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The efficiency improvements are obtained by maintaining a multiplicative decomposition of clique and separator potentials.
The model is based on the multiplicative decomposition of the deformation gradient.
In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts.
The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations.
First, the kinematics of large deformation based on multiplicative decomposition of the total transformation gradient is briefly recalled.
A multiplicative decomposition of the deformation gradient that factors out the dilation and the fiber stretch is proposed.
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These formulations are based upon distinct kinematic assumptions resulting from different multiplicative decompositions of the deformation gradient.
An empirical relation of Poiseuille number which contains the two opposite effects and has a better physical meaning is proposed in the form of multiplicative decomposition, and then is validated by available experimental and numerical results.
Multiplicative decomposition into elastic and plastic parts of the deformation gradient and micro-deformation are assumed, and the Clausius Duhem inequality is formulated in the intermediate configuration ¯¯¯¯B to analyze what stresses, elastic deformation measures, and plastic deformation rates are used/defined in the constitutive equations.
Multiplicative Decomposition: Here, the given time series data are treated as the product of the decomposed patterns.
Multiplicative Decomposition: Here, the given time series data are treated as the product of the decomposed patterns Xt = seasonal (St) (times) trend (Tt) (times) random.
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