High-performance large-scale simulation of multi-stable metastructures

Abstract

In this paper, we have developed a solver based on the message-passing interface (MPI) to enable rapid large-scale simulation of generic metastructures composed of bi- or multi-stable elements. The in-house solver has been thoroughly validated against a commercial numerical solver (Abaqus) and the well-established serial codes from the previous studies. We can achieve up to 4th-order solution accuracy with fully explicit Runge-Kutta (RK) methods, exceeding what many commercial structural analysis tools provide. With our parallel code dedicated to solving specific problem types, the absolute computational speed can be improved by three orders of magnitude, enabling the investigation of a large parameter space. More importantly, the in-house implementation enables an effective distribution of the computational load following the intrinsic structural periodicity, thus achieving efficient parallel scalability. To demonstrate our code's capability to handle massively large problems previously unattainable with existing solvers, we investigate the amplitude-dependent energy transmissibility of bi-stable metabeams and the stability of the transition wave's propagation speed. The achieved numerical and computational performance gains drastically expand the accessible analysis domains of general nonlinear metamaterial and metastructure architectures, thus opening up the potential to uncover new dynamics and enable practical implementations. Program summaryProgram Title:NM̂3 (Nonlinear MetaMaterials MPI) solverCPC Library link to program files:https://doi.org/10.17632/8f4n99jccf.1Developer's repository link:https://github.com/wonnie87/NMCubeLicensing provisions: MITProgramming language: FortranNature of problem:NM̂3 enables massively parallel simulations of strongly nonlinear metamaterials and metastructures, including 1D multi-stable lattice with coupled pendula (discrete sine-Gordon model), 1D lattice with quartic on-site potentials (discrete ϕ-4 model), and metabeam with a bi-stable microstructure.Solution method: Up to the 4th-order explicit Runge-Kutta (RK) methods are implemented in NM̂3. The Newmark-β (implicit) method with constant average acceleration is also available if unconditional numerical stability is desired.Additional comments including restrictions and unusual features: Running NM̂3 requires installation of Python (with NumPy library), MPI, and HDF5. A Python script is used to generate input files. The code use MPI system calls to allow a massive parallelization among the compute processes. The code uses HDF5 file format for data storage.