Modulus Gradient Research Articles

Mandible composition and properties in two selected praying mantises (Insecta, Mantodea).

Insects process their food with their cuticle-based mouthparts. These feeding structures reflect their diversity and can, in some cases, showcase adaptations in material composition, mechanical properties, and shape to suit their specific dietary preferences. To pave the way to deeply understand the interaction between mouthparts and food and to determine potential adaptations of the structures to the food, this study focuses on the mandibles of two praying mantis species. Gongylus gongylodes feeds mainly on Diptera, and Sphodromantis lineola forages on larger prey. Employing scanning electron microscopy, the mandibular morphologies were analyzed. The degree of the cuticle tanning was tested using confocal laser scanning microscopy. Furthermore, the contents of transition and alkaline earth metals in the mandible cuticle were studied using energy-dispersive X-ray spectroscopy and the mechanical properties tested by nanoindentation. We found that S. lineola mandibles show pronounced gradients of Young's modulus and hardness from the basis to the tip, which might be an adaptation against high stresses during biting and chewing. G. gongylodes, in contrast, did not show pronounced gradients, which may indicate that there is less stress involved in feeding-necessary to test in future studies. The mechanical properties of manidibles in both species are related to the degree of cuticle tanning but also positively correlate with the content of magnesium. These findings enrich our understanding of insect cuticle biology but also present new sets of data on praying mantis structures.

Layer-by-layer assembling boron nitride/polyethyleneimine/MXene hierarchical sandwich structure onto basalt fibers for high-performance epoxy composites

Interfacial adhesion directly affects the mechanical properties of basalt fiber (BF)-reinforced polymer composites. To construct a more superior interphase between BFs and epoxy resin (EP) than a weak interphase of the unmodified BF/EP, we propose a hierarchical sandwich structure consisting of sodium hydroxide–activated boron nitride (BNOH), polyethyleneimine (PEI), and MXene (MX, Ti3C2Tx) through facile layer-by-layer self-assembly. The fabricated BNOH/P/MX sandwich structure (P denoting “PEI”) can synergistically improve the interface adhesion by enhancing the mechanical interlocking and chemical bonding of the composites. When the composites reinforced by BF–BNOH/P/MX subject to the external loading, flexible PEI molecules allow two-dimensional (2D) rigid BNOH and MX nanosheets to slip at the interface by uncurling the molecular chains, dissipating a great amount of energy during the fracture progress. Meanwhile, the hierarchical BNOH/P/MX sandwich structure acts as an excellent interface and possesses multistage gradient modulus and wider thickness, uniformly and efficiently transferring the stress from the EP matrix to BFs. The interfacial shear strength, impact strength, and fracture toughness of BF–BNOH/P/MX-reinforced EP composite are substantially improved by 45.9 %, 60.6 %, and 148.9 %, respectively, compared with bare BF–based composites. This study can provide valuable references and inspirations for designing and constructing high-quality interfaces for high-strength and high-toughness BF structural materials, taking advantage of 2D materials.

Gradient Modulus Strategy for Alleviating Stretchable Electronic Strain Concentration

AbstractThe island‐bridge structural design is a common strategy for imparting stretchability to flexible electronic devices. In this structure, the low modulus regions bear most of the deformation, while the rigid islands, which house the electronic components, undergo minimal deformation. However, due to the modulus differences that can be several times or even several orders of magnitude larger, severe strain concentration occur at the edges of the rigid islands in high modulus regions. This strain concentration caused by rigid constraints not only reduces the stretchability of the soft substrate but also degrades the mechanical performance of the interconnected structures, thereby significantly affecting the overall stability of the device. Starting from finite element simulations, this paper introduces modulus gradient regions and optimizes geometric parameters, significantly alleviating the strain concentration at the edges of the rigid islands. Serpentine‐shaped circuits are then transferred to a substrate with strain isolation, which demonstrates better stretchability stability under 20% elongation compared to traditional strain isolation strategies. In addition, the stretchable light emitting diode (LED) system with gradient modulus has better stretchability compared to the system with conventional strategy. This suggests that this strategy has great potential in maintaining the stability of stretchable systems.

Revisiting the sequential evolution of sizing agents in CFRP manufacturing to guide cross-scale synergistic optimization of interphase gradient and infiltration

Using sizing agents instead of various nanoparticles to modify carbon fibers is widely recognized as the most practical approach to address processing issues and improve interfacial properties in carbon fiber reinforced polymer composites. However, a limited understanding of sizing agent evolution during composite manufacturing hinders comprehensive theoretical guidance for sizing treatment, thereby limiting further enhancement of composite performance. Here we disentangled the sizing agents into chemical anchoring and physical adsorption components, and elucidated the sequential wetting, diffusion, and crosslinking evolution processes of sizing agents across scales. By manipulating the proportion of chemical anchoring and physical adsorption in the sizing agents, the interfacial modulus gradient and infiltration efficiency were synergistically optimized. Consequently, significant improvements of 26.2 % in interfacial shear strength (IFSS) and 52.9 % in transverse fiber bundle tensile (TFBT) strength were achieved, indicating enhanced interfacial stress transfer and reduced internal defects in the composites. In summary, this work revisited the cross-scale evolution and mechanism of sizing agents during composite manufacturing, and thus provided a new paradigm for optimizing composite performance.

Tailored environments for directed mesenchymal stromal cell proliferation and differentiation using decellularized extracellular matrices in conjunction with substrate modulus

Decellularised extracellular matrix (dECM) produced by mesenchymal stromal cells (MSCs) is a promising biomaterial for improving the ex vivo expansion of MSCs. The dECMs are often deposited on high modulus surfaces such as tissue culture plastic or glass, and subsequent differentiation assays often bias towards osteogenesis. We tested the hypothesis that dECM deposited on substrates of varying modulus will produce cell culture environments that are tailored to promote the proliferation and/or lineage-specific differentiation of MSCs. dECM was produced on type I collagen-functionalised polyacrylamide hydrogels with discrete moduli (∼4, 10, and 40 kPa) or in a linear gradient of modulus that spans the same range, and the substrates were used as culture surfaces for MSCs. Fluorescence spectroscopy and mass spectrometry characterization revealed structural compositional changes in the dECM as a function of substrate modulus. Softer substrates (4 kPa) with dECM supported the largest number of MSCs after 7 days (∼1.6-fold increase compared to glass). Additionally, osteogenic differentiation was greatest on high modulus substrates (40 kPa and glass) with dECM. Nuclear translocation of YAP1 was observed on all surfaces with a modulus of 10 kPa or greater and may be a driver for the increased osteogenesis on the high modulus surfaces. These data demonstrate that dECM technology can be integrated with environmental parameters such as substrate modulus to improve/tailor MSC proliferation and differentiation during ex vivo culture. These results have potential impact in the improved expansion of MSCs for tailored therapeutic applications and in the development of advanced tissue engineering scaffolds. Statement of significanceMesenchymal stromal cells (MSCs) are extensively used in tissue engineering and regenerative medicine due to their ability to proliferate, differentiate, and modulate the immune environment. Controlling MSC behavior is critical for advances in the field. Decellularised extracellular matrix (dECM) can maintain MSC properties in culture, increase their proliferation rate and capacity, and enhance their stimulated differentiation. Substrate stiffness is another key driver of cell function, and previous reports have primarily looked at dECM deposition and function on stiff substrates such as glass. Herein, we produce dECM on substrates of varying stiffness to create tailored environments that enhance desired MSC properties such as proliferation and differentiation. Additionally, we complete mechanistic studies including quantitative mass spec of the ECM to understand the biological function.

Associations of circulating T-cell subsets in carotid artery stiffness: the Multi-Ethnic Study of Atherosclerosis.

Arterial stiffness measured by total pulse wave velocity (T-PWV) is associated with increased risk of multiple age-related diseases. T-PWV can be described by structural (S-PWV) and load-dependent (LD-PWV) arterial stiffening. T-cells have been associated with arterial remodeling, blood pressure, and arterial stiffness in humans and animals; however, it is unknown whether T-cells are related to S-PWV or LD-PWV. Therefore, we evaluated the cross-sectional associations of peripheral T-cell subpopulations with T-PWV, S-PWV, and LD-PWV stiffness. Peripheral blood T-cells were characterized using flow cytometry and the carotid artery was measured using B-mode ultrasound to calculate T-PWV at the baseline examination in a subset of the Multi-Ethnic Study of Atherosclerosis (MESA, n=1,984). A participant-specific exponential model was used to calculate S-PWV and LD-PWV based on elastic modulus and blood pressure gradients. The associations between five primary (p-significance<0.01) and twenty-five exploratory (p-significance<0.05) immune cell subpopulations, per 1-SD increment, and arterial stiffness measures were assessed using adjusted, linear regressions. For the primary analysis, higher CD4+CD28-CD57+ T-cells were associated with higher LD-PWV (β=0.04 m/s, p<0.01) after adjusting for co-variates. For the exploratory analysis, T-cell subpopulations that commonly shift with aging towards memory and differentiated/immunosenescent phenotypes were associated with greater T-PWV, S-PWV, and LD-PWV after adjusting for co-variates. In this cross-sectional study, several T-cell subpopulations commonly associated with aging were related with measures of arterial stiffness. Longitudinal studies that examine changes in T-cell subpopulations and measures of arterial stiffness are warranted.

A stretchable and self-powered strain sensor with elastomeric electret

Stretchable deformation sensors play an important role in the perception and autonomy of soft robots. While various sensors have been reported, the mechanical sensor with self-powered capability and stretchability to suit extreme environment is urgently required. In this study, a stretchable, self-powered, sensitivity adjustable, and long-term stability strain sensor based on the stretchable electret is researched for deformation monitoring. This stretchable and self-powered sensor is composed of the dielectric elastomer with designed elastic modulus gradient and the stretchable electret with elastomeric and Nano-particles. The electro-mechanical capability of this designed sensor is researched and optimized by multi-objective optimization approach. The sensor exhibits self-powered capability, stretchability (tensile strain from 0% to 20%), tunable sensitivity (optimized from 5.7 to 5.9 pC mm−1), and stability, where electromechanical performance remains stable after 8000 stretching cycles. The feasibility of its autonomous sensing which promotes a wide range of potential application in soft robotics is demonstrated. This elastic modulus gradient-induced and net charge design significantly broadened the potential applications with large deformation and low-attached stiffness.

Bioinspired stiff–soft gradient network structure for high-performance impact-resistant elastomers

Traditional impact-resistance materials relying on the combination of supporting materials and energy-dissipation elastomers can effectively reduce shock load, yet the sharp interface between two types of materials causes discontinuous stress transfer and cracking. Here, inspired by the squid beak, we report a type of high impact-resistance gradient elastomers with large-scale modulus gradient with about three orders of magnitude (modulus range of 7 × 103 ∼ 7 × 106 Pa) and high energy dissipation (loss factor > 0.6) over a wide temperature range by diffusively introducing stiff polymers in a highly damping elastomer with controlled mechanical properties. Under the action of an external force, our gradient elastomers exhibit soft-while-stiff attributes, combining cushioning and support. In drop hammer impact tests, our gradient materials can reduce impact strength by 80 %, significantly better than commercial protective gear. It is worth mentioning that the modulus of the bottom layer matches that of the tissues for better protection.

Boundaries identification of geological structure in lunar Oceanus Procellarum region using full gravity gradient tensor methodology

Boundary recognition visually delineates the horizontal extent of subsurface anomalies, providing a foundational basis for interpreting gravity data. Compared to gravity observations, gravity gradient data offers the benefits of multiple components and the enhancement of shortwave information in graphical representations. In our study, we investigated the delineation of geological structure boundaries in the lunar Oceanus Procellarum region using gravity gradient techniques. First, based on the observations from the Gravity Recovery and Interior Laboratory (GRAIL) mission, we obtained high-precision synthetic full tensor values of the gravity gradient as our primary research data. Moreover, to reduce curvature errors during large-scale terrain forward modeling, we applied the spherical prism of tesseroid to eliminate the effects of near-surface topography. Grounded on the Bouguer anomalies of gravity gradient, four distinct boundary recognition methods have been employed to explore the geological structure of the lunar Oceanus Procellarum region. It includes the Theta map method, the directional Theta map method, the combination of total horizontal derivative and the modulus of full tensor gravity gradient, and the improved edge detection method based on the Theta map method.The common feature of these methods is the utilization of the multi-component data combination from gravity gradient tensors, which can enhance the accuracy of edge detection. From the investigation results presented in the paper, we have found the following: 1) The improved edge detection method, based on the Theta map principle, enables better identification of the center of subsurface anomaly bodies during boundary recognition, utilizing a consistent single color in graphic displays. 2) According to the results of boundary recognition, numerous strip anomalies exist in the Oceanus Procellarum area that show less correlation with topographic relief. One possible explanation for these graphical anomalies of gravity gradient is that they serve as channels for the upwelling of mantle material during lunar evolution.

Exact solutions for the elastic-plastic response of functionally graded pipe under external pressure

This study investigates the influence of material gradient on the elastoplastic response of functionally graded (FG) thick-walled pipes subjected to external pressure. Closed-form solutions are derived for radial and circumferential stresses across various stages: purely elastic, partially plastic, and post-unloading from plastic regimes. Both the elastic modulus and yield stress exhibit radial variation defined by power-law functions, while Poisson's ratio remains constant. The stress distribution within the pipe depends not only on the external pressure but also on the material gradient index and the geometric dimensions of the pipe. A method is presented to accurately determine the first yielding position in a thin-walled tube based on the material gradient index by employing Tresca's yield criterion. Plastic zones nucleate at one or both surfaces as external pressure increases. The propagation of elastoplastic interfaces and stress distributions within each zone are examined in detail. Notably, following plastic deformation and complete unloading, FG thick-walled pipes may exhibit re-emergence of plastic deformation, depending on the pre-unloading stress state and the gradient of the elastic modulus. The conclusions of this work expected to aid in the design of FG pressure vessels and improve their load-carrying capacity and safety.

Homogenizing interfacial shear stress in brick-and-mortar structured composites via gradient modulus for enhanced mechanical properties

Homogenizing interfacial shear stress in brick-and-mortar structured composites via gradient modulus for enhanced mechanical properties

Constructing a Novel Moderately Modulus "Rigid-Flexible" Structure with Synergistic Reinforcement on the Carbon Fiber Surface to Enhance the Mechanical Properties of Carbon Fiber/Epoxy Composites at Elevated Temperatures.

To improve the mechanical performance of carbon fiber (CF)/epoxy composites in high-temperature environments, a moderately modulus gradient modulus interlayer was constructed at the interface phase region of composites. This involved the design of a "rigid-flexible" synergistic reinforcement structure, incorporating rigid nanoparticle GO@CNTs and a flexible polymer polynaphthyl ether nitrile ketone onto the CF surface. Notably, at 180 °C, compared to commercial CF composites, the CF-GO@CNTs-PPENK composites displayed a remarkable improvement in their mechanical characteristics (interfacial shear, interlaminar shear, flexural strength, and modulus), achieving enhancements of 173.0, 91.5, 225.7, and 376.4%, respectively. The principal reason for this the moderately modulus interface phase composed of GO@CNTs-PPENK (where GO and CNTs predominantly consist of carbon atoms with sp2-hybridized orbitals, forming highly stable C-C structures, while PPENK possesses a "twisted non-coplanar" structure), which exhibited resistance to deformation at high temperatures. Moreover, it greatly improved the mechanical interlocking, wettability, and chemical compatibility between CF and the epoxy. It also played a crucial role in balancing and buffering the modulus disparity. The interface failure behavior and reinforcement mechanisms of the CF composites were analyzed. Furthermore, validation of the presence of a moderately modulus gradient interlayer at the interface phase region of CF-GO@CNTs-PPENK composites was performed by using atomic force microscopy. This study has established a theoretical foundation for the development of high-performance CF composites for use in high-temperature fields.

Fabrication of GNPs sprayed carbon fiber and its effects on the interfacial and mechanical behavior of reinforced epoxy multiscale laminated composite

AbstractThe current research compares the effects of modifying carbon fiber [via spraying graphene nanoplates (GNPs)] and/or GNPs reinforcement on the mechanical and interfacial behavior of carbon fiber epoxy composites. Using a spraying method, the epoxy matrix was reinforced, and carbon fiber was modified with 0.2 and 1 wt% of GNPs, respectively. Tensile, interlaminar, and dynamic mechanical analyses (DMA) tests were conducted on the composite to assess the role of GNPs in enhancing mechanical, interfacial, and thermomechanical properties. The obtained results indicate that the spraying technique effectively enhanced the ultimate tensile strength (UTS) and interlaminar fracture toughness (ILFT) of the composite. The UTS improved by 31%, while the ILFT significantly improved by 38%. Additionally, assessing the modulus gradient through the interface shows improved interfacial interaction between modified carbon fiber and reinforced epoxy. Scanning electron microscopy examination of the fractured surfaces indicated that the existence of nanofillers with high surface area contributed to significant improvements in adhesion between the modified fiber and reinforced epoxy matrix, leading to enhanced interfacial, mechanical, and thermomechanical properties of CFRPs for structural applications.Highlights Incorporation of surface modified carbon fibers and GNPs reinforcement in the epoxy matrix to enhance the interfacial interaction. Evaluation of the effects of GNP nanofiller on interfacial and mechanical performance of the composite. Fracture surfaces in ILSS, tensile, and mode I test were analyzed using FESEM. Utilization of nanoscale modulus mapping for the fiber‐matrix interface assessment.

Giant Flexoelectric Effect in Snapping Surfaces Enhanced by Graded Stiffness

Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity; therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.

Surface wrinkling of a film coated to a graded substrate

We study the surface wrinkling of a stiff thin elastic film bonded to a compliant graded elastic substrate subject to compressive stress generated either by compression or growth of the bilayer. Our aim is to clarify the influence of the modulus gradient on the onset and surface pattern in this bilayer. Within the framework of finite elasticity, an exact bifurcation condition is obtained using the Stroh formulation and the surface impedance matrix method. Further analytical progress is made by focusing on the case of short wavelength limit for which the Wentzel–Kramers–Brillouin method can be used to resolve the eigenvalue problem of ordinary differential equations with variable coefficients. An explicit bifurcation condition is obtained from which the critical buckling load and the critical wavelength are derived asymptotically. In particular, we consider two distinct situations depending on the ratio β of the shear modulus at the substrate surface to that at infinity. If β is of O(1) or small, the parameters related to modulus gradient all appear in the higher-order terms and play an insignificant role in the bifurcation. In that case, it is the modulus ratio between the film and substrate surface that governs the onset of surface wrinkling. If, however, β≫1, the modulus gradient affects the critical condition through leading-order terms. Through our analysis we unravel the influence of different material and geometric parameters, including the modulus gradient, on the bifurcation threshold and the associated wavelength which can be of importance in many biological and technological settings.

Plasma etching-assisted polymerizable deep eutectic solvents for efficient construction of aramid fiber surface coatings enhancing aramid fiber/natural rubber interfacial bonding properties

In this study, plasma etching and polymerizable deep eutectic solvents (PDES) were employed to construct in-situ aramid fiber (AF) surface coatings, enhancing interfacial bonding with natural rubber (NR). Plasma etching heightened AF surface roughness, and PDES coating further increased roughness while forming a cross-linking network, forming the interfacial modulus gradient and mitigating stress concentration. The successful plasma etching and PDES coating were validated through FTIR spectroscopy, XPS, thermogravimetric analysis, SEM, TEM, AFM, etc. H pull-out experiments demonstrated improved interfacial bonding, with AF-PDES-3 exhibiting a 156.98 % increase in H pull-out force (15.83 N) compared to the original AF fiber. Consequently, plasma etching-assisted polymerizable deep eutectic solvents in-situ coating enhances AF/NR interfacial bonding, offering potential for aerospace tires and other applications.

Micropillar with Radial Gradient Modulus Enables Robust Adhesion and Friction.

The gradient modulus in beetle setae plays a critical role in allowing it to stand and walk on natural surfaces. Mimicking beetle setae to create a modulus gradient in microscale, especially in the direction of setae radius, can achieve reliable contact and thus strong adhesion. However, it remains highly challenging to achieve modulus gradient along radial directions in setae-like structures. Here, polydimethylsiloxane (PDMS) micropillar with radial gradient modulus, (termed GM), is successfully constructed by making use of the polymerization inhibitor in the photosensitive resin template. GM gains adhesion up to 84kPa, which is 2.3 and 4.7 times of soft homogeneous micropillars (SH) and hard homogeneous micropillars (HH), respectively. The radial gradient modulus facilitates contact formation on various surfaces and shifts stress concentration from contact perimeter to the center, resulting in adhesion enhancement. Meanwhile, GM achieves strong friction of 8.1 mN, which is 1.2 and 2.6 times of SH and HH, respectively. Moreover, GM possesses high robustness, maintaining strong adhesion and friction after 400 cycles of tests. The work here not only provides a robust structure for strong adhesion and friction, but also establishes a strategy to create modulus gradient at micron-scale.

Improved adhesion of rubber composites by developing environmentally friendly fiber impregnation coatings with good interfacial modulus transition gradients

Polyester (PET) fibers must undergo impregnation with a resorcinol-formaldehyde-latex (RFL) solution to ensure efficient adhesion with rubber. However, the harmful, carcinogenic resorcinol-formaldehyde (RF) resin in RFL impregnation solution negatively affects human health. In this paper, PET was pretreated with blocked isocyanate and epoxy resins to activate the fibers, and a new environmentally friendly fiber impregnation coating was developed. In the new impregnation coatings, ethylene glycol diglycidyl ether (EGDE) and m-xylylenediamine (MXDA) were applied to replace the resorcinol and formaldehyde. Moreover, glycidyl methacrylate (GMA) containing epoxy groups and double bonds was introduced to enhance interaction with rubber further, and then styrene-butadiene-vinyl-pyridine (VP) latex was mixed. The results show that the peel strength of the impregnated PET/rubber composites with the new impregnation coatings can reach 14.0 N/mm, representing an increase of 30.8 % compared to that of the sample with the pure RFL impregnation coatings, whose peel strength is only 10.7 N/mm. Furthermore, the mechanism for enhancing the interfacial adhesive properties of PET/rubber composites was performed by analyzing the chemical composition and morphological changes of the impregnated PET surface, as well as the change of sulfur content at the interface of the impregnated PET/rubber composites and the transition gradient of interfacial modulus.

Investigation of process-induced periodic structure on n-type 4H-SiC with corresponding mechanical characteristics estimation

A dicing process that combines the laser scribing and mechanical breaking procedures is demonstrated to achieve high-quality n-type 4 H-silicon carbide (SiC) without generating the edge defect and chipping phenomenon. Presented dicing process is successfully implemented on a 40 mm × 40 mm SiC workpiece with a thickness of 150 μm, and it separated 1 mm × 1 mm and 2 mm × 2 mm chips. However, the process-induced stress introduces stress-induced amorphization into the cut cross section of fabricated SiC. Moreover, vertical thermal cracking is found on the periodic tip region treated with laser scribing. To investigate the influence of stress-induced damage on mechanical characteristics of fabricated SiC, the nanoindentation technique is utilized to identify modulus gradient and mapping behavior. Analysis results reveal that damage-induced degradation on modulus behavior is observed from the edge of the periodic tip region to the hinterland region, which the measured reduced modulus results of aforementioned regions are 325.87±56.21 and 284.85±30.02 GPa, respectively. Moreover, the thickness of the damaged layer that covers the cut cross section is estimated to be at least 150 nm by utilizing continuous stiffness measurement (CSM) nanoindentation. The modulus mapping characteristics on the molten and unmolten regions are within the range of 90–160 GPa and 180–300 GPa, respectively. The composition of molten region is investigated by the EDS analysis and the corresponding reduced modulus results is revealed as 105.86±16.46 GPa.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton’s principle, the nonlinear governing equation of an axially functionally graded (AFG) pipe is established. The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam. Via the direct multi-scale method, the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method (DQEM). The influence of Young’s modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions. In general, the pipe in the supercritical region is more sensitive to the pulsating excitation. The nonlinearity changes from hard to soft, and the non-trivial equilibrium configuration introduces more frequency components to the vibration. Besides, the increasing Young’s modulus gradient improves the critical pulsating flow velocity of the parametric resonance, and further enhances the stability of the system. In addition, when the temperature increases along the axial direction, reducing the gradient parameter can enhance the response asymmetry. This work further complements the theoretical analysis of pipes conveying pulsating fluid.