In this manuscript, we propose an analytical equivalent linear viscoelastic constitutive model for fiber-reinforced composites, bypassing general computational homogenization. The method is based on the reduced-order homogenization (ROH) approach. The ROH method typically involves solving multiple finite element problems under periodic conditions to evaluate elastic strain and eigenstrain influence functions in an ‘off-line’ stage, which offers substantial cost savings compared to direct computational homogenization methods. Due to the unique structure of the fibrous unit cell, “off-line” stage calculation can be eliminated by influence functions obtained analytically. Introducing the standard solid model to the ROH method enables the creation of a comprehensive analytical homogeneous viscoelastic constitutive model. This method treats fibrous composite materials as homogeneous, anisotropic viscoelastic materials, significantly reducing computational time due to its analytical nature. This approach also enables precise determination of a homogenized anisotropic relaxation modulus and accurate capture of various viscoelastic responses under different loading conditions. Three sets of numerical examples, including unit cell tests, three-point beam bending tests, and torsion tests, are given to demonstrate the predictive performance of the homogenized viscoelastic model. Furthermore, the model is validated against experimental measurements, confirming its accuracy and reliability.

The multiscale computational method with asymptotic analysis and reduced-order homogenization (ROH) gives a practical numerical solution for engineering problems, especially composite materials. Under the ROH framework, a partition-based unitcell structure at the mesoscale is utilized to give a mechanical state at the macro-scale quadrature point with pre-evaluated influence functions. In the past, the “1-phase, 1-partition” rule was usually adopted in numerical analysis, where one constituent phase at the mesoscale formed one partition. The numerical cost then is significantly reduced by introducing an assumption that the mechanical responses are the same all the time at the same constituent, while it also introduces numerical inaccuracy. This study proposes a new partitioning method for fibrous unitcells under a reduced-order homogenization methodology. In this method, the fiber phase remains 1 partition, but the matrix phase is divided into 2 partitions, which refers to the “1 + 2” partitioning scheme. Analytical elastic influence functions are derived by introducing the elastic strain energy equivalence (Hill-Mandel condition). This research also obtains the analytical eigenstrain influence functions by alleviating the so-called “inclusion-locking” phenomenon. In addition, a numerical approach to minimize the error of strain energy density is introduced to determine the partitioning of the matrix phase. Several numerical examples are presented to compare the differences among direct numerical simulation (DNS), “1 + 1”, and “1 + 2” partitioning schemes. The numerical simulations show improved numerical accuracy by the “1 + 2” partitioning scheme.