Steven An, Theodore Kim and Doug L. James, Optimizing Cubature for Efficient Integration of Subspace Deformations, ACM Transactions on Graphics, 27 5), December 2008, pp. 164:16464:164
Steven S. An, Theodore Kim and Doug L. James, Optimizing Cubature for Efficient Integration of Subspace Deformations, ACM Transactions on Graphics (SIGGRAPH ASIA Conference Proceedings), 27 5), December 2008, pp. 164:16464:164
A fully nonlinear beam-column element estimates element deformations by numerical integration of the section deformations.
The plastic extension of material behind crack tip, Δyp, obtained by the integration of vertical plastic deformation perpendicularly to crack flank, is proposed here to quantify the residual plastic field.
This requires time differentiation and integration of all myocardial deformation (strain rate data) to obtain an averaged shortening and lengthening signal respectively.
Whereas the Lagrangian strain describes the deformation of an object with its length L t) relative to its initial length L t0)(εL t) = [ L t) − L t0)]/ L t0)), the natural strain is based on the temporal integration of the instantaneous deformation (dε) of the tissue (dε N t) = [ L(t + dt) − L t)]/ L t)) [ 17].
Their objective rates are based on the recently proposed logarithmic spin [Acta Mech. 124 (1997) 89] and on the fact that the logarithmic integration of the rate of deformation tensor results in the Hencky strain [Acta Mech. 124 (1997) 89].
Numerical experiments show that no oscillations are observed in simple shear and that the integration of the elastic rate of deformation exhibits proper elastic behavior.
The final PMFs allowed error evaluation of the PMF integration and the free energy of deformation of the ADP upon binding to PKA.
Without the deformations and cracks, the results indicate an excellent integrity for the integration of Cu TSV, Ag conductive glue and quartz resonator.
