrow joint reduces the upwarp critical temperature rise of the track slab by 53.26°C, a 48.4% reduction. (3) A unified expression, derived from the characteristic parameters of initial defects and dimensional analysis, can more accurately predict the upwarp critical temperature rise of the track slab.

Analyzing the chemical environment of bent bamboo (Phyllostachys iridescens) sections using XRD, XPS, and FTIR analysis

ABSTRACT Bamboo exhibits remarkable flexibility and bent shape stability in thermal-bending. To explore how bamboo responds to bending, this study investigated the chemical properties on the concave, middle and convex walls (marked as CW, MW, VW respectively) of bent bamboo Phyllostachys iridescens though XRD, XPS, and FTIR analyses. Results indicate a reduction in crystallinity from 42% of MW to 39% of CW and 40% of VW. Notably, the peak shifts of CW and VW indicates the neutral layer on CW and VW experience an offset toward the convex surface. Chemical degradation varies on the thermal bent bamboo sections, the O/C ratio increases from 0.26 of MW to 0.36 of CW, accompanied a decrease in the Cox/unox ratio from 0.93 of MW to 0.81 of VW. This indicates that VW undergoes more significant degradation of cellulose and hemicelluloses, while CW experiences a greater loss of extracts. Additionally, FTIR analysis indicates that the ester bond peak at 1731 cm−1 flattens on CW, while it splits into two peaks on VW, with one of the peaks shifting to a higher wavenumber of 1735 cm−1. This suggests a reduction in the intermolecular distance between lignin and hemicelluloses on CW, whereas a higher lignin content and compression stress on VW.

Designing highly efficient interlocking interactions in anisotropic active particles

Cluster formation of microscopic swimmers is key to the formation of biofilms and colonies, efficient motion and nutrient uptake, but, in the absence of other interactions, requires high swimmer concentrations to occur. Here we experimentally and numerically show that cluster formation can be dramatically enhanced by an anisotropic swimmer shape. We analyze a class of model microswimmers with a shape that can be continuously tuned from spherical to bent and straight rods. In all cases, clustering can be described by Michaelis-Menten kinetics governed by a single scaling parameter that depends on particle density and shape only. We rationalize these shape-dependent dynamics from the interplay between interlocking probability and cluster stability. The bent rod shape promotes assembly in an interlocking fashion even at vanishingly low particle densities and we identify the most efficient shape to be a semicircle. Our work provides key insights into how shape can be used to rationally design out-of-equilibrium self-organization, key to creating active functional materials and processes that require two-component assembly with high fidelity.

Rapid predictions of pressure and velocity fields in a 5 × 5 bending fuel assembly based on a POD-based black-box model

The fuel assembly is crucial in pressurized water reactors (PWRs) as it can undergo bending deformation due to flow-induced vibrations (FIVs), impacting its flow characteristics. To evaluate the effect of different bending scales on flow behaviors, the Computational Fluid Dynamics (CFD) model of 5 × 5 fuel assembly is developed. This configuration considers common beam-like deformations: 1st-order C-shape, 2nd-order S-shape, and 3rd-order W-shape. The flow characteristics of the 5 × 5 bending fuel assembly with bending scales of 1 mm and 2 mm are studied, aiming to explore how variations in deformation scales impact these flow characteristics. Subsequently, CFD simulations are conducted for various flow velocities, bending shapes, and scales, with the simulation results organized into a snapshot matrix. Through the Proper Orthogonal Decomposition (POD) method, both the POD coefficients and modes of the snapshot matrix are determined. A black-box model is subsequently utilized to predict the POD coefficients of non-sample cases. The research enables rapid predictions of pressure and velocity fields within a 5 × 5 fuel assembly for any given flow velocity, bending shape, and scale by integrating the predicted POD coefficients and modes. Relative to comprehensive CFD simulations, the POD-based black-box model presented in this study provides a rapid and precise approach for pressure and velocity fields prediction, demonstrating its effectiveness and accuracy.

Double-Helical Tiled Chain Structure of the Twist-Bend Liquid Crystal Phase in CB7CB

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πRmol, where Rmol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.

Visually encoding orthogonal planar graph drawings as graph mazes: An eye tracking study

There are various styles to visually represent relational data in the form of node-link diagrams. In particular, for planar graphs we can find orthogonal node-link diagrams consisting of links bending only at ninety degrees a successful and prominent variant. One of the benefits of such drawings is the tracking of longer paths through a network with the eyes due to their limited number of link orientations, changes, and variations, but on the negative side the links can have arbitrary bending shapes. In this article we developed a novel way to visualize such orthogonal planar drawings by making use of mazes that look more natural to the human eye due to the street-like visual metaphor that many people are familiar with. Tracking paths is one of the major tasks in such graph visualizations, similar to orthogonal node-link diagrams, however, we argue that mazes are a more natural way to find paths. To get insights in the visual scanning behavior when reading graph mazes we conducted a comparative eye tracking study with 26 male versus female participants of different experience levels while also alternating between orthogonal node-link drawings and graph mazes as well as different graph size levels. The major result of this comparative study is that the participants can track paths in both representation styles, including a geodesic path tendency in their visual search behavior, but typically have a longer fixation duration at branching nodes and locations in the mazes that lead to opposite directions to the geodesic path tendency, maybe the viewers had to start a reorientation phase in their visual scanning behavior. We also found out that the size, that is the number of graph vertices has an impact on the visual scanning behavior for both orthogonal node-link diagrams as well as street-like maze representations, but for the mazes we found this impact to be less strong (in terms of the eye movement data metrics fixation durations and saccade lengths) compared to the node-link diagrams. To conclude the article, we discuss limitations and scalability issues of our approach. Moreover, we give an outlook and future work for possible extensions.

Design and Driving Performance Study of Soft Actuators for Hand Rehabilitation Training.

To address the application requirements of soft actuators in rehabilitation training gloves, and in combination with ergonomic requirements, we designed a segmented soft actuator with bending and elongation modules. This actuator can achieve independent or coupled movements of the finger joints. A finite element model of the joint actuator was established to compare the driving performance of actuators with different structural forms. Numerical calculations were used to analyze the effects of structural size parameters on the bending characteristics and end output force of the actuator. The design was then refined based on these analyses. The joint actuator designed in this study demonstrated a 71% increase in bending angle compared to the standard fast pneumatic network structure. Key factors affecting the driving performance include the thickness of the constraint layer, the inner wall thickness of the chamber, chamber height, chamber width, chamber spacing, chamber length, and the number of chambers. After improvements, the bending angle of the joint actuator increased by 60.6%, and the output force increased by 145.9%, indicating significant improvement. This study designed and improved a soft actuator for hand rehabilitation training, achieving independent and coupled joint movements. The bending angle, bending shape, and joint driving force of the soft actuator meet the requirements for finger rehabilitation training.

Shape Sensing and Kinematic Control of a Cable-Driven Continuum Robot Based on Stretchable Capacitive Sensors.

A Cable-Driven Continuum Robot (CDCR) that consists of a set of identical Cable-Driven Continuum Joint Modules (CDCJMs) is proposed in this paper. The CDCJMs merely produce 2-DOF bending motions by controlling driving cable lengths. In each CDCJM, a pattern-based flexible backbone is employed as a passive compliant joint to generate 2-DOF bending deflections, which can be characterized by two joint variables, i.e., the bending direction angle and the bending angle. However, as the bending deflection is determined by not only the lengths of the driving cables but also the gravity and payload, it will be inaccurate to compute the two joint variables with its kinematic model. In this work, two stretchable capacitive sensors are employed to measure the bending shape of the flexible backbone so as to accurately determine the two joint variables. Compared with FBG-based and vision-based shape-sensing methods, the proposed method with stretchable capacitive sensors has the advantages of high sensitivity to the bending deflection of the backbone, ease of implementation, and cost effectiveness. The initial location of a stretchable sensor is generally defined by its two endpoint positions on the surface of the backbone without bending. A generic shape-sensing model, i.e., the relationship between the sensor reading and the two joint variables, is formulated based on the 2-DOF bending deflection of the backbone. To further improve the accuracy of the shape-sensing model, a calibration method is proposed to compensate for the location errors of stretchable sensors. Based on the calibrated shape-sensing model, a sliding-mode-based closed-loop control method is implemented for the CDCR. In order to verify the effectiveness of the proposed closed-loop control method, the trajectory tracking accuracy experiments of the CDCR are conducted based on a circle trajectory, in which the radius of the circle is 55mm. The average tracking errors of the CDCR measured by the Qualisys motion capture system under the open-loop and the closed-loop control are 49.23 and 8.40mm, respectively, which is reduced by 82.94%.

Flexible organic crystal with dual mechanical bending capabilities and optical waveguiding directionality

The study of organic luminescent crystal material has become a hot topic in the field of flexible optoelectronics. In this context, we report a crystal of 2,5-dihydro-3,6-bis (pentanamine) dimethyl terephthalate, which exhibits the unique property of self-doping, coupled with dual mechanical bending capabilities. Notably, the crystal exhibits optical waveguide properties, which highlights its potential application in flexible optoelectronics. In this work, through a simple "self-doping” process and controlled morphology, we obtained the synthesis of high-quality bulk organic crystals of varied sizes that not only bend elastically but also bend plastically as the molecular layer undergoes slippage. Subsequent, analysis of the crystal structure was conducted to investigate the reason for its dual mechanical bending capabilities. Our findings suggested that the optical waveguide is not only available in linear shape, elastic bending shape, and plastic bending shape, but also in large-size flake crystals. More importantly, the propagation of light in this crystal is directional owing to the anisotropy of the crystals. It is also proven that organic crystals have the potential to be applied in advanced optoelectronic devices, offering the possibility of their application as directional waveguide materials.

Origin of bent ridge-kink based on disclination relaxation

In this study, we have developed a geometric model for bent kinks by introducing sequences of ortho-connected kink bands into ridge-kinks to provide insights into the possible reasons why kinks are bent and the resulting geometry when they are bent. We first formulated the Frank angles and coordinates of the disclinations formed in the bent kinks, which enable our discussion on the influence of the introduction of ortho-kinks on the Gibbs energy by utilizing Romanov’s disclination model. It turns out that the introduction of ortho-kinks can relax the elastic strain energy and thus reduce the Gibbs energy of the system under compression states with lower external stresses. On the other hand, the introduction of ortho-kinks increases the Gibbs energy at higher compression stresses, implying sharp ridge-kinks are preferred under such conditions. This trend resembles the experimental observations reported by previous studies that the shapes of newly formed kinks tend to transition from pre-kinks with bent shapes to ridge-kinks with sharp shapes as the compression test progresses. The smoothly bent kink with smoothly distributed misorientation, formed by increasing the number of introduced ortho-kinks, can further reduce the Gibbs energy at lower applied stresses. Subsequently, based on the Rank-1 condition for the connection of kink bands, we further analyzed the geometry of such smoothly bent kinks and derived the analytical equations for the constraints on the orientation distribution. Finally, we conducted EBSD measurements on bent kinks observed in directionally solidified (DS) LPSO-Mg alloys and confirmed that the derived equations for the orientation distribution are in good agreement with the experimental results.

Experimental and Numerical Study of the Flow Around Rigid and Flexible Hydrofoils for Wetted and Cavitating Flow Conditions

Abstract The hydro-elastic response of a flexible NACA 0015 hydrofoil is investigated for both wetted and cavitating flow conditions. Computational fluid dynamics (CFD) analysis are performed using a fully implicit coupling between the ISIS-CFD solver (developed by the METHRIC team at Ecole Centrale de-Nantes) and a modal approach for the structure. The Reynolds-averaged Navier–Stokes (RANS) solver is first validated for wetted and cavitating flow conditions around a similar rigid hydrofoil, with experimental results carried out at the hydrodynamic tunnel of the French Naval Academy, including lift and drag measurements and high speed camera images. Then the numerical predictions for the flexible hydrofoil response are compared with experimental bending shapes and vibrations amplitudes, with a focus on cavitating flow conditions. For wetted flow conditions, numerical results show a good agreement with the experiments, for both rigid and flexible hydrofoils. For cavitating flow conditions, the hydro-elastic response is dominated by vibrations at the hydrofoil modal frequencies and the reentrant jet instability frequency. For the lowest values of the cavitation number, a large amplitude peak is experimentally observed in the frequency response spectra, due to lock-in between the first modal frequency and the reentrant jet frequency. Strong harmonics of this dominant peak also appear in the spectra, revealing a nonlinear response of the hydrofoil. While the amplitudes of vibrations are well predicted by the computations, the frequency lock-in observed in the experiments is not captured by the numerical model.

Influence of spatial variability in surrounding rock on fracture propagation in compressed air energy storage caverns

The expansion of fractures around underground caverns for compressed air energy storage (CAES) has a significant impact on engineering stability. We established a thermo-mechanical coupled random phase field model to investigate the trajectory of fractures in the heterogeneous surrounding rock of underground gas storage caverns. By simulating the different mechanical parameters under different coefficients of variation and autocorrelation distances, we explored the impact of spatial variability of rock mass on the fracture mode of surrounding rock in underground gas storage caverns. The results indicate that when only the spatial variability of elastic modulus is considered, the coefficient of variation primarily affects the inclination and curvature degree of fractures while the autocorrelation distance has a slight impact on the bending shape of fractures. When only the spatial variability of fracture energy release rate is considered, both the coefficient of variation and the autocorrelation distance have a negligible effect on fracture propagation. Compared with the elastic modulus of the rock mass, the fracture energy release rate has a more significant impact on the path of the cavern fractures.

The influence of the middle bending shape of the blade on the performance of a pump as turbine

As a kind of energy-saving and micro-hydropower utilization device, pump as turbine (PAT) is simple to construct with low operation and maintenance costs, which is widely used in the energy-consuming industrial processes and micro-hydro power generation. The variation law of blade angle from blade inlet to outlet has the characteristics of uncertainty and diversity, which determines the middle bending shape of the blade and has a direct impact on the fluid. Different blade bending shapes form different wrap angles on the premise of impeller outlet and inlet angles kept invariable. To investigate how the blade angle distribution affects the performance, four different impellers were created and analyzed based on computational fluid dynamics method. This paper investigates the effect of blade bending shapes on the performance characteristics, unsteady characteristics and energy loss of PAT. The numerical result shows due to the small blade wrap angle, the best efficiency of scheme 2 is the lowest among the four schemes, while the best efficiency of scheme 4 is the highest. The appropriate blade bending shape is beneficial to reduce the enstrophy dissipation and improve the efficiency and operating stability of PAT. These findings provide reference points for optimizing the blade profile in PAT.

Bending performance analysis of variable stiffness composite laminates

AbstractFor fiber‐reinforced polymer structures, the out‐of‐plane stiffness is much lower than the in‐plane stiffness and is extremely prone to damage and instability. The potential of variable stiffness (VS) laminates was explored to enhance the stiffness in the thickness direction. Based on the finite strip method (FSM), a semi‐analytical solution for bending problems of laminates was derived, which is called the variable‐stiffness discrete strip (VSDS) method. By comparing with traditional constant stiffness (CS) laminates, the influence of design parameters of VS laminates on the bending shape and stress distribution of laminates under two load cases were studied. Combining the results of FE models, the accuracy of VSDS has been verified, and the strategy of VS layout configuration design to improve the bending resistance was proved.Highlights Variable stiffness discrete strips (VSDS) method was presented based on FSM. Bending performances of VS laminates under two load conditions were studied. The method has the ability to reduce the computation cost of bending problems. The solutions of VSDS agree well with the results of FE models. The improvement mechanism of VS laminates on bending resistance was explored.

Is Simultaneous Binding to DNA and Gyrase Important for the Antibacterial Activity of Cystobactamids?

Cystobactamids are aromatic oligoamides that exert their natural antibacterial properties by inhibition of bacterial gyrases. Such aromatic oligoamides were proposed to inhibit α-helix-mediated protein-protein interactions and may serve for specific recognition of DNA. Based on this suggestion, we designed new derivatives that have duplicated cystobactamid triarene units as model systems to decipher the specific binding mode of cystobactamids to double stranded DNA. Solution NMR analyses revealed that natural cystobactamids as well as their elongated analogues show an overall bent shape at their central aliphatic unit, with an average CX-CY-CZ angle of ~110 degrees. Our finding is corroborated by the target-bound structure of close analogues, as established by cryo-EM very recently. Cystobactamid CN-861-2 binds directly to the bacterial gyrase with an affinity of 9 μM, and also exhibits DNA-binding properties with specificity for AT-rich DNA. Elongation/dimerization of the triarene subunit of native cystobactamids is demonstrated to lead to an increase in DNA binding affinity. This implies that cystobactamids' gyrase inhibitory activity necessitates not just interaction with the gyrase itself, but also with DNA via their triarene unit.

The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature.

Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (δK) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing δK forming the hallmark of aortic disease. Divergent δK is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8±1.7%. The analysis of δK can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes.