Design of non-linear, viscoelastic architected foams

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Flexible viscoelastic foams with relative density in the range of 5-50% are widely used to control interaction forces, notably in cushions for impact protection, shoes, mechanical grippers, etc. The design of new foams to improve performance is challenging, due to the lack of efficient models to connect cellular architecture, viscoelasticity of the base resin, and non-linear responses that stem from large deformation of open pores. This paper presents highly efficient solutions for the response of linearly viscoelastic, kinematically non-linear and shear-deformable struts that are loaded at an oblique angle to their axis. The models can be used to predict structure-property relationships for strut-based metamaterials, including non-linear stress-strain response and accompanying hysteresis. To illustrate this, the entire design space of a simple unit cell is mapped in terms of a broad range of strut angles and thicknesses; the unit cell is inspired by features in stochastic foams that dominate their response. An enormous range of stress-strain responses can be obtained from this single foam-like cell, including purely softening, purely stiffening, and non-monotonic stiffness with adjustable tangent moduli. The model is also used to illustrate connections between viscoelastic material parameters, loading rate, and hysteresis for two distinct classifications of non-linear stress-strain response.