By C. Truesdell (auth.)

The lectures right here stated have been first brought in August and September, 1965, for the dept of Mechanical and Aerospace Engi neering at syracuse collage, long island below the sponsorship of the recent York nation technology and know-how origin. Lectures 1-6 and 22-23 are revised from a model ready through Professor family members N. Tong at the foundation of a transcription of the lectures, kindly supplied through Professor S. Eskinazi. the rest of th~ textual content has been written out afresh from my very own notes. a lot of a similar floor was once lined in my lectures to the Austra lian Mathematical Society's summer season learn Institute at Melbourne in January and February, 1966, and for the components affected the textual content conforms to this latter presentation. i'm thankful to Professors C.-C. Wang and ok. N. Tong for feedback of the manuscript. those lectures represent a direction, no longer a treatise. Names are connected to theorems justly, to the easiest of my wisdom, yet aren't meant to switch a background of the topic or references to the sources.

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4) The isotropy group is the collection of all static density-preserving deformations from Ie at X that cannot be detected by experiment. Alternatively we may describe the isotropy group as the group of material synunetries. for every We have proved that every material has a non-empty' isotropy group Ie and X. 58 Orthogonal Part of the Isotropy Group. 1) yields and gT need not be orthogonal, but they may be. 7) for all non-singular deformation histories holds for a particular orthogonal tensor Ft.

Nearly all the exact solutions found in non-linear continuum theories are for incompressible materials. the distinction just made. In the next lecture we shall illustrate 47 LECTURE 5: HOMOGENEOUS MOTIONS OF SIMPLE BODIES. Significance of Homogeneous Motions. 24) determines its response to all deformation histories. 24) and record the stresses obtained. would amount to a determination of the response functional ~~ The results We now' ask whether such a program be possible in principle. 25)7 If the body force the answer is of course yes.

Symmetr~c tensor, and the operation the space of symmetric tensors. a cA(9)! 19) where q is a scalar factor. 16) yields the general constitutive equation for simple material subject to k simple frame-indifferent internal constraints. found for unconstrained materials. Examples of Internal Constraints. 1. A material is said to be incompressible if Incompressibility. 6)9' an appro- it can experience only isochoric motions. 19) yields ~ where p is an arbitrary scalar. 23) Thus we have verified a result due in effect to In an incompressible material, the stress is determinate from the motion only to within an arbitrary hydrostatic pressure.