Consolidation finite strain

In this section we reconstruct the theory of consolidation by introducing the concept of a finite strain and a nominal stress rate, which are given in Chap. 2. Note that in Chap. 5 a mixture theory was developed for a porous medium with multiple... 

Gibson et al. (1967) proposed an alternative ID consolidation theory under a finite strain condition however, if we ignore a volume change due to the deformation process of the solid skeleton, the consolidation theory is not completely correct. We present a finite strain ID consolidation equation based on the finite strain consolidation theory described in Sect. 6.3. 

Weak Form of the ID Finite Strain Consolidation Equation... 

To develop a finite element scheme we introduce a weak form of the strong form system (10.13)-(10.18). We integrate (10.13) after multiplying an arbitrary function w(X), which is null at X=a, and obtain the following weak form of the ID finite strain consolidation equation ... 

The actual field consolidation of soil around each drain is close to an axial symmetry, which should be converted into a plane strain condition for 2D finite element program. Hird et al. (1995) proposed a geometry and permeability matching equation from axisymmetry to plane strain as follows ... 

Sheet forming tools can benefit from real-time monitoring for clamping pressure, vacuum level between diaphragms, forming rate and consolidation. Trial runs can combine grid strain analysis (Krebs et aL, 1997) with finite element methods to validate performance. 

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