# Thermoplastic Materials for the Metal Replacement of Non-Structural Components in Marine Engines
## Appendix A Computational Details  
The Berendsen thermostat/barostat [27] with coupling time constants \(\tau_{T}\) = 0.1 s and \(\tau_{P}\) = 0.5 ps was used to handle temperature and pressure control during all MD calculations. To account for short-range intermolecular interactions in the fully atomistic macromolecular models, the Lennard-Jones 9-6 potential function with geometric mean combination criterion was applied. Long-range electrostatic interactions were managed _via_ the particle mesh Ewald (PME) [28] method to an accuracy of 0.001 kcal/mol. The length of the simulation cell was used as the cut-off distance for truncating any non-bonded interactions. Unless otherwise specified, all MD runs used the velocity Verlet approach with a 1 fs time step to integrate [PERSON]'s equations of motion. In order to determine the stress-strain relationship for the various polymer/(nano)composite systems, the first step in the simulation protocol consisted in reaching the minimum initial stress state for each equilibrated periodic box obtained as described above. Accordingly, MD simulations in the constant volume-constant temperature (NVT) and constant volume-constant energy (NVE) ensembles were run on each simulation box for 5 ns and 2 ns, respectively. To relieve initial stresses, each unit cell size was then relaxed using constant temperature-constant pressure (NPT) MD simulations (up to several thousand steps in length depending on the size of the simulation box), followed by 2 ns of further MD equilibration of the NVE ensemble. In order to preserve the filler shape, a 0.5% uniform strain field was applied to each equilibrated system along the necessary directions by maintaining the filler coordinates unchanged while proportionally scaling both the unit cell and positions of the atoms along the polymer chains. Each simulation cell was stressed using this computational method to determine the unidirectional tension/compression (UT/C) and hydrostatic tension/compression (HT/C), respectively. During UT/C simulations, one direction was subjected to strain in the first instance, and the procedure was then repeated for the other two directions starting with the unstrained cell. On the other hand, in HT/C simulations, the same strain field was concurrently applied to all normal directions. Stress is expressed at the atomic level as a virial form:  
\[\sigma_{ij}=-\frac{1}{V}\sum_{a}\left(M^{a}v_{i}^{a}v_{j}^{a}+\frac{1}{2}\sum _{b\
eq a}F_{i}^{ab}r_{j}^{ab}\right) \tag{1}\]  
where V is the simulation cell volume, denoted by the sum of each atom's volume V\({}^{a}\); the i-th and j-th components of atom a's velocity are denoted as v\({}_{i}^{a}\) and v\({}_{j}^{a}\), respectively; F\({}_{i}^{ab}\) is the i-th component of the force between atoms a and b; \(r_{j}^{ab}\) is the separation between the same two atoms. Tensile stress is to be expressed as a positive amount by the use of the negative sign. Since, in the context of continuum mechanics the assumptions that: (1) the polymer matrix and the pertinent (nano)composites are characterized by materialsymmetry, and (2) the linear relationship between stress and strain both hold, the equivalent continuum's generalized constitutive relation is as follows:  
\[ \begin{cases}\sigma_{11}\\ \sigma_{22}\\ \sigma_{33}\end{cases} = \begin{bmatrix}\text{C}_{11}&\text{C}_{12}&\text{C}_{12} \\ \text{C}_{12}&\text{C}_{11}&\text{C}_{12}\\ \text{C}_{12}&\text{C}_{12}&\text{C}_{11}\end{bmatrix}\begin{cases}\epsilon_{1 1}\\ \epsilon_{22}\\ \epsilon_{33}\end{cases}  \tag{10}\]  
where \(\text{C}_{\text{ij}}\) are the elastic constants (stiffness); \(\sigma_{\text{ij}}\) and \(\epsilon_{\text{ij}}\) are the stress and strain components, respectively. As mentioned in the main text, a 0.5% strain was applied to the undeformed cell along one direction at a time in order to anticipate stress-strain behaviour under unidirectional tension or compression. The only non-zero strain component in this scenario, using direction 1 as the default, is \(\epsilon_{11}\).