Mathematical Modeling and Investigation on the Soft Tissue Structures in Micro-indentation Tests Based on Cylindrical Shell Model | |
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( Volume 2 Issue 6,June 2016 ) OPEN ACCESS | |
Author(s): | |
Mei-Feng Liu | |
Abstract: | |
A new model for the micro-indentation test used to determine the material properties for the soft tissue is proposed in the present study. Based on the basic theory of elasticity, mathematical models such as infinite beam and circular plate are often adopted to describe the geometric characteristics of soft tissue. Other than the conventional simulations, say beam and plate, the author proposed a two-dimensional model for the tissue structure, which permits a hollow cylindrical shell with internal spring support and axial surface loads as the modelling of soft tissue. Different with the previous two, the shell model consists of two coupled differential equations involving both the transverse and longitudinal deformations as its main quantities. The proposed mathematical model offers additional information about the behaviours of the soft tissue in the micro-indentation test; meanwhile, the effect of residual stresses on the soft tissue with respect to both the transverse and longitudinal deformations can be thoroughly examined. The result of the present study matches the result by the simple beam model as long as the transverse displacement is under consideration; however, it reveals different illustration with that conducted by circular plate model due to the intrinsic variation on the governing equations. The longitudinal displacement of the soft tissue behaviour during indentation test is additionally presented in the study and the effect is shown to be parabolic-like in the case of stress free, however, it becomes almost linear when the residual stress is taken into account, and soon reaches its asymptotic state as the stress increases. |
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