Dresden 2017 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 7: Posters - Mechanics and Dynamics of 3D Tissues (Focus Session)

BP 7.4: Poster

Montag, 20. März 2017, 17:30–19:30, P3

Non-Linear Compliance of Elastic Layers to Indentation — •Adrian Fessel and Hans-Günther Döbereiner — Universität Bremen, Bremen, Deutschland

We present a single-exponent scaling model for description of large, non-linear deformations in elastic layers, based on analytical analyses and approximations of asymptotic behavior for small and large indentation upon variation of layer thickness. For very thin layers, the scaling model arises as an extension of an analytically exact model for small indentation. In conjunction with data from finite element simulations, investigation with the model leads to the conclusion that when drafting experiments, it is essential to recognize that separation of non-linear material properties from effects of geometrical confinement is conveniently possible only with thin layers. Furthermore, partition of strain-energy into parts associated with specific asymptotic regimes motivates introducing a scalar which we define in analogy to Poisson's ratio but for the ratio of principal strains in the layer geometry. Numerically, we find quantitative agreement between the scalar and the exponent characterizing the scaling model in the case of a thick, linear-elastic layer, and qualitative agreement in the non-linear case. We conjecture this effect to be due to higher-order contributions of geometrical confinement present even in linear-elastic settings.