Symmetry-enforcing neural networks with applications to constitutive modeling

The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art micromechanical modeling and advanced machine learning techniques to homogenize complex microstructures exhibiting non-linear and history dependent behaviors. The resulting homogenized model, termed smart constitutive law (SCL), enables the adoption of microstructurally informed constitutive laws into finite element solvers at a fraction of the computational cost required by traditional concurrent multiscale approaches. In this work, the capabilities of SCLs are expanded via the introduction of a novel methodology that enforces material symmetries at the neuron level, applicable across various neural network architectures. This approach utilizes tensor-based features in neural networks, facilitating the concise and accurate representation of symmetry-preserving operations, and is general enough to be extend to problems beyond constitutive modeling. Details on the construction of these tensor-based neural networks and their application in learning constitutive laws are presented for both elastic and inelastic materials. The superiority of this approach over traditional neural networks is demonstrated in scenarios with limited data and strong symmetries, through comprehensive testing on various materials, including isotropic neo-Hookean materials and tensegrity lattice metamaterials. This work is concluded by a discussion on the potential of this methodology to discover symmetry bases in materials and by an outline of future research directions.

Soft Tensegrity Systems for Planetary Landing and Exploration

During the last decade, tensegrity systems have been the focus of numerous investigations exploring the possibility of adopting them for planetary landing and exploration applications. Early approaches mainly focused on locomotion aspects related to tensegrity systems, where mobility was achieved by actuating the cable members of the system. Later efforts focused on understanding energy storage mechanisms of tensegrity systems undergoing landing events. More precisely, it was shown that under highly dynamic events, buckling of individual members of a tensegrity structure does not necessarily imply structural failure, suggesting that efficient structural design of planetary landers could be achieved by allowing its compression members to buckle. In this work, we combine both aspects of previous research on tensegrity structures, showing a possible lattice-like structural configuration able to withstand impact events, store pre-impact kinetic energy, and utilize a part of that energy for the locomotion process. Our work shows the feasibility of this proposed approach via both experimental and computational means.