4D printing is now commonly defined as a targeted evolution of a 3D printed structure to change its shape, properties, and functionality over time. In direct 4D printing this targeted evolution is embedded in the structure during the 3D printing process. A heat stimulus can be used to trigger a transition between the two states of a printed shape memory polymer. 3D and 4D printing have greatly expanded the design space of a variety of engineering parts. However, the simulation of the direct 4D printing process is still challenging and is often based on thermal expansion models that do not accurately reflect the actual shape memory behavior of the polymers. A more accurate model would be particularly interesting to simulate behavior such as cold programming and sequential deployment. In sequential deployment different regions of a structure can activate at different temperatures, thus creating issues for thermal expansion models without phase transitions. Here, it is shown how a laminate theory approach using FE shell elements can be combined with a custom ABAQUS UMAT material model to simulate accurate shape memory behavior for direct 4D printed PLA bilayers. The thermo-viscoelastic properties of PLA are experimentally determined, and a constitutive model combining viscoelasticity and phase transitions is applied. The constitutive equations serve as input in the ABAQUS UMAT material model. The proposed approach is tuned and verified using a novel, additively manufactured wave spring consisting of direct 4D printed PLA actuators. The proposed modeling approach enables inverse design of standard 4D printed components, such as the presented wave springs. It further enables the customized design of sequentially deployed, direct 4D printed structures.