An Integrated Introduction to Engineering Mechanics: A Continuum Approach

The essence of continuum mechanics, the internal response of materials to external loading, is often obscured by the complex mathematics of its formulation. Rather than introducing solid and fluid behavior as two distinct fields and waiting for an advanced course to demonstrate the mathematical connections between them, we have developed an integrated introduction to both fields. We will discuss the eight-year history of this course at Harvey Mudd and Lafayette Colleges, and the course materials we have developed. This one semester course covers material typically spread over several courses, including statics, strength of materials, and introductory fluid mechanics. We posit a spectrum of material behavior that has Hookean solids at one extreme, and Newtonian fluids at the other, with many interesting combinations (e.g. biomaterials, viscoelastic materials) in between. By building progressively from one-dimensional to higher dimension formulations, we are able to make continuum concepts such as the Cartesian stress tensor accessible to early undergraduate students. From this gradual development of ideas, with many illustrative case studies interspersed, students develop both physical intuition for how engineering materials behave, and the mathematical techniques needed to describe this behavior. We will discuss the rewards and challenges of introducing continuum mechanics early in the curriculum.