An elasto-viscoplastic model for vitrimer andvitrimer-based composites

A compact constitutive framework for modeling the nonlinear response of vitrimer materials,with primary emphasis on identifying and characterizing the in-situ matrix behavior withina vitrimer composite, is presented. The final model consists of a linear spring in parallelwith a Perzyna-type viscoplastic element, with a constant backstress activated only duringunloading. For the present study, the formulation is treated as a 6-parameter model becausethe unloading backstress is allowed to take different values for different loading–unloading paths,which improves the representation of experiment-specific unloading behavior while preservinga simple and physically interpretable structure.Starting from axial stress–strain measurements of ±45◦ carbon fiber reinforced vitrimerlaminates, the corresponding composite shear response is obtained and then used in a secantmodulus-based micromechanics relation to recover the in-situ matrix secant shear modulusat each data point. This, in turn, gives the matrix shear stress–strain curve, allowing theunderlying vitrimer matrix behavior inside the composite architecture to be identified. Theextracted matrix response is then fitted with the proposed constitutive model, showing thatthe framework captures the key nonlinear features of the matrix-dominated response. The samemodel is also shown to represent the overall composite response with good agreement. Overall,the work establishes a practical mechanics-based framework for recovering the in-situ matrixbehavior from experimentally measured laminate responses, and it also lays a foundation forthe future development of a temperature-dependent vitrimer model.