Regensburg 2019 – wissenschaftliches Programm
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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 52: Biomaterials and biopolymers I (joint session BP/CPP)
CPP 52.1: Vortrag
Donnerstag, 4. April 2019, 09:30–09:45, H10
A unifying perspective on rigidity in under-constrained materials — •Matthias Merkel1, 3, Karsten Baumgarten2, Brian Tighe2, and Lisa Manning1 — 1Department of Physics, Syracuse University, Syracuse, NY, USA — 2Delft University of Technology, Delft, The Netherlands — 3Centre de Physique Théorique, Université Aix-Marseille, France
We present a novel approach to understand rigidity in under-constrained materials, including sub-isostatic spring networks as well as 2D and 3D vertex models for dense biological tissues. We show that the onset of rigidity is determined by a purely geometric criterion. This allows us to analytically predict the elastic material properties close to the transition, which depend only on few geometric coefficients. We obtain exact expressions for the magnitudes of bulk modulus and shear modulus discontinuities at the rigidity transition, several scaling relations of the shear modulus, and the magnitude of the anomalous Poynting effect. Moreover, we show that the ratio of the excess shear modulus to the shear stress is inversely proportional to the critical shear strain with a prefactor of three, which we expect to be a general hallmark of rigidity in under-constrained materials induced by geometric incompatibility. This could be used in experiments to distinguish whether strain-stiffening as observed for instance in biopolymer networks arises from nonlinear characteristics of the microscopic material components or from effects of geometric incompatibility.