Mathematical Approaches for Structural Mechanics: Theory, Algorithms and Applications

Dear Colleagues,

Mathematical methods provide the basis for analyzing deformation, vibration, stability, and failure in engineering structures. Nonlinear behavior, material heterogeneity (including fractures and pores), and interactions with thermal and hydraulic processes raise questions about model formulation, solution accuracy, and computational efficiency. Analytical approaches and numerical methods address these questions at different scales, from material behavior to structural performance. The use of learning-based models also calls for mathematical analysis of approximation error, stability, and consistency with governing physical laws.  This Special Issue invites original research and review articles on the theory, algorithms, and applications of mathematical methods in structural mechanics. Contributions that connect mathematical developments with clearly defined problems in material and structural engineering are particularly welcome.  Topics of interest include, but are not limited to, the following: analytical and numerical methods for structural deformation, vibration, buckling, and stability; mathematical characterization of cracks, fracture networks, and pore structures, along with their effects on mechanical behavior; fractal geometry and scaling laws in material and structural engineering; constitutive modeling, homogenization, and multiscale analysis of heterogeneous materials; partial differential equations and solution methods for coupled thermal, hydraulic, and mechanical processes; variational and nonlocal approaches to damage, fracture, and structural failure; inverse problems, uncertainty quantification, and structural optimization; and physics-informed learning and operator learning for structural analysis, including convergence and error estimation.

Dr. Dayu Ye
Prof. Dr. Hongfei Duan
Dr. Danqi Li
Dr. Shuaishuai Ren
Guest Editors

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