A 3D fractional viscoelastic damage model for thermosetting polymer composites: Theory and FEM implementation

Driven by advances in structural reinforcement, composite technologies, and new energy systems, there is a growing engineering demand for epoxy resin-based materials, particularly in bonding, mechanical deformation, and damage management applications. Building an accurate constitutive model is essential for better understanding its deformation characteristics and improving the design of polymer-based material products. However, material damage degradation cannot be well captured by viscoelastic models while elasto-viscoplastic models need more parameters. In this study, a fractional viscoelastic damage model based on fractional calculus theory is developed to characterize the stress soften and nonlinear response of polymer-based materials, suitable for implementation in finite element software. An improved variable-order fractional damage evolution equation for 3D applications is proposed and successfully implemented in a user-defined subroutine via the finite difference method, with the complete modeling framework realized in commercial software Abaqus. Then, uniaxial tension and compression tests of epoxy-based materials were simulated in Abaqus, and corresponding error analyses were performed to show model’s accuracy. Furthermore, equi-biaxial tensile simulations of a cruciform specimen were carried out, confirming the model’s applicability under multiaxial loading. Moreover, the dependence of fractional parameters on material state variables provides useful perspectives for epoxy adhesive design and processing.