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1

Size‑dependent constitutive model incorporating grain refinement and martensitic transformation

Liu Shengqiang, Li Wei, Shen Jinxia, Yang Xiaoming, Wang Baoyu, Liu Jinping

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e38, 2023

EN

The deformation behaviour of materials at the micro-scale level is different from that at the macro-scale level due to the effect of grain size (GS). The mechanism of the influence on martensitic transformation by GS is still unclear, and there are relatively few studies on the relationship between grain refinement and martensitic transformation, most of which focus on the relationship between the initial GS of the material and martensitic transformation. Therefore, in this study, the interaction between grain refinement and martensitic transformation was investigated using a dislocation density-based multiscale constitutive model that incorporated dislocation sliding, strain-induced martensitic transformation (SIMT) related to grain size, and grain refinement. The proposed model evaluated the GS-dependent deformation behaviour of 316L stainless steel (SS). Subsequently, a genetic algorithm was used to determine the parameters of the established model, and the calculated results were compared with that of the experimental data to verify the accuracy of the model. The developed multiscale constitutive model was implemented in Abaqus user subroutine to further investigate the deformation mechanism and validate its accuracy. The results demonstrated that the GS had a significant effect on the SIMT, with the volume fraction of martensite increasing with a rise in the initial austenite GS. In addition, grain refinement affected SIMT and the growth rate of martensite content decreased with the grain refinement caused by deformation. The formation of martensite led to grain refinement, with the refined grains producing negative feedback on the SIMT, thus inhibiting the occurrence of martensitic transformation. This study revealed the microscopic deformation mechanism of 316L SS and provided a constitutive model for micro-forming.

2

Nonlinear forced vibration analysis of micro-rotating shaft-disk systems through a formulation based on the nonlocal strain gradient theory

Panahi Ramin, Asghari Mohsen, Borjalilou Vahid

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 2

art. no. e85, 2023

EN

The paper presents an upgraded size-dependent formulation for micro-rotating shaft-disks system to study their nonlinear forced vibration behavior. The novel formulation is based on the nonlocal strain gradient theory (NSGT). To achieve this goal, first of all, by incorporating the geometrical nonlinearity within the Rayleigh beam theory, the governing equations of the lateral motion of the system are derived by the Hamilton principle and then converted into a complex form. By defning some dimensionless parameters, the normalized form of the complex governing equation is also extracted. In the next step, the Galerkin method is implemented to establish an infinite set of ordinary differential equations (ODEs). Then, with the help of the method of multiple scales, the nonlinear ODE is solved to attain the vibrational amplitude of the system as well as its forward and backward natural frequencies. Lastly, an all-out parametric study is conducted to appraise the impact of some important factors like the nonlocal theory parameter, the strain gradient length scale parameter, the rotational speed, the amount of mass eccentricity and the internal damping coeffcient on the motion amplitude and natural frequencies. The numerical outcomes illuminate well that depending on the relative value of two non-classical parameters of NSGT, this theory have the potential to reflect the hardening or softening attribute of small-scaled mechanical elements.

3

Measurement and analysis of pocket milling features in abrasive water jet machining of Ti-6Al-4V alloy

Natarajan Yuvaraj, Raj K. L. Naresh, Tandon Puneet

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e42, 2023

EN

The present work deals with the size effect of abrasive water jet milling parameters on the square pockets of Ti-6Al-4V alloy. In this study, the abrasive mesh size, water jet pressure and traverse rate were chosen as milling variables and their effect on pocket features such as depth of cut, undercut, material removal rate, and surface roughness were examined. This study also characterizes the milled pocket surfaces under different milling conditions. Most of the measurements and surface characterizations were done using the Dino-Lite Digital Microscope. For both #80 and #100 abrasives, the AWJ-milled pockets were formed with variations in depth milled and rugged surface by increasing the water jet pressure from 175 to 200 MPa under all the selected traverse rate conditions. Also, the variations of depth of cut in successive trajectories found to have a speed bump effect. At these settings, distribution of energy to the work material was more due to deceleration of jet in the boundary close by and changes made in the feed directions in raster path from 0° to 90° at a step-over distance of 0.2 mm. This yielded undercuts in the milled pocket corners. However, there was a significant reduction in the undercut with a water jet pressure of 125 MPa and a traverse rate of 3500 mm/min were employed. Besides, the abrasive mesh size #100 had a better surface topography, and also strong jet footprints were observed with mesh size of #80. Based on the experiments results, the size effect of different milling parameters was seen having influence on the pocket geometry and surface features.

4

Influence of shear depth on seismic performance of shear wall reinforced with BFRP bars: mesoscale modelings

Jin Liu, Miao Liyue, Du Xiuli

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e4, 2023

EN

The seismic performances of 28 geometrically similar concrete shear walls reinforced with basalt fiber-reinforced polymer (BFRP) bars were simulated using a mesoscale modeling approach. In the modeling, concrete heterogeneities were explicitly described, and the interaction between BFRP bars and surrounding concretes was also considered. The influences of shear depth, shear span ratio and vertical reinforcement ratio on the failure of shear walls were investigated. The simulation results indicated that with the increase of shear depth, the failure modes were basically the similar, while the nominal shear strength decreased significantly, namely, the presence of size effect was demonstrated. The shear wall would exhibit different failure modes as the shear span ratio varies. Moreover, it was found that the vertical BFRP bar presented an ignorable influence on the failure mode, while the increase of vertical reinforcement ratio would obviously improve the shear strength of BFRP-RC shear wall. Finally, the present simulated shear strengths were compared with some available size effect laws and some codes.

5

Size effect of synthetic fibre reinforced concrete - investigation using a semi-discrete analytical beam model

Tóth Mária Erdélyiné, Pluzsik Anikó

Architecture Civil Engineering Environment

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2023

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Vol. 16, no. 3

117--129

EN

The size effect is a well-known characteristic of concrete structures. However, in the case of fibre-reinforced concrete (FRC), this issue is not thoroughly explored. Most design recommendations of FRC neglect the size effect or handle the behaviour of FRC structures in case of different structural sizes similar to plain concrete structures (assuming FRC is a homogeneous material). The aim of this paper is to show that the size effect of FRC can be divided, the share of the concrete matrix and the fibres in the size-dependent properties is separable. For the size effect research fifteen synthetic macro fibre reinforced concrete and six plain concrete beam specimens were prepared and tested in three different sizes and then evaluated with the semi-discrete analytical (SDA) model. The analysis of the experimental specimens has shown that the size effect significantly influences the concrete material in the case of FRC with softening material behaviour, but the residual loadbearing capacity which mainly arise from the local bridging effect of fibres is essentially independent of the structural size. It is also shown in this paper that the two defining parameters of the SDA model is independent of the structural size, so the model provides an excellent tool in case of the design of real-sized FRC structures.

6

Meso-scale modelling of size effect on pure torsional-shear of RC columns

Jin Liu, Zhu Huajie, Du Xiuli

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e36, 2022

EN

Under the action of earthquake, the reinforced concrete (RC) columns may subject to torsional moment, and the existence of torsion will change the failure mode of RC columns. Moreover, the torsional fracture of RC columns often presents a brittle fracture pattern, and thus may have an obvious size effect. In this work, a three-dimensional meso-scale simulation approach was utilized to study the torsional failure of RC columns. The influence of structural size, longitudinal reinforcement ratio, stirrup ratio and cross-sectional shape on torsional failure of RC columns was investigated. The results show that: (1) the tested RC columns show brittle failure patterns, the nominal torsional strength presents obvious size effect; (2) the longitudinal reinforcement presents little influence on the size effect; (3) columns with square cross-section present stronger size effect than the ones with circular shape; (4) stirrups can improve the torsional strength, while they would weaken the size effect on torsional strength. In addition, a novel size effect law that can describe the quantitative influence of stirrup ratio was established. Finally, based on the variable angle truss model, the formulas for calculating the pure torsional capacity of RC columns were modified, considering the quantitative influence of the stirrup ratio on the size effect.

7

Analytical and parametric analysis of thermoelastic damping in circular cylindrical nanoshells by capturing small-scale effect on both structure and heat conduction

Li Ming, Cai Youjie, Bao Li, Fan Rui, Zhang Hongbin, Wang Hongyan, Borjalilou Vahid

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e14, 2022

EN

This article intends to examine thermoelastic damping (TED) in circular cylindrical nanoshells by considering small-scale effect on both structural and thermal areas. To fulfill this aim, governing equations are extracted with the aid of nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model. Circular cylindrical shell is also modeled on the basis of Donnell–Mushtari–Vlasov (DMV) equations for thin shells. By inserting asymmetric simple harmonic oscillations of nanoshell into motion, compatibility and heat conduction equations, the size-dependent thermoelastic frequency equation is obtained. By solving this equation and deriving the frequency of nanoshell affected by thermoelastic coupling, the value of TED can be calculated through complex frequency approach. Results of this investigation are given in two sections. First, to appraise the validity of presented formulation, a comparison study is conducted between the results of this work in special cases and those reported in the literature. Next, by providing several numerical data, a detailed parametric study is performed to highlight the profound impact of nonlocality and dual-phase-lagging on TED value in simply supported cylindrical nanoshells. The influence of some determining factors such as mode number and type of material on TED is also evaluated.

8

Size effect at testing strength properties of concrete

Akram Amanda

Budownictwo i Architektura

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2021

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Vol. 20, no 4

37--45

EN

Various strength characteristics of concrete are considered as fracture parameters. The compressive strength of concrete is of paramount importance when designing concrete structures, whereas tensile strength of concrete is the basic property when estimating cracking resistance of a structure and analysing fracture processes in concrete. When testing the compressive strength of concrete, the results are dependent on the shape and dimensions of used specimens. Some findings reported in the literature suggest that size effect exists also when testing such fracture properties of concrete as tensile strength. Unfortunately this problem is much less recognized and described compared to size effect in compressive test results. In this paper, the experimental investigation is presented on how the length of cylindrical specimens influences the tensile splitting strength of concrete obtained by means of the Brazilian method. Additional variable parameters were: type of aggregate (natural gravel and crushed granite) and cement-water ratio (C/W = 1.8 and C/W = 2.6). In conducted laboratory experiments a higher splitting tensile strength of concrete was noted for all specimens with nominal dimensions of 150×150 mm, compared to specimens 150×300 mm in size, regardless of type of aggregate or cement-water ratio.

9

Modeling of dynamic growth of a micro-scaled void based on strain gradient elasto-plasticity

Ma Xinbing, Liu Jinxing, Wang Jiadong, Pan Hao

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 4

927--941

EN

Void initiation and growth serve as an important mechanism in ductile failures in metals. Particularly, on the micron-level, the extra hardening effect associated with strain gradient is accounted for by adopting strain gradient elasto-plasticity instead of the conventional plasticity. Effects of inertial, strain gradient hardening and thermal softening are formulated analytically for the case where a spherical void expands under external hydrostatic stress. As demonstrated by our results, the inertia effect firstly tends to hinder but then promotes the void growth. The threshold stress required for rapid void growth is lifted due to extra hardening of strain gradient so that the growth of a smaller void is delayed more remarkably. A considerable thermal softening phenomenon is observed here, which is caused by plastic work during the deformation process. The final void growth rate is mainly related to the maximum loading, which is consistent with the prediction based on the classical plastic theory.

10

On some problems in determining tensile parameters of concrete model from size effect tests

Marzec Ireneusz, Bobiński Jerzy

Polish Maritime Research

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2019

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nr 2

115--125

EN

The paper presents results of numerical simulations of size effect phenomenon in concrete specimens. The behaviour of in-plane geometrically similar notched and unnotched beams under three-point bending is investigated. In total 18 beams are analysed. Concrete beams of four different sizes and five different notch to depth ratios are simulated. Two methods are applied to describe cracks. First, an elasto-plastic constitutive law with a Rankine criterion and an associated flow rule is defined. In order to obtain mesh independent results, an integral non-local theory is used as a regularisation method in the softening regime. Alternatively, cracks are described in a discrete way within Extended Finite Element Method (XFEM). Two softening relationships in the softening regime are studied: a bilinear and an exponential curve. Obtained numerical results are compared with experimental outcomes recently reported in literature. Calculated maximum forces (nominal strengths) are quantitatively verified against experimental values, but the force – displacement curves are also examined. It is shown that both approaches give results consistent with experiments. Moreover, both softening curves with different initial fracture energies can produce similar force-displacement curves.

11

Influence of pre-tension on torsion of microscale Cu wires: a study via strain gradient theory

Ma Xinbing, Liu Jinxing

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 4

1055--1065

EN

Nonproportional plastic deformations on the microscale are an emerging topic. A simplified theory of strain gradient elasto-plasticity is developed to study the evolution of yield strength in a copper wire sequentially experiencing tension and torsion. The pre-tension deformation and stress are inherited to the upcoming torsion process, resulting in a nonproportional loading condition. With consideration of the extra hardening effect due to strain gradient, pre-tension weakens the extra hardening effect of the strain gradient and the dependence on the wire radius. Cyclic torsion behavior is also investigated. Anomalous Bauschinger effect and plastic softening are found.

12

An experimental investigation on fracture parameters and brittleness of self-compacting lightweight concrete containing magnetic field treated water

Salehi Hasan, Mazloom Moosa

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 3

803--819

EN

In this study, an experimental research on the fracture parameters of self-compacting lightweight concrete (SCLC) using tap and magnetic water (MW) is presented. For all SCLC mixtures, common fracture parameters were specified by means of both work of fracture method (WFM) and the size effect method (SEM). Three-point bending tests were carried out on 90 notched beams with six mix compositions. The beams were made from mixes with three different water to cement (w/c) ratios of 0.37, 0.47 and 0.52; also, both tap and magnetic water were consumed in the concrete mixes, separately. The results of this research showed that by using MW in SCLC and decreasing w/c ratio from 0.52 to 0.37: (a) both initial fracture energy Gf and total fracture energy GF increased; (b) the fracture toughness and the mechanical properties of SCLC improved. Additionally, the achieved data exhibited that there was a reasonable relation between the total fracture energy obtained by WFM and the initial fracture energy achieved through SEM. The average of GF to Gf ratio in SCLC was 2.70. Furthermore, by using MW in SCLC mixtures, compressive strength, splitting tensile strength and modulus of elasticity increased up to 18%, 9% and 10%, respectively.

13

Carbon nanotubes with controlled length – preparation, characterization and their cytocompatibility effects

Cendrowski K., Jedrzejczak-Silicka M.

Polish Journal of Chemical Technology

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2018

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Vol. 20, nr 2

71--79

EN

Multiwalled carbon nanotubes (MWCNTs) have attracted huge attention due to their multifunctionality. Their unique properties allows for covalent and noncovalent modifi cations. The most simple method for functionalization of carbon nanotubes is their decoration with the oxygen containing moieties which can be further simultaneously functionalized for design of new class carriers for targeting and imaging. Here, we present methodology for chopping nanotubes, characterization of MWCNTs, the effect of size on the biocompatibility in culture of L929 mouse fi broblasts using WST-1, LDH and apoptosis assays. The analysis provides the optimal carbon nanotubes length and concentration which can be used for functionalization in order to minimize the effect of the secondary agglomeration when interacting with cells.

14

Badanie efektu skali poprzez modyfikację odcinka pomiarowego próbki przy zginaniu obrotowym oraz ocena wpływu chropowatości

Niesłony A., Agrest D.

Modelowanie Inżynierskie

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2018

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T. 36, nr 67

44--48

PL

W artykule przedstawiono zarys historyczny badań nad zjawiskiem efektu skali. Opisane zostały warunki przeprowadzenia prób zmęczeniowych oraz uzyskane wyniki. Otrzymano zauważalny efekt skali podczas próby zginania obrotowego. W pracy przedstawiono także spostrzeżenia dotyczące wpływu wybranych czynników na wyniki badań. Zauważono, że jednym z istotnych czynników jest jakość powierzchni próbek. Przedstawiono wykresy wskazujące na zależność chropowatości powierzchni próbek na ich wytrzymałość podczas próby zginania obrotowego.

EN

The article presents a historical outline of research on the phenomenon of scale effect. The conditions for conducting fatigue tests and the results obtained have been described. A noticeable scale effect was obtained during a rotational bending test. The paper also presents observations regarding the influence of selected factors on test results. It was noted that one of the important factors is the surface quality of the specimen. The graphs show the dependence of the surface roughness of the specimen on their strength during a rotational bending test.

15

Vibration analysis of nanotubes based on two-node size dependent axisymmetric shell element

Soleimani I., Beni Y. T.

Archives of Civil and Mechanical Engineering

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2018

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Vol. 18, no. 4

1345--1358

EN

In this paper, size dependent axisymmetric shell element formulation is developed by using the modified couple stress theory in place of classical continuum theory. Since the study of nanoshells is conducted in nanodimensions, the mechanical properties of nanoshells are size dependent; therefore, taking into consideration the size effect, nonclassical continuum theories are used. In the present work the mass–stiffness matrix for axisymmetric shell element is developed, and by means of size-dependent finite element, the formulation is extended to more precisely account for nanotube vibration. It is shown that the classical axisymmetric shell element can also be defined by setting length scale parameter to zero in the equations. The results show that the rigidity of the nanoshell in the modified couple stress theory is greater than that in classical continuum theory, which leads to the increase in natural frequencies. The findings also indicate that the developed size dependent axisymmetric shell element is able to cover both cylindrical and conical shell elements and is reliable for simulating micro/nanoshells. Using size dependent axisymmetric shell element increases convergence speed and accuracy in addition to reducing the number of the required elements.

16

Efekt skali w próbach zginania obrotowego

Agrest D.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2017

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z. 108

7--10

EN

At work describes the size effect. Tests were carried out for specimens of varying length of the load segment. That is not standard approach because the size effect mainly is observed when the size of the cross section is modifying. The study was carried out on a series of cylindrical specimens. Received results were compared with the theoretical assumptions. It also discusses factors affecting the test results and announced further work in the area of size effect.

17

Ubiquitiformal fracture energy

Ou Z.-C., Yang M., Li G.-Y., Duan Z.-P., Huang F-L.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

1101--1108

EN

The ubiquitiformal fracture energy is proposed in the paper and its explicit expression is obtained. Moreover, the numerical results for concrete are found to be in good agreement with those for the critical strain energy release rate. The discrepancy between the numerical results of the traditional fracture energy and the critical strain energy release rate can be explained reasonably, which implies that the ubiquitiformal fracture energy should be taken as an available fracture parameter of materials. Finally, it is numerically found for some concrete that there is not size effect for the ubiquitiformal fracture energy.

18

Fatigue life prediction of aluminium profiles for mechanical engineering

Tomaszewski T., Sempruch J.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 2

497--507

EN

The study presents a method to determine the σa − N curve (high cycle fatigue) for profiles made of AW-6063 T6 aluminium alloy. Experimental material data for a mini specimen taken directly from the tested item and selected empirical correlations allowing for a size effect have been used. A model yielding the lowest relative error of estimating the fatigue life is presented.

19

Study on the size effect of auxetic cellular materials

Janus-Michalska M.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 3

749--757

EN

The objective of this paper is to investigate the effects of scale of an auxetic cellular material sample on the evaluation of elastic properties. Size and boundary effects are studied in detail. This is achieved by conducting computer simulations of the auxetic structure under the typical loading exerted by the compression and simple shearing test performed by means of ABAQUS FEA. The material microstructure is discretized by the plane network of Timoshenko beam elements. The results of the studies give insight to the scale effects. Structures with designed properties can be potentially used for engineering applications.

20

Imperfection sensitivity of the size-dependent postbuckling response of pressurized FGM nanoshells in thermal environments

Sahmani S., Aghdam M. M.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 3

623--638

EN

The purpose of the current study is to address the nonlinear buckling and postbuckling response of nanoscaled cylindrical shells made of functionally graded material (FGM) under hydrostatic pressure aiming to investigate the sensitivity to the initial geometric imperfection in the presence of surface effects and thermal environments. According to a power law distribution, the material properties of the FGM nanoshell are considered change through the shell thickness. Also, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account to eliminate the stretching-bending coupling terms. In order to acquire the size effect qualitatively, the well-known Gurtin-Murdoch elasticity theory is incorporated within the framework of the classical shell theory. Using the variational approach, the non-classical governing equations are displayed and deduced to boundary layer type ones. Afterwards, explicit expressions for the size-dependent radial postbuckling equilibrium paths of imperfect FGM nanoshells are proposed with the aid of a perturbation-based solution methodology. It is displayed that by moving from the ceramic phase to the metal one, the critical buckling pressure decreases, but the postbuckling stiffness increases, because in contrast to the ceramic phase, the surface modulus and residual surface stress associated with the metal phase have the same sign.