Mathematical Modeling and Numerical Simulation in Engineering: Nonlocal Theory and Intelligent Construction Technologies

Dear Colleagues,

We welcome contributions that demonstrate a strong, meaningful coupling between novel numerical techniques and modern experimental methods. This includes research utilizing advanced computational frameworks, such as finite element methods, isogeometric analysis, meshfree methods, and specialized approaches like the scaled boundary finite element method. A key emphasis is placed on peridynamics, the nonlocal theory using integral equations, for simulating complex fracture and multi-physics phenomena. Submissions that address the computational challenges of such methods through GPU-accelerated computation​ and multi-scale modeling frameworks​ are encouraged. Crucially, these numerical advancements should be integrated with physical evidence. We therefore seek studies that employ advanced experimental diagnostics—such as digital image correlation (DIC), acoustic emission, or high-speed photography—to capture full-field deformation and fracture evolution for model validation, calibration, and refinement. Topics of interest include, but are not limited to, novel frameworks for experiment-simulation synergy; multi-scale analysis of damage in quasi-brittle materials; fracture under dynamic loading or coupled thermal-mechanical conditions; and the development of experimentally informed constitutive models.

The scope of this Special Issue includes but is not limited to the following research areas:

Advanced numerical methods in engineering simulation: We welcome contributions on novel computational techniques including finite element methods, isogeometric analysis, meshfree methods, and specialized approaches such as the scaled boundary finite element method (SBFEM). Particular emphasis is placed on peridynamics, a nonlocal continuum theory proposed by Stewart A. Silling in 2000, which uses integral equations rather than partial differential equations to describe material behavior. This approach effectively overcomes the limitations of traditional differential equations in discontinuous problems, making it particularly valuable for simulating crack propagation, damage, and multi-physics coupling phenomena. Submissions addressing GPU-accelerated computation techniques and multi-scale modeling frameworks are particularly encouraged.

Intelligent construction and infrastructure development: This topic focuses on numerical simulation applications in smart infrastructure, including virtual design and construction, building information modeling (BIM), and digital twins for infrastructure lifecycle management. A special subtopic is intelligent compaction technology, which represents a transformative approach to quality control in geotechnical engineering. This technology utilizes integrated systems with GPS/GNSS positioning, inertial navigation, and real-time monitoring to achieve comprehensive control over compaction parameters such as rolling trajectory, number of passes, and compaction strength. Contributions may explore how these digital compaction technologies overcome traditional limitations including difficulty in controlling compaction quality, inability to trace process data, and challenges in avoiding human errors.

Inverse problems and mathematical modeling in engineering: This section addresses mathematical inverse problems in engineering applications, including parameter identification, optimization algorithms, and model calibration techniques. Research papers exploring the integration of machine learning with traditional numerical methods for solving inverse problems are welcome, as are contributions on uncertainty quantification in engineering simulations.

Engineering materials simulation: Contributions in this area should focus on multiscale modeling of material behavior, damage evolution, and failure mechanisms in various engineering materials. We encourage submissions that leverage peridynamics for simulating complex fracture phenomena in materials with inherent defects and spatial variability. For instance, the random peridynamics method (RPD) combines the advantages of peridynamics for simulating crack development with random field methods for characterizing spatial variability of material parameters, enabling more accurate modeling of real material states.

Mathematical physics methods in engineering applications: This topic encompasses the application of advanced mathematical physics methods to engineering challenges, including nonlocal models, fractional calculus, peridynamics, and other emerging mathematical frameworks that extend traditional continuum mechanics approaches. Papers may explore various peridynamics frameworks including bond-based, state-based, and non-ordinary state-based peridynamics models. Research addressing computational efficiency improvements through methods such as discontinuous Galerkin formulations and GPU parallelization are especially welcome.

This Special Issue invites original research articles, comprehensive review papers, and case studies that advance the integrated methodology for a more robust understanding and prediction of material fracture behavior. Submissions should emphasize methodological innovation, practical applicability, and cross-disciplinary connections. All manuscripts will undergo a rigorous peer-review process to ensure scientific excellence and relevance to the engineering simulation community.

We look forward to receiving your contributions and collectively advancing the state of the art in numerical simulation for engineering applications.

Dr. Zhiwei Yang
Dr. Yuan Ma
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• peridynamics
• intelligent compaction
• numerical simulation in engineering
• nonlocal models
• fractional PDE
• physics-informed neural networks
• crack propagation simulation
• inverse problems in engineering
• intelligent construction