A Computational Framework for Self-healing Vitrimer Polymers: Finite Element Implementation and Numerical Validation

  • Caggiano, Antonella Chiara (UPC / CIMNE)
  • Turon, Francesc (UPC / CIMNE)
  • Otero, Fermin (UPC / CIMNE)
  • Comellas, Ester (UPC / CIMNE)

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Polymers are typically classified as thermoplastics or thermosets. Thermoplastics can be reshaped upon heating, while thermosets undergo irreversible curing, offering superior mechanical performance but poor reprocessability. Vitrimers represent a unique class of polymers that bridge this gap by combining the mechanical properties of thermosets with the reprocessability of thermoplastics. This is enabled by dynamic covalent bonds, which can reorganise and effectively heal the material at certain temperatures. Building on a recently proposed constitutive model for vitrimer-based self-healing polymers, its numerical implementation into the finite element code FEMUSS [1] is presented. The model captures the evolution of isotropic mechanical damage and its recovery through thermally activated healing processes. FEMUSS is an open-source, object-oriented code for nonlinear simulations in solid mechanics, heat transfer, and multiphysics. In this study, the solid thermo-mechanics module is used with displacement-based quadrilateral (2D) and hexahedral (3D) elements. Constitutive equations are integrated at Gauss point level using an explicit scheme, and the global nonlinear thermo-mechanical problem is solved using a partitioned (staggered) approach with consistent tangent matrices under quasi-static loading. The numerical implementation was validated by comparing the FEM results with those from an existing MATLAB Gauss-point level integration scheme. Simulations followed four phases: loading until partial damage, unloading, temperature increase to activate healing, and loading until complete failure. Following verification, the model was applied to structural test cases, including three-point bending and uniaxial tensile specimens. The simulations reproduced key features observed in experiments, such as stiffness recovery after heating and delayed failure due to healing. While the current formulation is restricted to isotropic materials, the computational framework is designed to support future extensions, including anisotropy, pressure-dependent healing, and spatially varying thermal fields. This implementation establishes a robust foundation for simulating the mechanical response of self-healing polymers, supporting the design of more durable and sustainable polymer-based composite structures. REFERENCES [1] FEMUSS. Finite Element Multi-purpose Solver System. https://cimne.com/femuss/