Consequences of constitutive choices in soft and thin materials

Biopolymer gels and soft tissues are known to present rich nonlinear elastic responses, including strain-stiffening and a surprising tendency to develop a tensile stress perpendicular to the shearing direction (reverse Poynting effect). However, popular strain energies adopted for constitutive modeling fail to capture these responses, lead to universal relations that conflict with experimental data, and do not provide a satisfactory link with the mesoscale. For soft materials governed by quadratic energies, the choice of strain measure in which we expand the energy can be key to unlocking some of these behaviors. I will discuss that by adopting the Biot/Bell strain, instead of the usual difference in metrics, diverse nonlinear deformations can be captured, including a novel transition in the Poynting effect. Other overlooked consequences of the strain choice appear when deriving energies for thin structures. In fact, most strains lead to undesirable behaviors, such as materials that stretch under a pure moment. I will explain how to avoid this contamination between bending and stretching, which is of importance in the study of buckling and defects on thin sheets. This talk contains contributions from J. A. Hanna and C. O. Horgan.