Polymer foams often have anisotropic microstructures and consequently exhibit anisotropic mechanical behaviors. Microstructure anisotropy typically arises during the manufacturing process. For example, chemically blown polymer foams typically possess a rise direction, the direction of travel of the foam-air surface during the blowing process, and bubbles are elongated in this direction. Physically blown foams also can lock in non-spherical bubbles during the flow stage of the foam process. And, contemporarily, additively manufactured lattice foams are anisotropic by construction of the lattices themselves. High-fidelity simulations to assess foam behavior under difficult mechanical environments requires that the anisotropic behavior that emerges from such microstructures be well modeled.

 

For rigid polymer foams (deformed at a temperature well below the glass transition of the matrix material), phenomenological anisotropic viscoplastic constitutive models have had some success in representing anisotropic yield, compaction, temperature, and strain rate effects. However, for flexible and memory foams (in which the operating temperature is much higher than the glass transition temperature or nearly the glass transition temperature), well established anisotropic constitutive models are not available. Most constitutive models, whether micromechanically derived or phenomenological and empirically driven, focus on (initially) isotropic constitutive representations. But, as was recently explored in companion work, isotropic models are not capable of representing different directions of loading with a single parameter set, in particular as the microstructure anisotropy increases at lower and lower relative densities.

 

To address this gap in available constitutive models, we present our recent efforts to develop an empirically driven anisotropic model for polymer foams (with flexible and memory foam applications in mind). We will present the experimental basis for this work: uniaxial compression, compression-shear, and dynamic mechanical analysis testing of open cell, flexible polyurethane foams under room temperature, large deformation, and cyclic mechanical loading conditions for relative densities from 4\\% to 20\\%.  Next, we develop a rate-independent, orthotropic hyperelastic model in which the nine elastic stiffness parameters are independent functions of the current relative density in the deformed state of the foam. The rate independent, hyper-elastic anisotropic model is then extended via the theory of quasi-linear viscoelasticity with a single relation function to produce an anisotropic, viscoelastic model. We will then discuss the required experimental data to calibrate the model as well as the calibration procedure.    

 

This work was partially supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories, a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy?s National Nuclear Security Administration under contract DE-NA0003525. SAND2020-7064 A (UUR).


Constitutive Modeling of Anisotropic Flexible Foams

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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