Double 4-bar shear: A novel apparatus and method for simple shear mechanical analysis of membranes

A new constitutive modeling strategy based on QR decomposition has been introduced for analyzing biological membranes, which uniquely separates 2D deformation into three physically meaningful modes: dilation, extrusion, and simple shear. While dilation and extrusion can be measured with standard biaxial testing, experimentally isolating and measuring simple shear has remained a significant challenge, with most methods failing to capture all boundary conditions. To address this gap, a novel ”double 4-bar shear” apparatus was developed to apply a precise, rectilinear simple shear deformation while measuring all boundary loads and moments. The device was validated using 16 silicone membranes and 8 rat dorsal skin samples. Digital Image Correlation (DIC) analysis confirmed the apparatus successfully applies a homogeneous simple shear strain, as evidenced by the narrow distribution of strain components, and isolates it from other deformation modes. For the first time, the moments applied by the material on the clamps during simple shear were successfully measured, showing a clear increase with rising shear strain. The results demonstrated highly repeatable and linear stress–strain behavior for silicone and a characteristic non-linear, J-curve response for rat skin. By providing a method to obtain previously unavailable experimental data, this apparatus enables the complete characterization of membranes using advanced constitutive models, which can significantly advance the design of tissue-engineered replacements with more accurate physiological properties.