ABSTRACT Periodic boundary conditions (PBCs) are essential in multiscale modeling for computing the effective properties of heterogeneous materials via representative volume elements (RVEs). While several automated solutions have been developed for implementing PBCs in finite element software, many rely on structured node classification and predefined sets for surfaces, edges, and corners, often resulting in longer scripts and less flexibility when adapting to new geometries. This study presents a compact and generic algorithm for applying PBCs to RVEs with parallel faces. Instead of categorizing boundary nodes into predefined classes, the proposed method replaces this classification by a dynamic constraint list, while vectorized coordinate comparisons are used to identify corresponding node pairs. The elimination of vertex‐, edge‐, and face‐specific handling is achieved through a dynamic constraint construction that generically avoids duplicate constraints at corners and edges. Moreover, the set of constraints is independent from the actual deformation mode to be applied. Once the periodicity equations are defined, the deformation process is performed by boundary and/or load statements, that is step data in Abaqus or CalculiX, which explicitly represent the components of the macroscopic deformation gradient, nominal stress tensor, or a combination of both. Compared to a widely used reference implementation, the proposed approach reduces script length by more than 50% and shows up to 74% faster preprocessing time for fine meshes, while producing identical homogenized results. The algorithm is implemented in Python using Abaqus as the finite element solver. It simplifies the setup of RVE simulations and supports efficient and reproducible multiscale analysis. While demonstrated here for RVEs with simple geometry, the approach can serve as a basis for future extensions to more complex microstructures, such as those observed in 3D‐printed materials.
Sadeghpour et al. (Mon,) studied this question.