Finite element investigation of TPMS-inspired microplate structures for mechanical stability enhancement in sports equipment

Abstract

The development of lightweight but impact-resistant sports gear needs structural ideas that boost mechanical stability while also keeping good energy uptake characteristics. Here, we do a finite element look into TPMS inspired multilayer microplate designs under dynamic input, like real-time excitation. We choose three different TPMS cores, Primitive, Gyroid, and I-graph, wrapped into what we call a Wrapped Package-graph, to see how they affect the nonlinear vibration behavior and the energy dissipation in sandwich-type microplates. The mechanical setup is built on Mindlin–Reissner plate theory, but we also add von Kármán-style geometric nonlinearity, so the model can capture the moderate to large deflection effects properly. For size-related trends, we use the modified strain gradient theory (MSGT), in which several material length-scale parameters are brought in to represent microscale deformation mechanisms in a more faithful way. Furthermore, the way the microplate interacts with its supporting medium is treated through a nonlinear elastic foundation, so the behavior stays close to the more realistic operating conditions you see in sports equipment. A full finite element setup is built, where the nonlinear part of the deviatoric stretch-gradient vector is slipped into the governing equations. Then the nonlinear system is handled in order to pull out transient responses, mode shapes, and how kinetic, potential, and overall energies change in time. After that, parametric checks are run to see how the TPMS topology, the excitation intensity, the foundation stiffness, the geometric dimensions, and those MSGT length-scale parameters affect the structural performance. The numerical findings show clear gaps between the P, G, and IWP architectures when it comes to vibration behavior and the ability to absorb energy. Especially, TPMS-based multilayer microplates seem to provide better dynamic steadiness, together with a higher elastic strain energy, which suggests they could be used in next-generation high-performance sports hardware under impact and vibration loading.