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By P. Podio-Guidugli

I are looking to thank R. L. Fosdick, M. E. Gurtin and W. O. Williams for his or her specified feedback of the manuscript. I additionally thank F. Davi, M. Lembo, P. Nardinocchi and M. Vianello for invaluable feedback triggered by way of their examining of 1 or one other of the numerous prior drafts, from 1988 up to now. because it has taken me see you later to convey this writing to its current shape, many different colleagues and scholars have episodically provided worthwhile reviews and stuck error: a listing could possibility to be incomplete, yet i'm heartily thankful to all of them. eventually, I thank V. Nicotra for skillfully reworking my hand sketches into book-quality figures. P. PODIO-GUIDUGLI Roma, April 2000 magazine of Elasticity fifty eight: 1-104,2000. 1 P. Podio-Guidugli, A Primer in Elasticity. © 2000 Kluwer educational Publishers. bankruptcy I pressure 1. Deformation. Displacement allow eight be a third-dimensional Euclidean house, and allow V be the vector area linked to eight. We distinguish some degree p E eight either from its place vector p(p):= (p-o) E V with admire to a selected starting place zero E eight and from any triplet (~1, ~2, ~3) E R3 of coordinates that we may well use to label p. furthermore, we endow V with the standard internal product constitution, and orient it in a single of the 2 attainable manners. It then is sensible to think about the internal product a .

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28) 5. 25). 14. Material Symmetry It is common experience that certain rigid transfonnations of the reference shape are mechanically undetectable, in that two otherwise identical defonnational experiments, the one perfonned before and the other after anyone of those rigid 52 P. PODIO-GUIDUGLI transfonnations, give identical results in tenns of induced stresses and stored energies. For example, consider a square piece of a square-mesh net of elastic fibers (a window grate, say, or a handkerchief, or else, for a slightly different example, a reinforced concrete slab): we do expect the same force to be needed to pull apart either pair of opposite sides of the same amount.

1) with v = ft' the velocity field associated with m (cf. 12». ,(n) T . 2)1. u; (dunamis) == force. 1) if and only if T E Sym, a condition that we know from our discussion in Section 8 to be the pointwise equivalent of the second of Euler's axioms. 39 STRESS grad v (or, equivalently, the symmetric part of the latter). 3) suggest other pairs of dual stress and strain measures. The following forms involving Piola and Cosserat stresses are important in the mechanics of solids: p(s)(n) = f TR. F" 1n = f TR .

16) qo = lo(t). 2. 15), one has IDqo(n, f) . Wo = -2( la[cn) { (q - qo)Q:9 s +{ l[cn) (q - qo)Q9 b) . 17) 8. Stress. 4) of force and moment balances, as well as the characterization of these balance laws in terms of virtual power, is both global and local, in that it involves integrals, but over parts of arbitrary size and shape. Beside this partwise statement, a pointwise statement of force and moment balances becomes possible once a notion of stress has been built, and is in fact one of the assertions of a famous theorem of Cauchy.

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