## Experimental
### Finite Element Modeling of Time-Dependent Deformation of WPC Specimens  
Modeling the long-term deformation of an aquacultural geodesic spherical structure made from wood plastic composite lumber (as a thermoplastic and viscoelastic material) was performed using the Norton-Bailey [29; 30; 31; 44; 45; 46] power law model. The model uses the one-dimensional experimental flexural creep data from of WPC lumber tested for 200 days tested at three different stress levels. The time-dependent deformation of an aquacultural geodesic spherical frame structure with a diameter of 20 m made from WPC struts-lumbers was analyzed via a finite element model using the available commercial software, Abaqus [47; 48]. To implement the computed parameters of the Norton-Bailey power law model, a structural analysis of time-dependent deformation was carried out using the available commercial finite element analysis (FEA) software, Abaqus/CAE [47]. The Norton-Bailey power law model in time-hardening was adopted for the material. The 4-point bending tests were modeled using Timoshenko (shear flexible) beam elements (B31) (2-node linear beam in space) (i.e., six-degrees of freedom (dof) at each node of the element) [37; 49] that allow for transverse shear deformation. To investigate the time-dependent behavior of these elements to model the 200-day creep experiments, a preliminary quasi-static Abaqus model in a flat-wise 4-point pending with a value of L/h of 16:1 was conducted using B31 elements. The values of the apparent elastic moduli required for the models were 4340 MPa for the WPC lumber. The preliminary study encompassed a convergence study to the number of elements required to discretize the WPC and HDPE lumber in the 4-point bending models, and it was found that the discretized WPC lumber with the number of B31 elements greater than 10 elements have had the same values of the mid span deflection [point c in Figure 1, 17.6 mm (2% greater than the value of the experimental mid span deflection), and 32.6 mm (6% greater than the value of the experimental mid span deflection)] respectively. Thus, 95 elements type B31 were used to model the creep of WPC in four-point bending. The boundary conditions in the models were set as follows: (1) the supports had a free axial movement in the X-direction and free rotation around the Z-direction and had restricted axial movement in the Y- and Z-direction and restricted rotation around the X- and Y-direction (directions are illustrated in Figure 1); (2) the loading noses (where the flexural load was applied) had free axial movement in the X and Y-direction and free rotation around the Z-direction, whereas, the loading noses had a restricted axial movement in the Z-direction and restricted rotation around the X-direction and Y-direction. The time-step was selected to be instantaneous when the point load was applied during the creep modeling. The time-step (increment) used to model the creep behavior was in days. To minimize computational time for the model analysis, each time-increment (step) (t) was considered as 1 day. The FEA was carried out to model the creep behavior of WPC specimens subjected to 7, 14, and 29% of Fb. The creep models during the 250 days of all the three stress levels are reported in Figure 3. The FEA showed a good agreement with the experimental data. After conducting the one-dimensional (1D) modeling experiment to describe the 200-day flexural creep behavior of WPC lumber, testing was expanded to model the three-dimensional (3D) creep behavior of a 20-m-diameter aquacultural geodesic spherical rigid frame structure. The following assumptions and simplifications were considered in the model: (1) the WPC cross-section was assumed to have a rectangular cross-section where the grooved areas on the top layer were not included in the modeling computations. (2) The dead load was computed for the structure that included the struts and the steel mesh of the cage. However, the structure was analyzed as a space frame without considering the interaction among the struts and the steel mesh.