Toward Analytical Homogenized Relaxation Modulus for Fibrous Composite Material with Reduced Order Homogenization Method

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.