Mathematics

Numerical and Data-Driven Methods in Solid Mechanics
From Classical Modeling to Machine Learning

Editors: Mamta Kapoor, PhD
Geeta Arora, PhD

Numerical and Data-Driven Methods in Solid Mechanics

In Production
Pub Date: Forthcoming July 2027
Hardback Price: $190 US | £150 UK
Hard ISBN: 9781779649157
E-Book ISBN: 978-1-77964-916-4
Pages: Est. 388 pp w index
Binding Type: Hardback / ebook
Notes: 13 color and 55 b/w illustrations

This important volume, Numerical and Data-Driven Methods in Solid Mechanics: From Classical Modeling to Machine Learning , explores the rapidly evolving intersection of classical computational mechanics and modern data-driven intelligence. As advances in numerical methods, computational power, and machine learning continue to reshape engineering analysis, this volume demonstrates how traditional physics-based modeling and intelligent computational techniques can be integrated to address increasingly complex problems in solid mechanics.

Beginning with the governing differential equations, equilibrium principles, compatibility conditions, and constitutive relations that underpin the discipline, the book progresses through computational modeling techniques, collocation methods, thermo-rheological analysis, smart materials, and surface energy transmission. It then examines emerging approaches that combine numerical rigor with artificial intelligence, including machine learning, predictive modeling, density functional theory, optimization strategies, physics-informed neural networks, and hybrid data-driven numerical methods

Key Features:

  • Provides comprehensive coverage of classical numerical methods in solid mechanics.
  • Explores machine learning and data-driven computational approaches.
  • Demonstrates applications involving smart materials, composites, and thermo-rheological modeling.
  • Examines physics-informed neural networks and modern predictive modeling techniques.
  • Bridges established computational methods with next-generation intelligent engineering solutions.
Designed for researchers, graduate students, and professionals in solid mechanics, computational engineering, materials science, and applied mathematics, the book presents rigorous mathematical formulations alongside practical engineering applications. Throughout, the contributors illustrate how numerical and data-driven methods can improve predictive accuracy, deepen understanding of material behavior, and expand the capabilities of computational mechanics.

CONTENTS:
Preface

PART I: FOUNDATIONS OF SOLID MECHANICS
1. Governing Differential Equations in Solid Mechanics
Bhumika Shaw, Abhilasha, and Abhinav Singhal

2. Differential Equations Framework for Equilibrium, Compatibility, and Constitutive Relations in Solid Mechanics
A. J. D. Nanthakumar and Sadees M.

PART II: NUMERICAL METHODS AND COMPUTATIONAL MODELING
3. Solid Mechanics Modeling: Computational and Numerical Techniques
Ravneet Kaur, Mamta Kapoor, and Geeta Arora

4. Study of Singular Time-Dependent Partial Differential Equations Using the Bessel Collocation Method
Indu Bala

5. Numerical Analysis of Thermo-Rheological Behavior of LSR in Hybrid Solid Mechanics Applications
Akshat Mahajan, Jhunjhun Kumar Mishra, S. Ganesh, Tarunbir Singh, and Monika Verma

6. Study of Surface Energy Transmission in a PZT-7 Smart Material Layered Structure with an Imperfect Interface
Seema, Abhinav Singhal, and Umang Bareja

PART III: DATA-DRIVEN AND MACHINE LEARNING APPROACHES
7. Density Functional Theory: A Numerical and Data-Oriented Framework for Material Property Prediction
M. Nath and A. Bandyopadhyay

8. Machine Learning Foundations for Solid Mechanics
Amita Soni, Abhinav Singhal, Seema, and Shilpa Srivastava

9. Machine Learning Methods for Optimal Design and Control in Solid Mechanics
Nandkishor M. Sawai and Chandrmani Yadav

10. Predictive Modeling of Composite and Smart Materials
Kamlesh Paswan and Chandrmani Yadav

11. Physics-Informed Neural Networks (PINNs) for Solid Mechanics
Meriem Touil, Nassima Meftah, Abderrahim Achouri, and Rabiaa Benesseddik

12. Data-Driven Numerical Methods in Solid Mechanics
Abhilasha and Abhinav Singhal

13. Implementing the Collocation Approach to Solve the One-Dimensional Elastodynamic Wave Equation in Solid Mechanics
Geeta Arora

Index


About the Authors / Editors:
Editors: Mamta Kapoor, PhD
Associate Professor (Research), Marwadi University Research Center, Department of Mathematics, Faculty of Engineering & Technology, Marwadi University, Rajkot, Gujarat, India

Mamta Kapoor, PhD, is Associate Professor (Research) at the Marwadi University Research Center, Department of Mathematics, Faculty of Engineering & Technology, Marwadi University, Rajkot, Gujarat, India. She has approximately ten years of teaching experience and has published over 60 Scopus-indexed research articles. Her research focuses on linear and nonlinear partial differential equations, fractional partial differential equations, computational mathematics, and applied mathematics. She has served as guest editor for several respected international journals. In addition to her mathematical research, Dr. Kapoor has developed expertise in data science, with interests in data analytics, machine learning, and data visualization. She is proficient in Python, R, Tableau, Power BI, and Microsoft Excel for analyzing, interpreting, and presenting complex datasets.

Geeta Arora, PhD
Professor, Department of Mathematics, Lovely Professional University, Punjab, India

Geeta Arora, PhD, is Professor in the Department of Mathematics at Lovely Professional University, Punjab, India. She earned her PhD from the Indian Institute of Technology (IIT) Roorkee in 2011 and has more than 12 years of teaching experience. Her research centers on the development of numerical methods and statistics. She has published over 90 Scopus-indexed research papers and authored 15 book chapters. Dr. Arora has written the books Vedic Mathematics and Essential Statistics, edited a volume on numerical methods published by Taylor & Francis and IGI Global, and is currently contributing to books with Elsevier and Taylor & Francis. She received Research Appreciation Awards from Lovely Professional University in 2017, 2019, and 2024. She has organized numerous workshops on MATLAB and Vedic mathematics for students and faculty members and has supervised nine PhD scholars while currently guiding six more. She has also published eight books with national publishers and is working on five additional books with national and international publishers.




Follow us for the latest from Apple Academic Press:
Copyright © 2026 Apple Academic Press Inc. All Rights Reserved.