ENME E6363: Nonlinear Computational Mechanics
Step beyond linear assumptions and into the real world of engineering complexity. This course equips you with the theoretical insight and computational tools to tackle nonlinear phenomena at the heart of modern technologies—from plastic deformation in metals to dynamic contact in aerospace systems. Through a deep dive into nonlinear continuum mechanics, finite element methods, and advanced topics like damage and dynamics, you'll gain the fluency to model, simulate, and solve problems that standard methods can't handle—preparing you for challenges across aerospace, automotive, defense, and biomedical industries.
Course Overview
In a world where engineering systems are becoming increasingly sophisticated, this course delivers both the theory and technical fluency needed to meet emerging societal and industrial demands. It will equip you with the knowledge and skills to model nonlinear phenomena central to industries as diverse as aerospace, automotive, defense, and biomedicine.
Throughout the course, you’ll focus on six core areas:
- Fundamentals of nonlinear continuum mechanics
- Constitutive modeling (nonlinear elasticity, plasticity, and damage)
- Geometric nonlinearity
- Finite element discretization
- Solution strategies for large nonlinear systems
- Advanced topics such as contact mechanics and nonlinear dynamics.
You will learn how to model and simulate nonlinear behaviors in materials and structures using finite element methods. Bridging theory and application, you’ll explore real-world engineering problems where standard linear assumptions break down, such as plasticity, damage and fracture. You’ll also learn how to capture this nonlinear behavior, developing the essential tools for advanced design and analysis in industry and research.
A unique aspect of the course is its focus on computational implementation. You’ll develop and modify finite element code, learning both the mathematics and software architecture required for real-world nonlinear simulations. Object-oriented programming practices and tutorials on modular code design will equip you with coding skills that directly align with industry-standard simulation workflows.
By the end of this course, you will be fluent in both the language and logic of nonlinear simulation. With this core foundation, you’ll be empowered to design safer structures, optimize material performance, and solve interdisciplinary problems involving complex mechanical behavior.
Course Instructor
Jacob Fish
Robert A.W. and Christine S. Carleton Professor of Civil Engineering
Professor Jacob Fish is a leading authority in nonlinear computational mechanics with extensive contributions to the development of advanced numerical methods for nonlinear systems. His career spans over three decades of academic leadership, industrial collaboration, and groundbreaking research in nonlinear multiscale modeling, computational plasticity, damage mechanics, and coupled field problems. As the founding Director of Columbia's Multiscale Science and Engineering Center, his work has focused on creating robust and efficient algorithms capable of addressing the nonlinear behavior of materials and structures under complex loading conditions. His research has influenced simulation tools used in the aerospace, automotive, defense, and energy sectors.