P. Podio-Guidugli

Gianfranco Capriz was born in Gemona del Friuli on October 16, 1925. After grad- uating summa cum laude in mathematics at the Scuola Normale Superiore in Pisa (1948) and successfully attending a one-year doctoral course there (1949), he was appointed by Mauro Picone as a researcher at the Istituto Nazionale per Ie Appli- cazioni del Calcolo in Rome (1951-56). At the Institute, while working at his first research papers, he also served as a programmer in the staff operating the first general purpose computer ever installed in Italy. In Rome he met Barbara, who was shortly to become his wife, and became ac- quainted with Ennio De Giorgi, Gaetano Fichera, Tristano Manacorda, Carlo Pucci, Michele Sce, and Edoardo Vesentini, with all of whom he was to maintain friendly and scientific relationships thereafter. In the same period he started his research activity in rational mechanics under the supervision of Antonio Signorini. From Rome he moved to Stafford (UK) to work for the English Electric Company (1956-62) as a research mathematician and a programmer of DEUCE, the engineered version of the pilot machine ACE, originally designed by Alan Turing. This period of his life ended when Capriz was asked by Sandro Faedo to return to his country to contribute to the creation in Pisa of the largest concentration ever in Italy of research and development activities in computer science and information technology.

I want to thank R. L. Fosdick, M. E. Gurtin and W. O. Williams for their detailed criticism of the manuscript. I also thank F. Davi, M. Lembo, P. Nardinocchi and M. Vianello for valuable remarks prompted by their reading of one or another of the many previous drafts, from 1988 to date. Since it has taken me so long to bring this writing to its present form, many other colleagues and students have episodically offered useful comments and caught mistakes: a list would risk to be incomplete, but I am heartily grateful to them all. Finally, I thank V. Nicotra for skillfully transforming my hand sketches into book-quality figures. P. PODIO-GUIDUGLI Roma, April 2000 Journal of Elasticity 58: 1-104,2000. 1 P. Podio-Guidugli, A Primer in Elasticity. © 2000 Kluwer Academic Publishers. CHAPTER I Strain 1. Deformation. Displacement Let 8 be a 3-dimensional Euclidean space, and let V be the vector space associated with 8. We distinguish a point p E 8 both from its position vector p(p):= (p-o) E V with respect to a chosen origin 0 E 8 and from any triplet (~1, ~2, ~3) E R3 of coordinates that we may use to label p. Moreover, we endow V with the usual inner product structure, and orient it in one of the two possible manners. It then makes sense to consider the inner product a .

I want to thank R. L. Fosdick, M. E. Gurtin and W. O. Williams for their detailed criticism of the manuscript. I also thank F. Davi, M. Lembo, P. Nardinocchi and M. Vianello for valuable remarks prompted by their reading of one or another of the many previous drafts, from 1988 to date. Since it has taken me so long to bring this writing to its present form, many other colleagues and students have episodically offered useful comments and caught mistakes: a list would risk to be incomplete, but I am heartily grateful to them all. Finally, I thank V. Nicotra for skillfully transforming my hand sketches into book-quality figures. P. PODIO-GUIDUGLI Roma, April 2000 Journal of Elasticity 58: 1-104,2000. 1 P. Podio-Guidugli, A Primer in Elasticity. © 2000 Kluwer Academic Publishers. CHAPTER I Strain 1. Deformation. Displacement Let 8 be a 3-dimensional Euclidean space, and let V be the vector space associated with 8. We distinguish a point p E 8 both from its position vector p(p):= (p-o) E V with respect to a chosen origin 0 E 8 and from any triplet (~1, ~2, ~3) E R3 of coordinates that we may use to label p. Moreover, we endow V with the usual inner product structure, and orient it in one of the two possible manners. It then makes sense to consider the inner product a .