We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of grain-level deformation [1]. The method is derived directly from a variational reformulation of rigid-body DEM based on the Lagrange–d’Alembert prin- ciple, thereby embedding translational, rotational, and deformation degrees of freedom within a unified thermomechanical framework. Built on the LS-DEM representation of particle geometry [2], the approach naturally accommodates complex shapes, and their evolution due to interactions. The framework applies broadly to general particle geometries and topologies, and arbitrary deformation modes without restricting the kinematics to a single reduced space or impose narrow assumptions on admissible mode shapes. Its derivation from first principles makes all modeling assumptions explicit and the theoretical structure fully transparent. Deformation modes may be obtained from high-fidelity fully resolved simulations, statistical homogenization procedures, or geometry- and boundary-condition–informed analyses. The resulting deformable DEM retains the robustness, geometric clarity, and scalability of classical DEM while enabling physically grounded grain-level deformability at negligible additional computational cost. Comparisons with full finite-element simulations demonstrate excellent agreement at both particle and system scales, establishing a general and extensible foundation for modeling deformation in particulate systems across mechanics, materials science, and related fields.