  Liquid metals (LM) are embedded in an elastomer matrix to obtain soft
composites with unique thermal, dielectric, and mechanical properties. They
have applications in soft robotics, biomedical engineering, and wearable
electronics. By linking the structure to the properties of these materials, it
is possible to perform material design rationally. Liquid-metal embedded
elastomers (LMEEs) have been designed for targeted electro-thermo-mechanical
properties by semi-supervised learning of structure-property (SP) links in a
variational autoencoder network (VAE). The design parameters are the
microstructural descriptors that are physically meaningful and have affine
relationships with the synthetization of the studied particulate composite. The
machine learning (ML) model is trained on a generated dataset of
microstructural descriptors with their multifunctional property quantities as
their labels. Sobol sequence is used for in-silico Design of Experiment (DoE)
by sampling the design space to generate a comprehensive dataset of 3D
microstructure realizations via a packing algorithm. The mechanical responses
of the generated microstructures are simulated using a previously developed
Finite Element (FE) model, considering the surface tension induced by LM
inclusions, while the linear thermal and dielectric constants are homogenized
with the help of our in-house Fast Fourier Transform (FFT) package. Following
the training by minimization of an appropriate loss function, the VAE encoder
acts as the surrogate of numerical solvers of the multifunctional
homogenizations, and its decoder is used for the material design. Our results
indicate the satisfactory performance of the surrogate model and the inverse
calculator with respect to high-fidelity numerical simulations validated with
LMEE experimental results.
