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Mechanics of Soft Matter

This course offers an introduction to the physical principles and mechanical behavior of soft matter—from synthetic materials like polymers and gels, to living systems such as cells, tissues, and collective biological assemblies. Structured around five core modules, the course develops intuition and tools for understanding how soft materials deform, flow, and self-organize:

1. The nature of soft materials. What defines “softness”? Explore classes of soft matter, their structure, and how they respond to forces.
2. Continuum mechanics of soft matter. Learn how stress, strain, and flow arise in elastic, viscous, and poroelastic materials.
3. Transport, diffusion, and interfacial phenomena. Study how molecules and particles move through soft media, and how interfaces shape material behavior.
4. Constitutive laws and material models. Examine how to model the behavior of complex materials using viscoelastic, plastic, and active frameworks.
5. Emergence and collective behavior. Discover how local interactions lead to global organization in materials and living systems, from phase separation to tissue morphogenesis.

The course combines theory, simple models, and real-world examples from both engineered and biological systems. It is open to students across physics, engineering, mathematics, chemistry, and biology. Some background in solid mechanics and calculus is recommended, but all key concepts will be introduced in an accessible way. If you’ve ever wondered how cells crawl, how polymers deform and flow, or how living agents form collective swarms, this course will give you the tools to explore the mechanics of the soft and living world.

Continuum Mechanics

This course offers a comprehensive introduction to continuum mechanics, the theoretical foundation for describing the mechanical behavior of solids, fluids, and materials that deform continuously under force. It serves as a gateway to advanced applications in structural engineering, biomechanics, aerospace, geophysics, and materials science. Structured around five core modules, the course equips students with the tools to model and analyze material behavior across a wide range of physical systems:

1. Fundamental principles. Develop a deep understanding of stress, strain, and deformation. Learn how these concepts describe the internal forces and responses in continuous media.
2. Mathematical framework. Build fluency with the tensor calculus and differential equations essential to formulate balance laws and constitutive models in continuum mechanics.
3. Material behavior. Study how materials respond to different types of loading. Topics include linear elasticity, viscoelasticity, and plasticity, with emphasis on the connections between theory and physical behavior.
4. Advanced and nonlinear mechanics. Explore nonlinear elasticity, large deformations, and time-dependent materials. Introduction to computational methods, including how continuum principles underpin modern numerical simulations.
5. Applications across science and engineering. Apply continuum mechanics to real-world systems, from structural components to biological tissues and soft materials. Learn how to model, predict, and interpret material responses in diverse contexts.

The course combines rigorous theory with practical examples, preparing students for research and professional work involving the mechanics of materials and structures. It is open to students in engineering, applied physics, and materials science. A solid background in calculus, differential equations, and basic mechanics is recommended, but all core ideas are built up from first principles.

Mechanics of snow

This course explores the complex mechanics of snow, bridging fundamental principles in solid mechanics with real-world phenomena like snowpack evolution, structural failure, and avalanche initiation. Spanning a wide range of time and length scales, the course integrates theory, modeling, and application to understand snow as a complex and dynamic material. Structured around five core modules, the course develops tools to analyze how snow deforms, weakens, and fractures:

1. The structure of snow and ice. Investigate the crystallographic and cellular architecture of snow and how its microstructure evolves over time. Learn how this evolution governs macroscopic mechanical properties.
2. Snow as a solid material. Apply principles of elasticity, viscoelasticity, and cellular solids to describe how snow behaves under load. Study micromechanics to connect structure to bulk behavior.
3. Failure and damage mechanics. Understand how snow fails. Learn about damage accumulation under stress, and how localized weakening can trigger instabilities and fracture.
4. Fracture and avalanche initiation. Explore how local defects in the snowpack can lead to large-scale fracture. Analyze theoretical and experimental criteria for avalanche release, considering skier-triggered loads and terrain effects.
5. Applications in avalanche science and snow engineering. Use the concepts learned to tackle real-world challenges, from interpreting avalanche risk to designing snow structures. Topics may include skier impacts, mountain curvature, tree anchoring, and the tribology of snow surfaces.

The course combines lecture, discussion, and problem sets with a student-designed final project on a topic of choice, from snowshoe loading to igloo mechanics. It is ideal for students in engineering, geophysics, environmental science, or anyone interested in the mechanics of snow and avalanches. A background in solid mechanics and calculus is recommended, but key ideas will be introduced in an accessible and applied way.