“…According to the Hertz contact law, 38,44,45 during loading, the contact force F can be determined as follows where α refers to the indentation and k c is the Hertz contact stiffness. It was mentioned that the contact stiffness can be evaluated by 38,44,45 where v p and E p are Poisson’s ratio and elastic modulus of the projectile, respectively, and r p is the projectile radius. It should be noted that equation (9) only gives the contact law during the indentation process loading and cannot take into account permanent indentation.…”
Section: Framework Of the Impact Analysismentioning
confidence: 99%
“…It should be noted that equation (9) only gives the contact law during the indentation process loading and cannot take into account permanent indentation. The contact law during unloading and subsequent reloading can be expressed, respectively, as 38,44,45 where F m refers to the maximum value of contact force reached before unloading and αm and α0 are the maximum indentation and the permanent indentation, respectively. The value of α0 is equal to zero when the maximum indentation becomes lower than a critical value αcr, otherwise can be obtained as 38,44,45 Figure 3.An MMNC beam impacted by a spherical projectile.…”
Section: Framework Of the Impact Analysismentioning
confidence: 99%
“…Usually, Hertzian law is used to examine the low-velocity impact on the composite structures. According to the Hertz contact law, 38,44,45 during loading, the contact force F can be determined as follows…”
Section: Framework Of the Impact Analysismentioning
confidence: 99%
“…For instance, there is a strong framework of research to analyze the lowvelocity impact behavior of CNT-reinforced nanocomposite structures. [38][39][40] A systematic study in the case of the effect of ceramic nanoparticles on the dynamic behavior of MMNCs is needed to establish a design method to make composite structures more reliable and safer for low-velocity impact loads. There is a lack of information in the literature regarding the low-velocity impact behavior of structures made of MMNCs containing SiC nanoscale particles.…”
An efficient multiscale analysis is proposed to investigate the dynamic behavior of metal matrix nanocomposite beams reinforced by SiC nanoparticles under low-velocity impact loads. First, an analytical micromechanics model is developed to obtain the effective elastic properties of ceramic nanoparticle-reinforced metal matrix nanocomposite, and then the finite element method is used to predict the dynamic response of beams made of this nanocomposite material. Two important microstructural features, including size effect and agglomeration of nanoscale particles, are incorporated into the micromechanical analysis. The present simulation results for the elastic modulus and low-velocity impact response show good agreement with previously published results. The effects of volume percent, diameter and dispersion type of ceramic nanoparticles, geometrical features and boundary conditions of nanostructure, velocity and size of projectile on the contact force, and center deflection time histories of metal matrix nanocomposite beams are extensively examined. Analysis shows that homogenously distributed SiC nanoparticles into the metal matrix nanocomposites can obviously increase the nanostructure/projectile contact force and decrease both the beam center deflection and impact duration which is due to the enhancement of elastic properties. However, the ceramic nanoparticle agglomeration has an effect on the decrease of contact force and the increase of both the center deflection and impact duration. Also, it is concluded that decreasing nanoparticle size can increase the contact force and decrease the beam center deflection.
“…According to the Hertz contact law, 38,44,45 during loading, the contact force F can be determined as follows where α refers to the indentation and k c is the Hertz contact stiffness. It was mentioned that the contact stiffness can be evaluated by 38,44,45 where v p and E p are Poisson’s ratio and elastic modulus of the projectile, respectively, and r p is the projectile radius. It should be noted that equation (9) only gives the contact law during the indentation process loading and cannot take into account permanent indentation.…”
Section: Framework Of the Impact Analysismentioning
confidence: 99%
“…It should be noted that equation (9) only gives the contact law during the indentation process loading and cannot take into account permanent indentation. The contact law during unloading and subsequent reloading can be expressed, respectively, as 38,44,45 where F m refers to the maximum value of contact force reached before unloading and αm and α0 are the maximum indentation and the permanent indentation, respectively. The value of α0 is equal to zero when the maximum indentation becomes lower than a critical value αcr, otherwise can be obtained as 38,44,45 Figure 3.An MMNC beam impacted by a spherical projectile.…”
Section: Framework Of the Impact Analysismentioning
confidence: 99%
“…Usually, Hertzian law is used to examine the low-velocity impact on the composite structures. According to the Hertz contact law, 38,44,45 during loading, the contact force F can be determined as follows…”
Section: Framework Of the Impact Analysismentioning
confidence: 99%
“…For instance, there is a strong framework of research to analyze the lowvelocity impact behavior of CNT-reinforced nanocomposite structures. [38][39][40] A systematic study in the case of the effect of ceramic nanoparticles on the dynamic behavior of MMNCs is needed to establish a design method to make composite structures more reliable and safer for low-velocity impact loads. There is a lack of information in the literature regarding the low-velocity impact behavior of structures made of MMNCs containing SiC nanoscale particles.…”
An efficient multiscale analysis is proposed to investigate the dynamic behavior of metal matrix nanocomposite beams reinforced by SiC nanoparticles under low-velocity impact loads. First, an analytical micromechanics model is developed to obtain the effective elastic properties of ceramic nanoparticle-reinforced metal matrix nanocomposite, and then the finite element method is used to predict the dynamic response of beams made of this nanocomposite material. Two important microstructural features, including size effect and agglomeration of nanoscale particles, are incorporated into the micromechanical analysis. The present simulation results for the elastic modulus and low-velocity impact response show good agreement with previously published results. The effects of volume percent, diameter and dispersion type of ceramic nanoparticles, geometrical features and boundary conditions of nanostructure, velocity and size of projectile on the contact force, and center deflection time histories of metal matrix nanocomposite beams are extensively examined. Analysis shows that homogenously distributed SiC nanoparticles into the metal matrix nanocomposites can obviously increase the nanostructure/projectile contact force and decrease both the beam center deflection and impact duration which is due to the enhancement of elastic properties. However, the ceramic nanoparticle agglomeration has an effect on the decrease of contact force and the increase of both the center deflection and impact duration. Also, it is concluded that decreasing nanoparticle size can increase the contact force and decrease the beam center deflection.
“…Since FG-CNTRC's impact response analysis gradually matured recently, scholars have researched lots of FG-CNTRC structures' impact response [25][26][27][28]. Wang et al [29] discussed FG-CNTRC plates' low-velocity impact response on the basis of von Kármán nonlinearity as well as a high-order shear deformation theory.…”
The low-velocity impact response of the sandwich curved panels with functionally graded carbonnanotube-reinforced composite (FG-CNTRC) surface and isotropic foam core is discussed in this paper. Five types of stacking arrangements including uniform distribution of FG-CNTRC considering thermal environment were analysed. Using the Hertz contact law and rule of mixture model as well as the Kármán-type equations, the nonlinear formulations were built and solved by the two-step perturbation method. The carbon nanotubes' volume fraction, the structure size, the original impact velocity, temperature, relative thickness and the influence of gradient forms on the panels' impact behaviours were analysed. The outcomes show that the stiffness of the non-contact surface has large influence on contact response and various types of FG-CNTRC can be used for different operating conditions providing stiffness or cushion performance.
Low velocity impact behavior of carbon fiber reinforced thermoplastic laminates are analyzed in this article. Governing equations are derived based on the first‐order shear deformation theory and Hamilton's principle. The impact contact force history between the impactor and laminate is formulated by the Hertzian contact law. A Ritz‐based solution in space domain for various boundary conditions is developed. Solutions of the system equations in time domain are solved by the Newmark's time integration scheme. Impact parameters such as impact force history, indentation history, and contact time are considered. The accuracy of this method is validated by comparing the obtained results with those from the ABAQUS/Explicit software simulation. The effects of impact velocity, plate geometrical parameters, stacking sequence, and temperature on the dynamic response of laminates under clamped boundary condition and support boundary condition were discussed.
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