What's wrong with Applied Mechanics?

(Originally posted on Applied Mechanics News in 16 May 2006)

Applied Mechanics is a discipline that studies the response of matter to external forces, such as flow of a liquid, fracture of a solid, sound in the air, and vibration of a string. Applied Mechanics bridges the gap between fundamental physical sciences and wide-ranging applications. Representive questions are how a gecko climbs, how an earthquake occurs, how a computer chip fails, how an airplane flies, or how the Twin Towers fell. Major approaches include formulating concepts and theories, discovering and interpreting phenomena, as well as developing experimental and computational tools. For well over a century, Applied Mechanics has been a flagship discipline in the innovation of research, eduction, and community building in many branches of engineering, including Mechanical Engineering, Civil Engineering, Aerospace Engineering, Materials Engineering, and Bioengineering.

Despite the intellectual depth and practical utility, the discipline of Applied Mechanics is in a state of crisis, largely due to its own success. Like many sophisticated fields of science and engineering, Applied Mechanics constitutes a large chunk of knowledge, accumulated over millennia, represented by texts, equations, graphics, photos, audios, videos. This large quantity of knowledge has made it hard for any individual to master (and to add to) the field, a fact at least partially responsible for turning many talented young people away from the field. However, nobody has ever questioned the immense value of Applied Mechanics to a broad range of human activities today and to our posterity. Furthermore, new problems constantly emerge that requires ingenious use of existing knowledge, or fundamental progress in Applied Mechanics.

Still, the question remains, How do we impart this large chunk of knowledge to individuals within a reasonable amount of time, so that they still have time left to innovate?

A classical answer to this question dates back at least to Stephen P. Timoshenko, considered by many the father of modern Applied Mechanics. Starting early last century, Timoshenko and his followers divided the field of Applied Mechanics into subfields (such as strength of materials, theory of elasticity, theory of vibration, plates and shells, structural instabilities), and then summarized the "essential knowledge" in each subfield in a textbook. The success of this divide-and-conquer approach is immense, as attested by the rising importance of Applied Mechanics in engineering curriculum, by the fundamental progress (e.g., in fracture mechanics and in nonlinear continuum mechanics), and by pervasive use of Applied Mechanics in engineering practice.

This approach, however, is not scalable. As more results accumulate in a subfield, its textbook becomes thicker and more abstruse. As new subfields emerge, new textbooks are added to the pile. Furthermore, what is considered essential knowledge for a practicing engineer is very different from that for an undergraduate student. This and other idiosyncrasies of people lead to more textbooks, each with smaller audience. Individuals agonize over which cherries to pick, leaving most fruits untasted. Sadly, few mechanicians today consider writing textbooks professionally rewarding. Sadder still, the approach has led the discipline to fragment.

The fragmentation has been partially mitigated by the rise of computational mechanics. Over the last half century or so, the use of computer to solve complex, nonlinear boundary-value problems in the field of Applied Mechnaics has flourished, leading to commercial software like ABAQUS. Using such software, an electrical engineer, say, with a rudimentary understanding of mechanics, can analyze the strain field in the channel of a transistor. While computational mechanics has begun to unify Applied Mechanics, this unification is incomplete. For one, not all problems are suitable for numerical computation; many problems are solved by experiments combined with scaling laws, and by relating to previously solved problems. Some problems are solved more sensibly by trial and error. (Nobody learns to ride a bicycle by numerical simulation.) Also, to make a fundamental contribution to Applied Mechanics, one has to go beneath software and acquire a holistic understanding of the field.

I believe that the Internet will further unify Applied Mechanics by going beyond numerical computational aspects of mechanics, by making the labor of discovering and synthesizing knowledge more efficient and meaningful, and by making Applied Mechanics useful to more people.