Strain engineering is effective for tuning the electronic properties of Dirac materials via pseudomagnetic fields. However, current understanding of pseudo-Landau levels and pseudospin polarization is largely limited to graphene, leaving other complex hexagonal lattices with Dirac cones uncharted for quantum materials exploration. To address the above challenge, in this study, we develop a universal partial unitary transformation framework to derive a unified form of Dirac Hamiltonian, applicable to a wide range of complex hexagonal Dirac materials. Our results show that the strain-induced pseudomagnetic field has a universal analytical form in these lattices, while the sensitivity of its strength to strain is determined by intrinsic parameters including effective velocity and effective energy. The pseudo-Landau spectra predicted by our theory ($E\propto \sqrt{\left|n\right|}$) are in excellent agreement with numerical simulations by the tight-binding method. Furthermore, we clarify the underlying physical condition governing the sublattice polarization of the $n=0$ Landau level: the specific sublattice composition of pseudospin states. This insight explains the dramatic differences in polarization observed across various lattices. This work opens up a broader material platform for strain electronics and pseudospintronics, and provides a rich set of candidates and a firm theoretical basis for the design of future quantum devices.

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• 2-dimensional systems
• Dirac semimetal
• Strain engineering
• Tight-binding model