Rheol Acta (2014) 53:75–83 DOI 10.1007/s00397-013-0738-y ORIGINAL CONTRIBUTION A new approach for calculating the true stress response from large amplitude oscillatory shear (LAOS) measurements using parallel plates Zahra Fahimi · Chase P. Broedersz · Thomas H. S. van Kempen · Daniel Florea · Gerrit W. M. Peters · Hans M. Wyss Received: 8 July 2013 / Revised: 25 September 2013 / Accepted: 2 October 2013 / Published online: 8 November 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract The parallel plates geometry is often deemed unsuitable for nonlinear viscoelasticity measurements because the strain field, and thus the nonlinear response, varies across the sample. Although cone–plate and Couette geometries are designed to circumvent this prob- lem by ensuring a uniform strain field, it is not always easy to shape the material to the complex shapes that is required for these geometries. This has motivated the devel- opment of techniques to accurately determine the nonlinear stress response using the more convenient plate–plate geom- etry. Here, we introduce a new approach to obtain this true material response in large amplitude oscillatory shear (LAOS) experiments using the plate–plate geometry. By tracing the Fourier components of the torque response and their derivatives with respect to the maximum applied defor- mation, we accurately obtain the material’s true stress–strain response from parallel plate measurements. The approach does not require any assumptions about the material’s vis- coelastic behavior. We test our approach experimentally Z. Fahimi · D. Florea · G. W. M. Peters · H. M. Wyss () Department of Mechanical Engineering, Eindhoven University of Technology, 5612AZ Eindhoven, the Netherlands e-mail: H.M.Wyss@tue.nl Z. Fahimi · D. Florea · H. M. Wyss Institute for Complex Molecular Systems, Eindhoven University of Technology, 5612AZ Eindhoven, the Netherlands T. H. S. van Kempen Department of Biomedical Engineering, Eindhoven University of Technology, 5612AZ Eindhoven, the Netherlands C. P. Broedersz Lewis-Sigler Institute for Integrative Genomics and the Department of Physics, Princeton University, Princeton, NJ 08544, USA on fibrin biopolymer gels, as well as numerically on a Giesekus model. We confirm in both cases that our approach captures the detailed shape of the true stress response in LAOS measurements. Moreover, we also show that our method is less sensitive to experimental noise present in the data than the previous standard method. Our approach for obtaining the true stress response from parallel plate mea- surements is directly applicable to measurements on a wide range of solid-like nonlinear materials, including biological networks, tissues, or hydrogels. Keywords Large amplitude oscillatory shear · Biopolymer · Fourier transform rheology · Stress–strain curve · Viscoelasticity · Nonlinear viscoelasticity Introduction One main advantage of the simple parallel plates geom- etry often used in rotational rheometers is that the gap size can be freely chosen for each experiment, provid- ing access to a wide range of shear rates. Moreover, flat, solid-like samples can be measured without the need for creating complex sample shapes; the gap can readily be adjusted to fit the sample of interest. A range of com- monly investigated solid-like materials, including hydro- gel materials, biofilms, or biological tissues, are difficult to shape into the geometries required for cone–plate or Couette measurements (Lopez-Suevos and Frazier 2006). However, these materials can often be shaped readily into a flat film shape, making the parallel plates geom- etry the best available option for performing rheological measurements. A major drawback of parallel plates, however, is that this geometry results in a strain field that is not uniform across