Stiffness Properties Research Articles

Multi‐Material Gradient Printing Using Meniscus‐enabled Projection Stereolithography (MAPS)

AbstractLight‐based additive manufacturing methods are widely used to print high‐resolution 3D structures for applications in tissue engineering, soft robotics, photonics, and microfluidics, among others. Despite this progress, multi‐material printing with these methods remains challenging due to constraints associated with hardware modifications, control systems, cross‐contamination, waste, and resin properties. Here, a new printing platform coined Meniscus‐enabled Projection Stereolithography (MAPS) is reported, a vat‐free method that relies on generating and maintaining a resin meniscus between a crosslinked structure and bottom window to print lateral, vertical, discrete, or gradient multi‐material 3D structures with no waste and user‐defined mixing between layers. MAPS is compatible with a wide range of resins shown and can print complex multi‐material 3D structures without requiring specialized hardware, software, or complex washing protocols. MAPS's ability to print structures with microscale variations in mechanical stiffness, opacity, surface energy, cell densities, and magnetic properties provides a generic method to make advanced materials for a broad range of applications.

Viscoelastic negative stiffness metamaterial with multistage load bearing and programmable energy absorption ability

ABSTRACT The mechanical properties of negative stiffness (NS) metamaterial could be customized and tuned in a wide range for various requirements, achieving programmable performances by the design from the aspect of structure and material. This work investigates the viscoelastic NS metamaterial based on double curved beams using a combined approach of experiments, simulations, and analytical modeling with an emphasis on multistage loading bearing and programmable energy absorption ability. Numerical simulations are first implemented based on the finite element models of three types of metamaterial cells, which provide comparisons of load bearing and energy absorption properties. Further, the effects of geometric parameters of multistage metamaterial element and the mechanisms are analyzed. An analytical discrete model is then innovatively developed to provide straightforward understandings of the geometric effects and reveal the role of viscoelasticity by examining the instantaneous loading responses and rate-dependent behaviors. Experimentally, we fabricate the metamaterial samples using 3D-printing technique and perform compression tests to validate the properties based on different boundary conditions, loading rates and cyclic loading and unloading. Results of this work show the potential of wide programmable room for mechanical properties through structure and functional material design, such as multistage load bearing capacity and energy absorption ability.

Experimental study on the influence of subgrade moisture content on compaction quality control indexes

ABSTRACT Intelligent compaction (IC) technology, which is based on the relationships between the subgrade stiffness properties and intelligent compaction measurement values (ICMVs), has been widely used in the compaction quality control (QC) of subgrade construction. The influence of moisture content (MC) on the stiffness properties is significant and well known but is often ignored in the current practice of IC. In this study, the relationship between the vibration compaction value (VCV) and subgrade reaction modulus (K 30) considering the influence of moisture content is investigated. The results show that the influence of MC on quality control indexes gradually becomes significant, especially in the later stage of compaction. Furthermore, K 30 is more sensitive than the VCV to moisture content, which means that the influence of MC is easy to ignore when taking the VCV as the ICMV. Finally, the specified VCV should be obtained when the MC is on both sides of the optimum moisture content (OMC) to ensure the accuracy of the QC of compaction.

Internal shear damage evolution of CFRP laminates ranging from −100 °C to 100 °C using in-situ X-ray computed tomography

Carbon Fiber Reinforced Polymer (CFRP) composites have been widely used in aerospace due to their high specific stiffness, strength, and fatigue properties. However, the ambient temperature significantly influences CFRP's mechanical properties and damage evolution, deriving from the temperature effect on the microstructural behavior and the mesoscopic damage evolution. In this study, the temperature-dependent in-plane shear failure behavior of CFRP composites was investigated. In-situ X-ray Computed tomography (CT) tensile experiments of laminates ([45°/-45°]2s) at RT, −100 °C, and 100 °C were carried out to study the in-plane shear failure mechanisms. The 3D fracture morphology was extracted with internal damage evolution process estimated and quantified. The in-situ 3D deformation fields of critical regions were acquired using the Digital Volume Correlation (DVC) method. The effect of temperature on strain field and the correlation between the high-strain region and the fracture location were analyzed. The results revealed the temperature correlations and failure mechanisms of CFRP's mechanical characteristics and internal damage evolution process. Compared to room temperature (RT), the delamination damage area of the sample increased by 80 % at 100 °C. Meanwhile, the shear modulus of CFRP decreases by 78.4 % from −100 °C to 100 °C, and the fracture strain increases by 95 % from RT to 100 °C. The DVC results indicated a dispersion of high-strain regions at −100 °C, reflecting the brittle damage characteristics, while an extensive ductile deformation region was captured at 100 °C. Fiber-matrix debonding is the dominant failure mode of composites under shear loading, whereas significant matrix cracking was observed at −100 °C and partial fiber pullout occurred at 100 °C.

Optimization of Dynamic Characteristics of Rubber-Based SMA Composite Dampers Using Multi-Body Dynamics and Response Surface Methodology

The suspension system of a commercial vehicle cab plays a crucial role in enhancing ride comfort by mitigating vibrations. However, conventional rubber suspension systems have relatively fixed stiffness and damping properties, rendering them inflexible to load variations and resulting in suboptimal ride comfort under extreme road conditions. Shape memory alloys (SMAs) represent an innovative class of intelligent materials characterized by superelasticity, shape memory effects, and high damping properties. Recent advancements in materials science and engineering technology have focused on rubber-based SMA composite dampers due to their adjustable stiffness and damping through temperature or strain rate. This paper investigates how various structural parameters affect the stiffness and damping characteristics of sleeve-type rubber-based SMA composite vibration dampers. We developed a six-degree-of-freedom vibration differential equation and an Adams multi-body dynamics model for the rubber-based SMA suspension system in commercial vehicle cabins. We validated the model’s reliability through theoretical analysis and simulation comparisons. To achieve a 45% increase in stiffness and a 64.5% increase in damping, we optimized the suspension system’s z-axis stiffness and damping parameters under different operating conditions. This optimization aimed to minimize the z-axis vibration acceleration at the driver’s seat. We employed response surface methodology to design the composite shock absorber structure and then conducted a comparative analysis of the vibration reduction performance of the optimized front and rear suspension systems. This study provides significant theoretical foundations and practical guidelines for enhancing the performance of commercial vehicle cab suspension systems.

Static analysis and non-probabilistic reliability evaluation of supporting structure of insulation platform

Abstract The insulation platform is a kind of high-altitude live working equipment commonly used in complex terrain environments. Due to the harsh working conditions, the safety of the insulation platform is highly required. The supporting structure of the insulation platform is responsible for carrying the operators, which determines the safety performance of the insulation platform. In this paper, static analysis is conducted on the supporting structures of the rotary insulation platform and rotary lifting insulation platform to study their strength and stiffness properties. Then the reliability of supporting structures is analyzed based on the interval non-probabilistic reliability theory and the reliability of structures is evaluated under different size conditions.

Multi-level stiffness property and isolating-based design of high damping rubber bearings

This study presents the development and analysis of high damping rubber bearings (HDRBs) with enhanced stiffness properties to improve seismic isolation performance. The proposed HDRBs exhibit displacement-dependent nonlinear stiffness and significant damping effects, especially under large deformations caused by various seismic events. A deformation history integral model, calibrated with experimental data, is employed to accurately simulate the mechanical behavior and stiffness-damping characteristics of the HDRBs. The numerical simulations are validated through experimental tests, providing a solid basis for parameter design and performance assessment. The results show that the equivalent stiffness coefficient of the HDRBs increases with deformation amplitude, effectively limiting extreme deformations. Parametric analyses and case studies across a wide range of earthquake scenarios demonstrate that the enhanced stiffness and high damping effects of HDRBs significantly improve seismic isolation efficiency while controlling isolation layer displacement. The performance-based design methodology developed in this research effectively limits bearing deformation, thereby preventing potential superstructure failures. Moreover, the adaptive characteristics of the HDRBs allow for the adjustment of deformation levels according to seismic intensity, ensuring the structural safety of buildings under varying earthquake conditions.

Flexible and lightweight carbon fiber/silicone resin composites with the “soft-rigid” structural interface for thermostable and antistatic applications

To avoid a large difference in modulus between carbon fiber (CF) and silicone resin (SR) and unstable thermal properties, the “soft-rigid” structural interface is constructed by coating polydopamine-polyethyleneimine@octaphenyl-silsesquioxane (PDA-PEI@octaphenyl-POSS) on the fiber surface. The tensile strength of the CF-AE@3P/SR composite was 24.35 % higher than that of the unmodified CF/SR. The mechanism of mechanical enhancement revealed that the rigid layer with nanoparticles effectively deflected the crack and prolonged the path, and the hydrogen bonds and van der Waals forces helped disperse the stress concentration at the interface. The defects in the soft–rigid structural interface were reduced, and the decomposition of the fibers and composites was effectively inhibited, thereby increasing the heat transmission in the composites. After heating for 20 s on the heating plate at 200 °C, the surface temperature of the CF-AE@3P/SR composite was 155.4 °C, which is higher than that of the unmodified CF/SR (131.4 °C). Therefore, the thermal stability of the CF-AE@3P/SR composites was significantly improved compared to that of unmodified CF/SR after holding at 350 °C for 3 h. Surface resistance analysis showed that the soft–rigid modification maintained the antistatic properties of the composites at room and high temperatures. It was also found that the CF-AE@P/SR composites exhibited good flexibility, lightweight, and hardness for application in sealing and electronic components. This work provides ideas for forming a seamless transition and effective bonding between high-modulus carbon fibers and a low-modulus elastomer matrix, increasing the thermal stability and mechanical properties, and maintaining the flexibility, stiffness, lightweight, and antistatic properties of composites at high temperatures

Influence of inherent anisotropy on the mechanical properties of normally consolidated clays with a wide range of plasticity indices

Inherent (fabric) anisotropy is one of the most important properties of earthen materials which has a significant influence on their strength and stiffness characteristics. In this study, a comprehensive series of unconfined and constrained compression tests is performed on normally consolidated (NC) clay samples with different plasticity indices to examine the effect of inherent anisotropy on their mechanical characteristics. Accordingly, several cylindrical clay samples with different proportions of kaolinite and bentonite are reconstituted at a wide range of deposition angles and then subjected to both unconfined and constrained compressive loadings. According to the experimental results, for a clay sample with a particular plasticity index, the highest and lowest values of the unconfined compressive strength (UCS), the secant modulus (E50), and the constrained Young's modulus (Eoed) are observed to be associated with the deposition angles of 0o and 90o, respectively. The results also show that at a certain bedding plane angle, the sample containing 30% bentonite (PI = 110%) exhibits the highest UCS, E50, and Eoed values. Several practical empirical correlations are developed to estimate the strength and stiffness properties of NC clays using their plasticity indices and bedding plane directions. Scanning Electron Microscopy (SEM) analysis is also conducted to explore the microstructure of samples containing varying percentages of kaolinite and bentonite.

Heart failure with preserved ejection fraction in pigs causes shifts in posttranscriptional checkpoints.

Left ventricular pressure overload (LVPO) can lead to heart failure with a preserved ejection fraction (HFpEF) and LV chamber stiffness (LV Kc) is a hallmark. This project tested the hypothesis that the development of HFpEF due to an LVPO stimulus will alter posttranscriptional regulation, specifically microRNAs (miRs). LVPO was induced in pigs (n = 9) by sequential ascending aortic cuff and age- and weight-matched pigs (n = 6) served as controls. LV function was measured by echocardiography and LV Kc by speckle tracking. LV myocardial miRs were quantified using an 84-miR array. Treadmill testing and natriuretic peptide-A (NPPA) mRNA levels in controls and LVPO were performed (n = 10, n = 9, respectively). LV samples from LVPO and controls (n = 6, respectively) were subjected to RNA sequencing. LV mass and Kc increased by over 40% with LVPO (P < 0.05). A total of 30 miRs shifted with LVPO of which 11 miRs correlated to LV Kc (P < 0.05) that mapped to functional domains relevant to Kc such as fibrosis and calcium handling. LVPO resulted in reduced exercise tolerance (oxygen saturation, respiratory effort) and NPPA mRNA levels increased by fourfold (P < 0.05). RNA analysis identified several genes that mapped to specific miRs that were altered with LVPO. In conclusion, a specific set of miRs are changed in a large animal model consistent with the HFpEF phenotype, were related to LV stiffness properties, and several miRs mapped to molecular pathways that may hold relevance in terms of prognosis and therapeutic targets.NEW & NOTEWORTHY Heart failure with preserved ejection fraction (HFpEF) is an ever-growing cause for the HF burden. HFpEF is particularly difficult to treat as the mechanisms responsible for this specific form of HF are poorly understood. Using a relevant large animal model, this study uncovered a unique molecular signature with the development of HFpEF that regulates specific biological pathways relevant to the progression of this ever-growing cause of HF.

Investigating the influence of bending stiffness and processing parameters on single-leg bending geometries of additively manufactured composites

In less than a decade, additive manufacturing technologies have been developed so successfully that they already produce small and medium-sized lot sizes of prototypes or customised components in the industry. With its new possibilities such as combining materials and technologies, the benefits of different technologies can be merged and broaden future application fields. One way is to print with one technology on a part produced by another. Thus, a thermally bonded part composed of, e.g., selectively sintered and material-extruded components can be created. This combination of technologies was considered in this study to investigate the bonding strength of extrusion-based layers on selectively sintered surfaces and the impact of nozzle temperature, orientation, and thickness of imprinted materials. The extrusion-based layers covered stiff (fibre-reinforced polyamide) and soft (thermoplastic polyurethane) material properties with pre-cracked single-leg bending (SLB) specimens to study their effect on delamination tendencies. This combination of materials and additive manufacturing technologies has not yet been studied for the SLB testing method. The scope of this study is to obtain more information on how relatively hard-hard and hard-soft combinations behave for this special testing method. The results of this testing method were evaluated using two different fracture mechanical approaches to determine the energy release rate. A clear trend towards an improved bonding, thus, higher values, was found for higher nozzle temperatures. Furthermore, a limitation regarding the required bending stiffness of the composites was found. Overall, the single-leg bending testing method enables a relative ranking for material combinations with a certain bending stiffness.

The computational design of corrugated tube lattice structure with negative stiffness property under axial compression load

The computational design of corrugated tube lattice structure with negative stiffness property under axial compression load

Synthesis of Stearyl Alcohol/Polyethylene Glycol Hybrids as Water-Repellent Finishes for Cotton/Polyester Blended Fabric

AbstractNowadays, developing and innovation of new finishing agents that are cost effective, efficient, durable, and safe for the consumer as well as the environment are greatly required by the textile manufactures. In that concern, new stearyl alcohol/polyethylene glycol (SA/PEG) hybrids were synthesized, characterized, and applied as textile finishes to impart cotton/polyester fabric with water repellency. Such hybrids were synthesized by reaction of SA with PEG of molecular weight 1000 or 4000 Da in the presence of ammonium persulfate (APS) as initiator. The optimum conditions of the synthesis reaction are: APS/PEG, 20%; PEG/SA, 15%; reaction temperature, 80 °C and reaction time, 45 min. The synthesized hybrids are self-water dispersible that form oil-in-water stable emulsions. The results indicated that treating cotton/polyester fabric with easy-care finishing formulation containing 60 g/L of dimethyloldihydroxyethylene urea as a cross-linker, and 60 g/L of any of such hybrids emulsions imparts the treated fabric with water repellency, softness, and stiffness properties. Moreover, increasing the PEG molecular weight from 1000 to 4000 Da leads to a reduction in extents of softness and contact angle along with an enhancement in stiffness of treated fabric. Furthermore, the prepared hybrids emulsions-treated fabric samples are durable up to five washing cycles. The FTIR analysis confirmed the chemical structure of the synthesized SA/PEG1000 hybrid. The transmission electron microscope (TEM) revealed that the particles size of SA/PEG4000 hybrid emulsion is in the range of 34–70 nm and reaches to 185 nm in case of the SA/PEG4000 hybrid emulsion. The surface of SA/PEG1000 hybrid emulsion-treated fabric was characterized via scanning electron microscope (SEM).

3D micromechanics assisted finite element approach for bending analysis of straight/wavy CNT-reinforced multi-scale hybrid composite plate

This study examines the micromechanical and structural behavior of straight and wavy carbon nanotube (CNT) reinforced multi-scale fiber-reinforced hybrid composite (MFRHC) plates. An important feature of MFRHC is the incorporation of nano-scale CNTs into two-phase carbon fiber-reinforced composites (CFRC), enhancing their micromechanical and macroscopic properties, particularly the bending and stress behaviors. In CNT fiber-reinforced composites, the fiber waviness can arise from manufacturing imperfections which demands in-depth analysis of MFRHC plates reinforced with both straight or wavy CNTs to characterize their relative influences. In this work, the CNTs are assumed to be continuous and distributed uniformly within the CFRC, and the waviness is considered to be sinusoidal spanning both longitudinal and transverse planes. A mathematical formulation is devised, based on a three-dimensional mechanics of materials (MOM) model, to analyze the micromechanical behavior of the hybrid composite and the model’s accuracy are compared with the multi-inclusion Mori-Tanaka method and the Voigt/Reuss rule of mixtures. The MOM model indicates that the waviness pattern of the CNTs significantly influences the effective stiffness properties of MFRHC in comparison to that of the straight CNTs. Following this, a finite element model is constructed to investigate the bending deflection and stress properties of a simply-supported symmetric cross-ply (0/90/0) MFRHC laminate under sinusoidal transverse loading, utilizing first-order shear deformation theory (FSDT). The results suggest that the bending deflection decreases for the MFRHC laminate when the waviness factor ( Ψ ) is ≤ 0.05 , but increases when Ψ > 0.05 . Finally, the bending stress behavior is examined for both straight and wavy CNT-reinforced MFRHC laminates considering their geometrical parameters ( a / h , z / h ), and the CNTs’ waviness factor ( Ψ ), respectively.

The Abrasive Water Jet Cutting Process of Carbon-Fiber-Reinforced Polylactic Acid Samples Obtained by Additive Manufacturing: A Comparative Analysis

Carbon-fiber-reinforced polymer (CFRP) composites are widely used across industries due to their enhanced strength and stiffness properties. Fused deposition modeling (FDM) enables the cost-effective production of polymer samples, such as carbon-fiber-reinforced PLA (CFR-PLA). However, CFRP’s hardness and anisotropic nature present significant challenges in conventional machining, including rapid tool wear and thermal sensitivity. Consequently, abrasive water jet machining (AWJM) has proven to be an effective alternative for machining CFRP materials, offering benefits such as reduced tool wear, minimized thermal damage, and improved cutting quality. This study focuses on a comparative analysis of the effects of AWJM parameters on PLA and CFR-PLA samples, specifically to evaluate the influence of carbon fiber reinforcement on machining performance. The findings highlight the critical role of reinforcements in machining behavior. The results suggest that optimizing cutting parameters significantly reduces taper formation and improves machining accuracy. In particular, adjustments to process parameters resulted in lower taper angles and reduced surface roughness in the cutting zones of the CFR-PLA samples.

Performance analysis of vertical smart isolator based on magnetorheological elastomer

ABSTRACT As one of the field-dependent smart materials whose stiffness and damping properties can change instantaneously and reversibly, magnetorheological elastomer (MRE) has been extensively utilized on base isolation for vibration reduction. However, most previous studies have focused on the shear dynamic performance of MRE isolators, and there are few reports on the vertical extrusion performance of basic isolators within construction equipment. In this paper, MRE materials with strong bearing capacity and suitable vertical stiffness were fabricated by comprehensively considering the selection of raw materials, particle ratio, and sample size. The tension-compression viscoelasticity of the prepared MRE under varying magnetic fields and strain amplitudes was experimentally evaluated using an MRE axial MR testing system. Eventually, a single-degree-of-freedom dynamic test rig for vibration isolation of equipment in buildings, which integrates a vertical isolator with MRE as the core component, was constructed to perform a series of experimental investigations on the alterable frequency vibration capability of the designed MRE vertical isolator. The test results reveal that the controllable stiffness-damping properties of the prepared MRE in the axial tension-compression mode can enable the developed vertical isolator to exhibit superior frequency shifting and vibration attenuating characteristics in structural vibration.

Design and Evaluation of a Novel Variable Stiffness Hip Joint Exoskeleton.

An exoskeleton is a wearable device with human-machine interaction characteristics. An ideal exoskeleton should have kinematic and kinetic characteristics similar to those of the wearer. Most traditional exoskeletons are driven by rigid actuators based on joint torque or position control algorithms. In order to achieve better human-robot interaction, flexible actuators have been introduced into exoskeletons. However, exoskeletons with fixed stiffness cannot adapt to changing stiffness requirements during assistance. In order to achieve collaborative control of stiffness and torque, a bionic variable stiffness hip joint exoskeleton (BVS-HJE) is designed in this article. The exoskeleton proposed in this article is inspired by the muscles that come in agonist-antagonist pairs, whose actuators are arranged in an antagonistic form on both sides of the hip joint. Compared with other exoskeletons, it has antagonistic actuators with variable stiffness mechanisms, which allow the stiffness control of the exoskeleton joint independent of force (or position) control. A BVS-HJE model was established to study its variable stiffness and static characteristics. Based on the characteristics of the BVS-HJE, a control strategy is proposed that can achieve independent adjustment of joint torque and joint stiffness. In addition, the variable stiffness mechanism can estimate the output force based on the established mathematical model through an encoder, thus eliminating the additional force sensors in the control process. Finally, the variable stiffness properties of the actuator and the controllability of joint stiffness and joint torque were verified through experiments.

Harnessing plasticity in sequential metamaterials for ideal shock absorption.

Mechanical metamaterials exhibit interesting properties such as high stiffness at low density1-3, enhanced energy absorption3,4, shape morphing5-7, sequential deformations8-11, auxeticity12-14 and robust waveguiding15,16. Until now, metamaterial design has primarily relied on geometry, and materials nonlinearities such as viscoelasticity, fracture and plasticity have been largely left out of the design rationale. In fact, plastic deformations have been traditionally seen as a failure mode and thereby carefully avoided1,3,17,18. Here we embrace plasticity instead and discover a delicate balance between plasticity and buckling instability, which we term 'yield buckling'. We exploit yield buckling to design metamaterials that buckle sequentially in an arbitrary large sequence of steps whilst keeping a load-bearing capacity. We make use of sequential yield buckling to create metamaterials that combine stiffness and dissipation-two properties that are usually incompatible-and that can be used several times. Hence, our metamaterials exhibit superior shock-absorption performance. Our findings add plasticity to the metamaterial toolbox and make mechanical metamaterials a burgeoning technology with serious potential for mass production.

Fabrication of Green Composite Materials Using the Weight Sum Method (WSM) Method

The quest for sustainable materials the investigation into natural fibers for composite materials has been prompted by this development., aiming to reduce the environmental impact of traditional synthetic composites. In this study, we investigate the potential of flax, hemp, jute, kenaf, and ramie fibers as reinforcements in green composites fabricated using the Water Soaking Method (WSM). The evaluation parameters considered include density (g/cm3), fiber diameter (μm), tensile strength (MPa), Young’s modulus (GPa), and elongation at break (%). Through meticulous experimentation and analysis, it is revealed that jute emerges as the frontrunner among the alternatives, exhibiting superior performance across multiple evaluation parameters. Jute-based green composites demonstrate commendable strength and stiffness properties, coupled with a moderate density, making them promising candidates for various structural applications. Conversely, kenaf fiber-based composites exhibit the lowest performance in terms of evaluated parameters, indicating potential limitations in its suitability for high-performance applications. The comparative assessment underscores the significance of material selection in composite fabrication, emphasizing the diverse mechanical properties exhibited by different natural fibers. Furthermore, the utilization of the WSM method showcases its effectiveness in producing green composites with desirable characteristics, signifying its potential as a viable manufacturing technique for sustainable materials. eco-friendly composites, highlighting the importance of considering multiple factors such as fiber type and fabrication method in achieving optimal performance and environmental sustainability in composite materials. Further research may delve into refining fabrication techniques and exploring novel fiber combinations applications.

Stochastic optimization of a mass-in-mass cell with piecewise hybrid nonlinear–linear restoring force

This article investigates the optimization under uncertainty of a mass-in-mass meta-cell for its potential use within a metamaterial. The specificity of the proposed mass-in-mass system stems from the hybrid nonlinear–linear stiffness at the inner level. It is well known that these systems are highly sensitivity to small perturbations in loading conditions or design parameters. In fact, the sensitivity is such that the system can exhibit discontinuous behaviors. Therefore the proposed optimization approach not only accounts for sources of uncertainties but also can handle discontinuous responses. The objective of the stochastic optimization is to find the stiffness properties of the mass-in-mass system which minimize the expected value of a specific efficiency metric. In order to better understand the system’s dynamic behavior and the origins of the discontinuities, slow invariant manifolds and frequency response curves are provided. The efficiency of the optimized system with hybrid stiffness is compared with that of a similar optimized system featuring pure cubic nonlinearity.