<p>The constitutive behavior of polymeric materials is commonly described using viscoelastic models. However, conventional viscoelastic constitutive models often require significant simplifications, making it challenging to fully capture the complex nonlinear behavior of such materials. To address this challenge and complement existing analytical approaches, this study proposes a thermodynamically consistent multi-internal-variable neural network (MIV-NN) framework for viscoelastic constitutive modeling, which can flexibly represent the material’s linear or nonlinear viscoelastic behavior. The proposed framework consists of free energy and dissipation potentials. The free energy is decomposed into equilibrium and nonequilibrium parts, where each internal variable corresponds to one nonequilibrium free energy and dissipation branch. The equilibrium free energy is represented using a fully convex neural network (FC-NN). To enhance training efficiency and facilitate the determination of internal variables, a fully convex shared neural network (FC-SNN) is constructed to describe the nonequilibrium free energy and dissipation potentials. In addition, an adaptive method is developed to automatically determine the optimal number of internal variables required to characterize the viscoelastic behavior. During training, a single long short-term memory (LSTM) network is employed to generate internal variables, enhancing efficient and flexible model training. The proposed framework is systematically validated using model-generated synthetic data and experimental data. The results demonstrate that the MIV-NN constitutive model can accurately capture both linear and nonlinear viscoelastic behaviors.</p>