## 3 Results
### Elastic Modulus
To investigate the source of variance in the calculated [PERSON]'s modulus, the contributing factors were decomposed into virial stress components, including pairwise energy, bond energy, long-range Coulombic interactions, and kinetic energy contributions (Figure 7a). Notably, the pairwise stress component (green curve) closely overlaps with the total stress (black curve) across all SOCs, confirming that short-range interactions alone account for nearly all of the mechanical response characteristics. The analysis reveals that pairwise interactions play a dominant role in the observed changes in stiffness, while kinetic and long-range contributions remain minimal and stable. This dominance of pairwise interactions emphasizes the importance of short-range bonding changes in determining mechanical properties under varying SOC conditions. The pairwise energy contribution arises from interactions between four types of particles: Li\({}^{+}\), Co\({}^{3+}\), Co\({}^{4+}\), and O\({}^{2-}\). The corresponding pairwise energy components are shown in Figure 7b. As the SOC decreases, the population of Co\({}^{3+}\) ions diminishes, while that of Co\({}^{4+}\) ions increases. Since Co\({}^{4+}\) has a smaller ionic radius, local contraction of Co-O bonds occurs, which is confirmed by the reduction in lattice constants. The localized lattice contraction introduces internal stress gradients, particularly at low SOCs, which can serve as points of structural instability initiation. Figure 6: Evolution of the elastic constant as a function of SOC for the Buckingham potential (Buck) and Deep Potential (DP) models. Experimental references include Ref. [47] (TDTR, time-domain thermoreflectance) and Refs. [44, 48, 49], (NI, nanoindentation). DFT values from Refs. [42, 43, 50] are also included for comparison. Additionally, Co4+ carries a higher positive charge than Co3+, resulting in stronger electrostatic interactions with neighboring oxygen ions. These intensified interactions further promote localized stress buildup in specific regions, as shown by the sharp increase in Co4+ stress contribution at SOC < 0.4. Figure 8 presents the spatial distributions of shear strain fields at representative low, medium, and high SOCs, illustrating the structure at low SOC exhibits higher shear strain distribution. Moreover, Co4+ forms stronger Co-O bonds compared to Co3+, enhancing localized stiffening. This combination of lattice contraction, intensified Coulombic interactions, and bond stiffening generates a stress mismatch, which promotes crack initiation and propagation, particularly at low SOCs. Notably, in Figure 7a, the pairwise contribution dominates the total stress profile, reinforcing its primary role in stress evolution, while bonds and long-range interactions remain minimal. The abrupt increase in total stress near SOC ~0.4 may indicate a critical point for mechanical instability, potentially linked to lattice distortions or defect accumulation. Conversely, contributions from Li+-O2- and Co3+-O2- interactions decrease, further contributing to the decline in stiffness as SOC is reduced. These combined effects highlight the potential mechanical instability that emerges as SOC decreases, emphasizing the importance of considering SOC-dependent stress distributions when evaluating material degradation mechanisms. Figure 7: Stress component \(\sigma_{\mathrm{x}}\) as a function of SOC. (**a**) Decomposition of the total stress into kinetic, pair, bond, and long-range contributions. (**b**) Element-specific contributions to stress. The stress-strain curves for various SOC conditions, calculated using the machine learning-based DP model, are shown in Figure 9. The slope of these curves was used to calculate the stiffness values, which are presented in Figure 6. The results exhibit a clear monotonic decrease in stiffness with SOC, with a minor increase observed at 0.5 SOC. This slight peak may be attributed to a transient strengthening effect linked to optimal cation distribution or localized bonding rearrangements.