Introduction to Coupled Theories in Solid Mechanics

The coupled response of solid materials to multiple fields, such as deformation, heat, electricity, and magnetism, plays a crucial role in modern engineering applications, from soft robotics to energy storage. Advancing theoretical models and numerical implementations for these coupled behaviours in solids is a challenging and exciting frontier in mechanics.

This textbook introduces some foundational coupled theories in solid mechanics by starting from fundamental principles of mechanics, thermodynamics, and electrodynamics, and specializing to model particular 'smart materials'. Numerous representative simulations are provided, demonstrating key coupled behaviours and engineering applications for each theory.

The large deformation coupled theories discussed in this book have been numerically implemented in the open-source finite element program FEniCS, and representative simulations which illustrate key coupled behaviors are presented for each theory. The FEniCS codes for the representative simulations shown in this book are available online on the book's companion website: https://solidmechanicscoupledtheories.github.io/.

Ideal for graduate students, researchers, and practicing engineers, Introduction to Coupled Theories in Solid Mechanics serves as both an introduction to the field and a foundational resource for building the coupled theories and simulation tools of the future.

Lallit Anand, Warren and Towneley Rohsenow Professor of Mechanical Engineering, Massachusetts Institute of Technology,Eric M. Stewart, Assistant Professor of Mechanical Engineering, University of Cincinnati,Shawn A. Chester, Associate Professor of Mechanical Engineering, New Jersey Institute of Technology

Lallit Anand received his undergraduate degree from IIT Kharagpur and his doctorate from Brown University. After a few years in industry at U.S. Steel's Fundamental Research Laboratory, he joined the MIT faculty, where he is currently the Rohsenow Professor of Mechanical Engineering. The honors he has received include: ICES Eric Reissner Medal, 1992; ASME Fellow, 2003; Khan International Plasticity Medal, 2007; IIT Kharagpur Distinguished Alumnus Award, 2011; ASME Drucker Medal, 2014; MIT Den Hartog Distinguished Educator Award, 2017; Brown University Engineering Alumni Medal, 2018; SES Prager Medal, 2018; and SES Fellow, 2024. He was elected to the U.S. National Academy of Engineering in 2018.



Eric M. Stewart obtained a B.S in Aerospace Engineering from Georgia Tech in 2018. He then obtained M.S. and Ph.D. degrees in Mechanical Engineering from MIT in 2021 and 2025, where he was a recipient of the National Defense Science and Engineering Graduate (NDSEG) Fellowship. He joined the faculty of the University of Cincinnati in 2025, where he is currently an Assistant Professor in the Department of Mechanical and Materials Engineering.


Shawn A. Chester obtained his BS and MS in Mechanical Engineering from NJIT, and his PhD from MIT. After a postdoc at Lawrence Livermore National Laboratory, he joined the faculty at NJIT. He is the recipient of several honors and awards, including an NSF CAREER award, the ASME Thomas J.R. Hughes Young Investigator Award, the Newark College of Engineering Rising Star Research Award, and the NJIT Excellence in Research Award.

Part I - Finite Elasticity of Elastomeric Materials1. Finite elasticity of elastomeric materials2. Numerical implementation of finite elasticity3. Representative simulationsPart II - Viscoelasticity of Elastomeric Materials4. Viscoelasticity of elastomeric materials5. Numerical implementation of the viscoelasticity theory6. Representative simulationsPart III - Thermoelasticity of Elastomeric Materials7. Thermoelasticity of elastomeric materials8. Numerical implementation of thermoelasticity of elastomeric materials9. Representative simulationsPart IV - Poroelasticity of Elastomeric Gels10. Poroelasticity of elastomeric gels11. Numerical implementation of poroelasticity of elastomeric gels12. Representative simulationsPart V - Thermally-Responsive Elastomeric Gels13. Thermally responsive elastomeric gels14. Numerical implementation of theory for thermally responsive gels15. Representative simulationsPart VI - Cahn-Hilliard Theory for Species Diffusion Coupled with Elastic Deformations16. Cahn-Hilliard theory for species diffusion and phase segregation17. Coupled chemo-mechanical theory for species diffusion and phase segregation18. Numerical implementation of the coupled chemo-mechanical theory19. Representative simulationsPart VII - Electro-Elasticity of Dielectric Elastomers20. Electroelasticity of dielectric elastomers21. Numerical implementation of the theory for dielectric elastomers22. Representative simulationsPart VIII - Electro-Viscoelasticity of Dielectric Elastomers23. Electro-viscoelasticity of dielectric elastomers24. Numerical implementation of the electro-viscoelasticity theory25. Representative simulations for dielectric viscoelastomersPart IX - Electro-Chemo-Elasticity of Ionic Polymers26. Electro-chemo-elasticity of ionic polymers27. Numerical implementation of theory for ionic polymers28. Representative simulationsPart X - Magneto-Elasticity of Hard-Magnetic Soft-Elastomers29. Magneto-viscoelasticity of hard-magnetic soft-elastomers30. Numerical implementation of the theory31. Representative simulationsPart XI - Magneto-Elasticity of Soft-Magnetic Soft-Elastomers32. Magneto-viscoelasticity of soft-magnetic soft-elastomers33. Numerical implementation of the theory for s-MREs34. Representative simulationsAppendices