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ISBN-13: 9780120121243

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Extra resources for Advances in Computers, Vol. 24

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1. In the current context, we interpret the components of u, denoted as O"ij, as representing forces per unit areas in the spatial configuration at a given spatial point :1:. It will be necessary to consider related measures of stress defined in terms of the other configurations we have discussed; in particular, the reference and rotated configurations are of particular interest. 5h). 75) where n is the unit normal vector to the plane in question. 2 The IBVP in the Finite Strain Case 25 ---- --,.

Thus, one may write X = {XJ}, and:1; = {Xi}. 18 2. 3. Basic notation for the finite strain boundary value problem. p . p have been omitted for convenience. One of the first uses for the deformation gradient is to quantify local volume change for a point X in n. 44) = detF. 2 The IBVP in the Finite Strain Case 19 J is the Jacobian determinant of the transformation between coordinates XI and Xi, the conditions for invertibility of the deformation gradient F depend upon it. 46) J? o. 46) has the physical interpretation that the material is not allowed to interpenetrate itself, and mathematically ensures that the inverse of F, F- 1 , exists and is unique.

Several time-stepping algorithms have been proposed for this incremental problem we have posed. So that we might have a template with which to work, we will consider perhaps the most pervasive of these schemes, the Hilber-Hughes-Taylor (HHT) family of temporal integrators ([HHT77]). 203) where a, (3 and 'Y are algorithmic parameters that define the stability and accuracy characteristics of the method. In particular, when a = 1, the algorithm reduces to the classical family of integrators examined by Newmark in [New59].

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Advances in Computers, Vol. 24


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