Exact Solutions to Large Strain Bending of Highly Elastic Soft Plate Strips With Non‐Symmetric Strain‐Stiffening Effects

ABSTRACT

Large strain bending responses of highly elastic soft plate strips with non‐symmetric strain‐stiffening effects are accurately studied in a two‐fold sense of constitutive modeling and large strain analysis. Namely, non‐symmetric strain‐stiffening effects in tension and compression are accurately simulated, and nonlinear coupling complexities at large strain are accurately treated. Toward this objective, an explicit form of the multi‐axial elastic potential of decoupled nature is established based upon two well‐designed invariants of Hencky's logarithmic strain. With the new model, multiple data sets for benchmark deformation modes can be accurately matched, and, in the meantime, exact solutions are for the first time obtainable for the varying neutral axis position, the bending moment as well as non‐symmetric tensile and compressive stress distributions. Numerical examples for sulfur rubber and poly‐dimethylsiloxane compare well with experimental data.