Bending Stiffness Research Articles

Scale-inspired programmable robotic structures with concurrent shape morphing and stiffness variation.

Biological organisms often have remarkable multifunctionality through intricate structures, such as concurrent shape morphing and stiffness variation in the octopus. Soft robots, which are inspired by natural creatures, usually require the integration of separate modules to achieve these various functions. As a result, the whole structure is cumbersome, and the control system is complex, often involving multiple control loops to finish a required task. Here, inspired by the scales that cover creatures like pangolins and fish, we developed a robotic structure that can vary its stiffness and change shape simultaneously in a highly integrated, compact body. The scale-inspired layered structure (SAILS) was enabled by the inversely designed programmable surface patterns of the scales. After fabrication, SAILS was inherently soft and flexible. When sealed in an elastic envelope and subjected to negative confining pressure, it transitioned to its designated shape and concurrently became stiff. SAILS could be actuated at frequencies as high as 5 hertz and achieved an apparent bending modulus change of up to 53 times between its soft and stiff states. We further demonstrated both the versatility of SAILS by developing a soft robot that is amphibious and adaptive and tunable landing systems for drones with the capacity to accommodate different loads.

Numerical Evaluation of the Influence of Using Carbon-Fiber-Reinforced Polymer Rebars as Shear Connectors for Cross-Laminated Timber–Concrete Panels

Carbon fiber-reinforced polymer (CFRP) sheets have been used to reinforce cross-laminated timber (CLT)–concrete systems in recent years. The existing studies have indicated that the use of CFRP rebars as shear connectors in CLT–concrete panels can improve the structural performance of these elements. However, the application and understanding of CFRP rebars as shear connectors still need to be improved, since comprehensive studies on the subject are not available. Therefore, this research aimed to evaluate the structural performance of CLT–concrete panels with CFRP rebars as shear connectors through finite element (FE) numerical simulation. A parametric study was conducted, varying the connector material, the number of CLT layers, the connector insertion angle, and the connector embedment length. According to the results, panels with CFRP connectors showed a higher maximum load, bending strength, and maximum bending moment than panels with steel connectors. The regression models revealed that the parameters analyzed explained between 80.2% and 99.9% of the variability in the mechanical properties under investigation. The high explanatory power (R2) of some regression models in this study underscores the robustness of the models. The number of CLT layers and the connector material were the most significant parameters for the panels’ maximum load, displacement at the maximum load, ductility, bending strength, and maximum bending moment. The number of CLT layers and the connector insertion angle were the most significant parameters for the panels’ effective bending stiffness. This research highlights the importance of studies on CLT–concrete composites and the need to develop equations to estimate their behavior accurately. Moreover, numerical simulations have proven very valuable, providing results comparable to laboratory results.

Numerical Study on the Mechanical Performance of a Flexible Arch Composite Bridge with Steel Truss Beams over Its Entire Lifespan

Steel truss–arch composite bridge systems are widely used in bridge engineering to provide sufficient space for double lanes. However, a lack of research exists on their mechanical performance throughout their lifespan, resulting in uncertainties regarding bearing capacity and the risk of bridge failure. This paper conducts a numerical study of the structural mechanical performance of a flexible arch composite bridge with steel truss beams throughout its lifespan to determine the critical components and their mechanical behavior. Critical vehicle loads are used to assess the bridge’s mechanical performance. The results show that the mechanical performance of the bridge changes significantly when the temporary piers and the bridge deck pavement are removed, substantially influencing the effects of the vehicle loads on the service life. The compressive axial force of the diagonal bar significantly increases to 33,101 kN near the supports during the two construction stages, and the axial force in the upper chord of the midspan increases by 4.1 times under a critical load. Moreover, the suspender tensions and maximum vertical displacement are probably larger than the limit of this bridge system in the service stage, and this is caused by the insufficient longitudinal bending stiffness of truss beams. Therefore, monitoring and inspection of critical members are necessary during the removal of temporary piers and bridge deck paving, and an appropriate design in steel truss beams is required to improve the life cycle assessment of this bridge system.

Curvature programming of freestanding 3D mesostructures and flexible electronics based on bilayer ribbon networks

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

Damage detection for continuous beams by using the tap-scan method

Damage detection for bridges using a passing vehicle has drawn much interest. Recent studies demonstrate that the tap-scan method is an efficient way to detect the change of beam bending stiffness. A quantitative relationship between the change of beam bending stiffness and the acceleration of a vehicle can be evaluated. However, the reported relationship is calibrated for a simply-supported beam, which may be unsuitable for continuous beams due to inherent structural differences. Addressing this, an analytical solution for damage detection for continuous beams using the tap-scan method is presented in this paper. Case studies reveal that damage relationships across different spans of continuous beams show negligible dependence on modal parameters and beam lengths. Consequently, the damage identification within any span of a continuous beam can be accomplished using the same damage relationship calibrated on a simply-supported beam. But it should be noticed that the damage relationship might differ by beam structural forms. The above result holds substantial implications for practical engineering scenarios, notably by diminishing the labor and complexity associated with the calibration of damage relationships for continuous beams.

Shear behavior of seawater sea-sand concrete beams reinforced with BFRP bars after seawater dry-wet cycling

The shear behavior of 27 basalt fiber-reinforced polymer reinforced seawater sea-sand concrete (BFRP-SSC) beams after seawater dry-wet cycling was comprehensively investigated. Parameters considered included stirrup diameter and spacing, shear span-to-depth ratio, stirrup surface treatment, cycling duration, concrete cover thickness, and seawater temperature. Results indicate that seawater dry-wet cycling increases cracking load and decreases bending stiffness in BFRP-SSC beams. Increasing shear span-to-depth ratio from 1.55 to 2.35 led to load reductions of 31.3 % and 49.7 % at 6.5 mm mid-span deflection. Seawater dry-wet cycling, particularly temperature and duration, significantly impacts the mechanical properties of stirrups. This results in diminished shear contribution and reduced efficacy in inhibiting diagonal crack propagation, leading to a shift in beam failure mode from diagonal compression failure to shear compression failure and diagonal tension failure. Increasing cycling duration from 60 to 120 days decreased tensile strength retention by 19.1 % and 33.3 % respectively. Based on experimental data, Arrhenius theory, and the time shift factor (TSF) method, a predictive model was developed for the shear capacity retention of beams subjected to seawater dry-wet cycling. Results indicate that after 100 years in a tidal environment (70 % and 90 % relative humidity), shear capacity damage factors of 0.77 and 0.52, respectively, can be applied to account for the impact of seawater dry-wet cycling on the shear capacity of BFRP-SSC beams.

Toward the Manufacturing of a Non-Toxic High-Performance Biobased Epoxy-Hemp Fibre Composite.

This study describes the production of a new biobased epoxy thermoset and its use with long hemp fibres to produce high-performance composites that are totally biobased. The synthesis of BioIgenox, an epoxy resin derived from a lignin biorefinery, and its curing process have been optimised to decrease their environmental impact. The main objective of this study is to characterise the rheology and kinetics of the epoxy system with a view to optimising the composite manufacturing process. Thus, the epoxy resin/hardener system was chosen considering the constraints imposed by the implementation of composites reinforced with plant fibres. The viscosity of the chosen mixture shows the compatibility of the formulation with the traditional implementation processes of the composites. In addition, unlike BPA-a precursor of diglycidyl ether of bisphenol A (DGEBA) epoxy resin-BioIgenox and its precursor do not have endocrine disrupting activities. The neat polymer and its unidirectional hemp fibre composite are characterised using three-point bending tests. Results measured for the fully biobased epoxy polymer show a bending modulus, a bending strength, a maximum strain at failure and a Tg of, respectively, 3.1 GPa, 55 MPa, 1.82% and 120 °C. These values are slightly weaker than those of the DGEBA-based epoxy material. It was also observed that the incorporation of fibres into the fully biobased epoxy system induces a decrease in the damping peak and a shift towards higher temperatures. These results point out the effective stress transfers between the hemp fibres and the fully biobased epoxy system. The high mechanical properties and softening temperature measured in this work with a fully biobased epoxy system make this type of composite a very promising sustainable material for transport and lightweight engineering applications.

Exploring the influence of native minerals in coal gangue on CG/PE composite manufacturing and performance: Examining SiO2's role in interfacial compatibility

AbstractThis study delves into the influence of inherent minerals within coal gangue (CG) on the preparation and performance of coal gangue /polyethylene (CG/PE) composites, focusing on the role of SiO2 in interfacial compatibility. A systematic examination unveils the consequences of varying SiO2 content on physical, mechanical, thermal, and microstructural attributes of the composites. SiO2 incorporation significantly improves physical properties, boosting density and hardness but impacting tensile strength negatively. It enhances bending strength and modulus while diminishing tensile strength. Judicious SiO2 addition enhances thermal stability, but excess SiO2 may compromise thermal decomposition. Microstructural analysis, including SEM and FTIR, elucidates SiO2‐PE interactions, primarily through physical entanglement. SiO2 introduction promotes more ordered PE molecular chain arrangements, elevating composite crystallinity. In summary, this study provides in‐depth insights into SiO2's mechanistic impact on CG/PE composite properties, laying a robust foundation for designing environmentally friendly composites. These findings hold promise for advancing sustainable materials science and engineering. Future research may explore SiO2 optimization for specific applications and synergistic effects with other fillers in composites.Highlights SiO2 greatly improves the properties of CG/PE composites with detailed exploration. Reveals the specific SiO2‐PE interaction mechanism for a better comprehension. Performs structural analysis via XRD with valuable findings presented. Promotes pioneering advancements in eco‐friendly materials with broad significance.

Broadening bandgaps in a multi-resonant piezoelectric metamaterial plate via bandgap merging phenomena

Locally resonant metamaterials usually have narrow bandgaps, which significantly limits their applications in realistic engineering environments. In this paper, an optimization method based on the genetic algorithm is proposed to broaden bandgaps in multi-resonant piezoelectric metamaterial through the merging of multiple separated bandgaps. Using the effective medium theory, the equivalent bending stiffness and dispersion relationship of a metamaterial plate are first obtained. Then, the criteria for determining the bandgap ranges for the two cases with and without damping are provided and analyzed. Furthermore, based on the bandgap merging phenomena, an optimization method for widening the bandgap is proposed based on the genetic algorithm. By investigating the bandgap widening effects in cases without and with damping, it is found that, when there is no damping, the bandgap can only be slightly widened; while after introducing damping into the transfer functions, the bandgap can be significantly widened by more than 200%. The bandgap widening effects are verified by comparing with finite element simulation results.

Phase-State-Dependent Silica Nanoparticle Uptake of Giant Unilamellar Vesicles.

We quantify endocytosis-like nanoparticle (NP) uptake of model membranes as a function of temperature and, therefore, phase state. As model membranes, we use giant unilamellar vesicles (GUV) consisting of 1,2-dipentadecanoyl-sn-glycero-3-phosphocholine (15:0 PC). Time-series micrographs of the vesicle shrinkage show uptake rates that are a highly nonlinear function of temperature. A global maximum appears close to the main structural phase transition at T = Tm + 3 K = 37 °C and a minor peak at the pretransition T = Tp = 22 °C. The quality of linear fits to the shrinkage, and thus uptake kinetics, reveals a deviation from the linear trend at the vesicle shrinkage peaks. Taking values for the bending modulus as a function of temperature from literature and Helfrich's model allows us to draw qualitative conclusions on the membrane tension and the adhesion of the NP to the membrane as a function of temperature. These findings provide valuable insights into the dynamic interplay between temperature, membrane phase transitions, and NP uptake, shedding light on the complex behavior of biological membranes.

Novel computational model for the failure analysis of composite pipes under bending

This study presents a novel computational model to investigate the bending behaviour of thin- and thick-walled composite pipes made from fully bonded fibre-reinforced thermoplastic composite materials. The primary objective is to analyse the stress state and predict potential failure modes of these pipes, which have gained significant interest in the oil and gas industry due to their advantageous properties. The developed model is validated through comparisons with finite element analysis and published results, demonstrating its accuracy and adaptability. Utilising the validated computational model, safety zones for composite pipes with various stacking sequences are established, providing valuable insights into the optimal design of composite pipes under bending loads. Furthermore, the method is employed to determine the maximum bending moment and critical bendable radius of the pipe, revealing the direct correlation between maximum bending moment and bending stiffness, independent of the bending radius. The findings of this study offer practical guidance for the design and optimisation of composite pipes in the oil and gas industry, promoting their adoption as a viable alternative to traditional metal pipes. The developed computational model serves as an efficient and reliable tool for engineers to make informed decisions in the design and selection of advanced composite materials for pipe applications, enabling the optimisation of pipe performance under various bending load scenarios.

Flexoelectric and surface effects on bending deformation and vibration of piezoelectric nanolaminates: Analytical solutions

In this paper, a model of double-layer rectangular piezoelectric nanolaminates with different upper and lower surface properties is established. The bending and vibration behavior of the piezoelectric nanolaminates are evaluated and analyzed, taking into consideration the flexoelectric and surface effects. Utilizing the surface piezoelectric model, flexoelectric theory, and Kirchhoff plate theory, this study provides analytical solutions for the bending deflection and natural frequency of rectangular piezoelectric nanolamination materials under various boundary conditions. The results indicate that the effects of flexoelectric and surface influences on piezoelectric nanolaminates are associated with residual surface stress and flexoelectric coefficients. These effects can enhance the bending stiffness and decrease the natural frequency of the piezoelectric nanolaminates. Furthermore, altering the residual stress on the upper and lower surfaces of the laminates separately will result in different trends in bending deflection, while causing a consistent trend in natural frequency change. When the electric potential direction of piezoelectric nanolaminates is different, the bending deflection of piezoelectric nanolaminates will change accordingly. The natural frequency of piezoelectric nanolaminates is determined by the absolute value of the flexoelectric coefficients, and is independent of their positive or negative values. Both the surface effect and the flexoelectric effect are influenced by size-dependent behaviors. When the thickness of the laminates is sufficiently large, both the surface effect and flexoelectric effect can be disregarded. This paper's research methods and results provide theoretical models and analytical methods for the microstructure design, multi-physical field characterization, and bending deformation behavior of intelligent components containing rectangular piezoelectric nanolaminates.

Synthesis of a syringaldehyde derivative to enhance the fire resistance and structural strength of epoxy resin

AbstractIn light of growing environmental apprehensions, the threat of global warming, and the depletion of oil reserves, it is advisable to opt for bio‐epoxy resins sourced from sustainable materials. In response to these issues, syringaldehyde (SH) flame retardant epoxy resin derivatives have been formulated and synthesized. Initially, SH was reacted with 4, 4‐diaminodiphenylmethane (DDM) to yield an intermediate compound, DDM‐SH. Subsequently, the inherently flame‐retardant curing agent (DDM‐SH‐DOPO) and the bio‐based epoxy monomer (DDM‐SH‐EP) were produced by reacting with DOPO and epichlorohydrin, respectively. These resulting compounds were then integrated into bisphenol A epoxy resin, enhancing its flame retardant and mechanical characteristics. The flammability was assessed through limiting oxygen index (LOI), UL‐94, and cone calorimeter tests. The DDM‐SH‐EP‐20/5 sample exhibits notable improvements. It elevates the LOI to 25.3%, achieving a UL‐94 rating to V‐0 and effectively reducing smoke and heat release from the epoxy resin. The ternary cross‐linking network formed between DGEBA, DDM‐SH‐EP, and DDM‐SH‐DOPO primarily contributes to this mechanical enhancement, DDM‐SH‐EP‐20/5 has excellent overall performance, bending strength and bending modulus are 103% and 108% higher than DGEBA/DDM. This study offers a viable solution for producing flame‐retardant epoxy resin with superior mechanical properties.

Eco-friendly, lightweight, and high-strength sandwich corrugated particleboard from tea oil camellia (Camellia oleifera Abel.) shells

This study investigates the potential of developing corrugated panels from tea oil camellia shell (TOCS), an abundant agricultural waste in the southern provinces of China, with an annual production of approximately 4 million tons, using experimental and computational methods. Hence, various corrugated geometries were designed using AutoCAD software, and finite element analysis (FEA) was conducted using Ansys Mechanical software to optimize the panel geometry based on TOCS engineering data. Bending performance simulations revealed that a trapezoidal geometry with a 3 mm edge radius exhibited superior bending performance. Therefore, this geometry was selected to fabricate corrugated panels of different densities to assess the impact of density variation. Mechanical characterization included evaluation of bending stiffness, maximum moment, total deflection, compression strength, ultimate strength, dowel bearing strength, and face screw resistance of the panels was performed. Furthermore, specific energy absorption and failure mechanisms of mechanical tests were analyzed. The results indicate that TOCS-based sandwich panels, characterized by their lightweight and sustainable nature, not only meet, or exceed the criteria specified in APA PS 2–10 for use as structural materials but also mitigate the environmental hazards associated with landfill disposal or burning of agricultural waste.

Element-wise parallel deep learning for structural distributed damage diagnosis by leveraging physical properties of long-gauge static strain transmissibility under moving loads

The Transmissibility Function (TF) has gained considerable interest in structural damage detection because of its relatively high sensitivity to damage and robustness to excitation. This study proposed a distributed damage diagnosis method for beam-like structures based on a long-gauge static strain TF defined as the ratio of the Fourier transform of static strain response under moving loads from a target long-gauge sensor to that from the reference sensor. It has been discovered that each long-gauge static strain TF is independent of moving loads, making it an ideal damage indicator. It exhibits direct proportionality to the ratio of bending stiffness between the two measured zones covered by the target and reference long-gauge strain sensors while being unaffected by the stiffness of any other zones not covered by these two sensors. Moreover, the TF at zero frequency was proved to be equivalent to the ratio of static strain time history areas, relying solely on the stiffness of the covered zones. Leveraged by the physical properties of long-gauge static strain TF, an element-wise parallel deep neural network architecture was developed to decompose damage diagnosis into independent sub-tasks on the element level, utilizing a variational autoencoder (VAE) in the Bayesian inference framework for extracting features from the long-gauge strain TF and a regressor for mapping the features to elemental stiffness reduction. The divide-and-conquer strategy and element-wise parallel learning architecture allow for a significant reduction in the number of labeled training samples generated based on the updated numerical baseline model as it only requires simulated scenarios involving a single damage element. The efficiency and robustness of the proposed method were demonstrated through a numerical simply supported beam and a laboratory experiment on a two-span bridge.

One step production from the monomer of poly(L‐lactide)/flax biocomposites by thermoplastic resin transfer molding: Mechanical properties and aging

AbstractDevelopment of biocomposites is becoming a necessity due to environmental concerns. Polylactide is a matrix of choice, regarding its bio‐sourced and compostable nature along with its mechanical properties. In this study, poly(L‐lactide)/flax biocomposites were produced using thermoplastic resin transfer molding (TP‐RTM) in one step process from the monomer, affording sustainable and fully compostable composite materials. The polymerization of L‐lactide (L‐LA) monomer was promoted by tin octoate, affording poly(L‐lactide) (PLLA) matrices displaying monomer conversions superior to 96% and mass‐average molar masses above 140,000 g/mol. Flax fibers were used as received without any functionalization which is usually conducted to prevent the hydroxyl groups to conduct side reactions. Mechanical testing revealed bending modulus of 9.3 GPa and bending strength of 177 MPa comparable to existing literature values for PLLA/flax composites produced by other techniques. Digital microscopy analysis provided insights into impregnation quality and void characterization within the composites. In addition, the durability of these biocomposites was also evaluated via accelerated aging tests.Highlights PLLA/flax biocomposites were produced by TP‐RTM for the first time. In situ polymerization of the PLLA matrix associated with non‐functionalized flax fabrics was conducted. Bending properties were found in line with those of PLLA/flax composites produced by compression molding. Aging tests under UV at 50°C of PLLA/flax biocomposites were conducted.

Evaluation on Configuration Stiffness of Overconstrained 2R1T Parallel Mechanisms

Currently, two rotations and one translation (2R1T) three-degree-of-freedom (DOF) parallel mechanisms (PMs) are widely applied in five-DOF hybrid machining robots. However, there is a lack of an effective method to evaluate the configuration stiffness of mechanisms during the mechanism design stage. It is a challenge to select appropriate 2R1T PMs with excellent stiffness performance during the design stage. Considering the operational status of 2R1T PMs, the bending and torsional stiffness are considered as indices to evaluate PMs' configuration stiffness. Subsequently, a specific method is proposed to calculate these stiffness indices. Initially, the various types of structural and driving stiffness for each branch are assessed and their specific values defined. Subsequently, a rigid-flexible coupled force model for the over-constrained 2R1T PM is established, and the proposed evaluation method is used to analyze the configuration stiffness of the five 2R1T PMs in the entire workspace. Finally, the driving force and constraint force of each branch in the whole working space are calculated to further elucidate the stiffness evaluating results by using the proposed method above. The obtained results demonstrate that the bending and torsional stiffness of the 2RPU/UPR/RPR mechanism along the x and y-directions are larger than the other four mechanisms.

Non-Classical Euler Buckling and Brazier Instability in Cylindrical Liquid Droplets.

Crystalline monolayers prevalent in nature and technology possess elusive elastic properties with important implications in fundamental physics, biology, and nanotechnology. Leveraging the recently discovered shape transitions of oil-in-water emulsion droplets, upon which these droplets adopt cylindrical shapes and elongate, we investigate the elastic characteristics of the crystalline monolayers covering their interfaces. To unravel the conditions governing Euler buckling and Brazier kink formation in these cylindrical tubular interfacial crystals, we strain the elongating cylindrical droplets within confining microfluidic wells. Our experiments unveil a nonclassical relation between the Young's modulus and the bending modulus of these crystals. Intriguingly, this relation varies with the radius of the cylindrical crystal, presenting a nonclassical mechanism for tuning of elasticity in nanotechnology applications.

Characterization of pressure-dependent nonlinear bending behavior of yarns and its application in modeling the compression of 2D woven fabrics

This paper investigates the pressure-dependent nonlinear bending behavior of yarns, which is essential for the application of the virtual fiber modeling (VFM) method in the mechanical analyses of fabrics. An experimental method, along with a theoretical model based on classical beam theory, is presented to characterize the varying bending stiffness of yarns under different pressures. A tailored beam user element is then developed, incorporating the nonlinear bending behavior and combined with a truss element to create a physics-based virtual fiber formulation. Utilizing this formulation, the original kinematic VFM method is extended for modeling the mechanical response of 2D woven fabrics under compression. The predicted results of the proposed model closely match the reported experiment, demonstrating the significance of introducing the nonlinear bending behavior of yarns. This method can be a valuable tool for the fabric compression process and generating realistic mesoscale geometries for textile composites.

Heterogeneous flexibility can contribute to chromatin segregation in the cell nucleus.

The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution,which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This "inversion" is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP1α-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.