Thesis
1) Overall stiffness is a concave function of the stiffness of a portion of the material (article):
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Together with a Taylor series (weak contrast expansion), this shows that heterogeneous materials become softer with increasing heterogeneity. The concave property is a result of an eigendecomposition relation between overall stiffness and the stiffness of a part of the material, tested by a sphere in a spherical domain.
2) Networks of dissimilar springs/beams are softer than networks with elements of average stiffness(article).
This results from the newly introduced relation between the change in stiffness of a network by adding a new spring:
The scalar c describes the unknown response of the network to the mode of deformation which the spring will resist, and a describes the deformation of the network before adding the new spring. Together with a Taylor series (weak contrast expansion) this shows that heterogeneous networks become softer with increasing heterogeneity.
Postdoc research
3) An enhanced law of Laplace for aortic measurement and decision.
4) The squared fluid injection pressure required to tear a cut-open portion of aortic tissue, is proportional to characteristic tearing energy, differential tissue stiffness, and inverse square root of the initially torn area of tissue (article)
5) In a cylindrical vessel, in the presence of luminal pressure the pressure of intramural delamination follows from (article, at Ann. Biomed. Eng.)
5) Constitutive model of decrease of the volume of collagen gels with strain, modeling Poisson effect (article)
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