TY - JOUR
T1 - A three-scale asymptotic expansion for predicting viscoelastic properties of composites with multiple configuration
AU - Yang, Zhiqiang
AU - Sun, Yi
AU - Cui, Junzhi
AU - Ge, Jingran
N1 - Publisher Copyright:
© 2019 Elsevier Masson SAS
PY - 2019/7/1
Y1 - 2019/7/1
N2 - A novel three-scale asymptotic expansion used to evaluate viscoelastic analysis of composites with multiple configuration is systematically studied. The heterogeneities of composite structures are described by periodic layout of unit cells on the microscale and mesoscale. Firstly, the three-scale asymptotic formulations based on homogenization approach and Laplace transform are established, and the local cell solutions in microscale and mesoscale are also defined. Further, two kinds of homogenized coefficients are derived by upscaling methods, and the homogenized equations are obtained on whole macroscopic domain. Also, the strain and stress fields are constructed as three-scale asymptotic solutions by assembling the unit cell solutions and homogenized solutions. Then, the finite element algorithms based on inverse Laplace transform and the three-scale asymptotic homogenization are proposed. Finally, some typical numerical results are employed to validate the presented approaches. They illustrate that the three-scale asymptotic approaches proposed in this paper are efficient and accurate for analyzing the viscoelastic problems of the composites with multiple configuration.
AB - A novel three-scale asymptotic expansion used to evaluate viscoelastic analysis of composites with multiple configuration is systematically studied. The heterogeneities of composite structures are described by periodic layout of unit cells on the microscale and mesoscale. Firstly, the three-scale asymptotic formulations based on homogenization approach and Laplace transform are established, and the local cell solutions in microscale and mesoscale are also defined. Further, two kinds of homogenized coefficients are derived by upscaling methods, and the homogenized equations are obtained on whole macroscopic domain. Also, the strain and stress fields are constructed as three-scale asymptotic solutions by assembling the unit cell solutions and homogenized solutions. Then, the finite element algorithms based on inverse Laplace transform and the three-scale asymptotic homogenization are proposed. Finally, some typical numerical results are employed to validate the presented approaches. They illustrate that the three-scale asymptotic approaches proposed in this paper are efficient and accurate for analyzing the viscoelastic problems of the composites with multiple configuration.
KW - Laplace transform
KW - Viscoelastic problems
KW - three-scale asymptotic homogenization
UR - http://www.scopus.com/inward/record.url?scp=85065013187&partnerID=8YFLogxK
U2 - 10.1016/j.euromechsol.2019.04.016
DO - 10.1016/j.euromechsol.2019.04.016
M3 - Article
AN - SCOPUS:85065013187
SN - 0997-7538
VL - 76
SP - 235
EP - 246
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
ER -