The behavior of Cross-linked Polymers in finit defortemations is is often charachterized by hyperelastic behaviour. Proposing a simple, yet ccurate machine learned constitutive behavior remains as a challenging task, since most  current models can describe the response of elastomer in one-type of loading, but, very few of them can accurately capture the behavior of them during different loading scenarios i.e. uniaxial, biaxial, pure shear. In addition, elastomers show a softening effect known as the Mullins effect after the first extension.  The Mullins effect causes previous maximum loading to affect the stress-strain behavior of the material. In current modeling effort, the hyperelastic behavior is often modeled through changes in the strain energy density function. Current analytical models can be classified into two main categories of phenomenological and micromechanical  approaches; where each  has some advantages and disadvantages.  A review of available strain energy density functions shows that we can, rarely, capture the behavior of the material under different loading conditions and inelastic response of them simultaneously. On the other hand, the recent rise of machine learning as a powerful technique for the analysis of data has provide us with a unique tool to address this problem. So far, machine learned constitutive models often fail to predict material response in multiple directions and also do not sho application for constitutive models requires its combination with continuum mechanics and physics laws. Another advantage of data-driven modeling is that unlike mathematical models, it can be trained for each experimental data set. Hence, this paper utilizes a machine learning-based approach by taking into account the advantages of both phenow convergence.  
Here, we propose to embded an artificial neural network (ANN) within a micro-mechanical model and thus to enforce certain physical restrictions of  an amorphous network such as directional dependency and history-dependency of the constitutive behavior of rubber-like materials during loading and unloading. Accordingly, a strain energy density function is assumed for a single chain based on ANN and trained with experimental data set. Summation of the energies provided by ANNs in different directions can determine the strain energy density function of the matrix. Stress-strain relation is derived from strain energy density function. Polyconvexity is enforced to assure minimized potential energy, a global solution for an optimization problem, and thermodynamic consistency that show the model cannot generate energy. The model is validated against multiple sets of experimental data, e.g. uniaxial, shear and biaxial deformation available in the literature. This model not only captures the loading and unloading paths but also captures the inelastic response of these materials such as the Mullins effect and permanent set. The model can be   generalized to other materials and other inelastic effects as well.  
 


A Phyics-Informed Neural Network Constitutive Model for Cross-Linked Polymers

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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