A Guide to Arithmetic [Lecture notes] by Robin Chapman

By Robin Chapman

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Sample text

1 [ €2 [ €3 ¤ ;. 4, to elastic motions of a body occupying a domain with a piecewise smooth boundary €. x/, i D 1; 2; 3, are fixed at every point x 2 € where the normal n exists.

While, for example, steel obeys Hooke’s law in a relatively wide band of loading parameters, such materials as cast iron deviate from the linear behavior even at relatively small stresses. 55) where C is the elastic modulus tensor of the fourth rank. The components of the tensor C do not depend on the spatial coordinates in the case of homogeneous media. As the stress and strain components depend on the orientation of the Cartesian coordinate system, the components of the elastic modulus tensor must also comply with this dependence.

X/ W : Here, C 1 is the elastic compliance tensor inversed to the tensor C . This object is of the fourth rank and has the same symmetry properties as C . By using either eq. 55) or eq. 63) WC 1W : 2 As it has been already mentioned, the maximal number of elastic moduli in the elastic modulus tensor is 21. Such kind of material anisotropy is named as aeolotropy. , electric conductivity, refractive index) of a body depend on the direction in which they are measured. Note that the number of elastic moduli relates to material symmetry.

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