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ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

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3. MATHEMATICAL MODELLING<br />

According to TPM [4] that we employ to model the PDL, the fibrous network and the<br />

fluid phase within the PDL are modelled assuming that the solid and the fluid phase<br />

coexist in a homogenized way throughout the PDL. We assume that every point p of<br />

the reference configuration ΩB of the PDL is occupied by a material point of both<br />

phases α, where α can be either S (solid phase) or F (fluid phase). Each point p is<br />

therefore moved according to two different motions f α (p,t) (see Figure 1). Every<br />

spatial point x at time

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