EM 388F Term Paper: Theory and analysis tech for the use of a DCB specimen for determining the toughness of PC-3 Prostate Cancer

A double cantilever beam (DCB)
specimen is created by affixing the two halves together using a bi-layer of
PC-3 prostate cancer cells. The specimen is pinned at a bottom corner, and the
upper corner on the same end is displaced with the force-displacement profile
being recorded. This upper corner is displaced until the crack, a portion of
the specimen where cell grown has been selectively inhibited, propagates
through the cell layer. The critical value of force at which the crack
propagates through the cell layer is used, in conjunction with the initial
crack length, to determine the toughness via the compliance-energy method (Ripling, et al. 1971). A method for performing a FE analysis of the
specimen is developed with increasing complexity. The basic model involves
computing the J-integral (Rice 1968) on a finite element model that has had the
predicted critical value of force applied to it. The first extension involves
modeling the cell layer as springs, applying a predetermined critical force,
and computing the J-integral (Song 1994). The final enhancement
involves the use of a traction-separation law for the cells through the use of
cohesive elements in a F.E. model. The traction-separation law is determined by
experimental work. This model is then used to determine the critical value of
force and toughness via the J-integral.

Rice, J. R. (1968). "A path independent integral and the approximate
analysis of strain concentration by notches and cracks." ASME Journal
of Applied Mechanics 35: 379-386.

Ripling, E. J., S. Mostovoy, et al. (1971). Fracture Mechanics: A Tool for Evaluating Structural Adhesives, Taylor & Francis. 3: 107 - 123.

Song, S. J., Waas, A. M. (1994). " A spring foundation model for mode I failure of laminated composites based on an energy criterion." J. Eng. Mater. Technol. (Trans. ASME) 116(4): 512-516.
 

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