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In this study, a finite deformation phase-field formulation is developed toinvestigate the effect of hygrothermal conditions on theviscoelastic-viscoplastic fracture behavior of epoxy nanocomposites undercyclic loading. The formulation incorporates a definition of the Helmholtz freeenergy, which considers the effect of nanoparticles, moisture content, andtemperature. The free energy is additively decomposed into a deviatoricequilibrium, a deviatoric non-equilibrium, and a volumetric contribution, withdistinct definitions for tension and compression. The proposed derivationoffers a realistic modeling of damage and viscoplasticity mechanisms in thenanocomposites by coupling the phase-field damage model with a modified crackdriving force and a viscoelastic-viscoplastic model. Numerical simulations areconducted to study the cyclic force-displacement response of both dry andsaturated boehmite nanoparticle (BNP)/epoxy samples, considering BNP contentsand temperature. Comparing numerical results with experimental data shows goodagreement at various BNP contents. In addition, the predictive capability ofthe phase-field model is evaluated through simulations of single-edge notchednanocomposite plates subjected to monolithic tensile and shear loading.

Cyclic viscoelastic-viscoplastic behavior of epoxy nanocomposites under hygrothermal conditions: A phase-field fracture model