In the context of growing global environmental challenges and innovative mobility concepts, lightweight multi-material design has become a key driver in engineering, such as automotive and aerospace. Semi-structural adhesives are essential for these modular structures, serving in applications ranging from windshield bonding to thermal management in electric vehicle battery housings. Unlike stiff structural adhesive joints, semi-structural adhesive joints with a typical 1-5 mm adhesive layer thickness combine increased strength with high energy absorption and ductility, enabling the compensation of thermal expansions and manufacturing tolerances. The mechanical behavior of these adhesives is characterized by relatively low stiffness, large deformation capabilities, and high failure strains. Their response is fundamentally non-linear, including strain-rate and load-case dependent elasticity, plasticity, and failure, resulting in a visco-elastoplastic behavior with complex damage evolution. Additionally, the failure mechanisms can be distinguished in volumetric damage, driven by cavitation under hydrostatic tension, and isochoric damage under shear loading. This contribution presents an approach for modeling the non-linear viscoelastic-viscoplastic material behavior of semi-structural adhesive joints based on the Three-Network-Model (TNM). We extend the flow rules and develop a rate-dependent damage formulation that accounts for the split between isochoric and volumetric failure. The resulting constitutive model is implemented as a user-defined material model (UMAT) in LS-DYNA with a focus on high predictive accuracy while ensuring numerical efficiency for industrial use. We utilize experimental results from typical shear lap and butt joint tests for the parameter calibration of specific industrial adhesives. This enables reliable product design and accurate failure predictions for semi-structural joints within feasible simulation timeframes in industrial applications.