2015 Computer methods in biomechanics and biomedical engineering
* On modelling large deformations of heterogeneous biological tissues using a mixed finite element formulation.
- This study addresses the issue of modelling material heterogeneity of incompressible bodies. It is seen that when using a mixed (displacement-pressure) finite element formulation, the basis functions used for pressure field may not be able to capture the nonlinearity of material parameters, resulting in pseudo-residual stresses. This problem can be resolved by modifying the constitutive relation using Flory's decomposition of the deformation gradient. A two-parameter Mooney-Rivlin constitutive relation is used to demonstrate the methodology. It is shown that for incompressible materials, the modification does not alter the mechanical behaviour described by the original constitutive model. In fact, the modified constitutive equation shows a better predictability when compared against analytical solutions. Two strategies of describing the material variation (i.e. linear and step change) are explained, and their solutions are evaluated for an ideal two-material interfacing problem. When compared with the standard tied coupling approach, the step change method exhibited a much better agreement because of its ability to capture abrupt changes of the material properties. The modified equation in conjunction with integration point-based material heterogeneity is then used to simulate the deformations of heterogeneous biological structures to illustrate its applications.
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Overview of verb compare
The verb compare has 4 senses (first 3 from tagged texts)
1. (57) compare -- (examine and note the similarities or differences of; "John compared his haircut
to his friend's"; "We compared notes after we had both seen the movie")
2. (12) compare -- (be comparable; "This car does not compare with our line of Mercedes")
3. (9) compare, liken, equate -- (consider or describe as similar, equal, or analogous; "We can
compare the Han dynasty to the Romans"; "You cannot equate success in financial matters with greed")
4. compare -- (to form the comparative or superlative form on an adjective or adverb)
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