Asymmetric sample shapes complicate planar biaxial testing assumptions by intensifying shear strains and stresses

Abstract

Planar biaxial testing offers a physiologically relevant approach for mechanically characterizing thin deformable soft tissues, but often relies on erroneous assumptions of uniform strain fields and negligible shear strains and forces. In addition to the complex mechanical behavior exhibited by soft tissues, constraints on sample size, geometry, and aspect ratio often restrict sample shape and symmetry. Using simple PDMS gels, we explored the unknown and unquantified effects of sample shape asymmetry on planar biaxial testing results, including shear strain magnitudes, shear forces measured at the sample’s boundary, and the homogeneity of strains experienced at the center of each sample. We used a combination of finite element modeling and experimental validation to examine PDMS gels of varying levels of asymmetry, allowing us to identify effects of sample shape without confounding factors introduced by the nonlinear, spatially variable, and anisotropic properties of soft tissues. Both biaxial simulations and experiments, which showed strong agreement, revealed that sample shape asymmetry led to significantly larger shear strains, shear forces, and overestimation of principal stresses. Excluding these shear forces resulted in an underestimation of shear moduli during inverse mechanical characterizations. Even in the simplest of deformable biomaterials, sample shape asymmetry should be avoided as it can induce drastic increases in shear strains and shear forces, invalidating traditional planar biaxial testing analyses. Alternatively, sample shape asymmetry may be exploited to generate more robust estimates of constitutive parameters in more complex materials, which could lead to a refined understanding and inference of mechanical behavior.