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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 12: French-German Session: 2D Materials, Thin Films and Interfaces I
CPP 12.2: Vortrag
Montag, 9. März 2026, 15:30–15:45, ZEU/0255
Increase in elastic modulus of thin elastic films and membranes containing rigid inclusions - revisiting Einstein’s relation in two dimensions — •Konstantin Zisiadis and Andreas Menzel — Otto-von-Guericke-Universität Magdeburg
Elastic matrices with well-separated inclusions can be described by effective elastic moduli obtained via homogenization methods. Probably the most basic relation for dilute systems is the Einstein equation ηeff = η (1+2.5 φ). We consider the two-dimensional geometry of an elastic matrix in two dimensions with two-dimensional elastic moduli as counterparts to the three-dimensional case. Both plane-stress and plane-strain geometries are treated. We employ a generalized stresslet formalism. Our derived formulae for the effective moduli of the two-dimensional geometry are expressed using the two-dimensional elastic moduli for an arbitrarily compressible matrix. We find that the plane-stress and plane-strain equations for the effective moduli have the same form, while the associated two-dimensional moduli differ. Our results are consistent with previous research based on different approaches. For an incompressible matrix, we recover the known effective shear modulus µeff = µ (1+2 φ).
We acknowledge support by the German Research Foundation (DFG) through Research Unit FOR 5599 on structured magnetic elastomers.
Keywords: Einstein relation; linear elasticity; Papkovich-Neuber potentials; rigid inclusions