Scientists solve one of the hardest problems in the computational atomic-scale mechanics of materials

12/12/2024

Graphical abstract. Credit: Macromolecules (2024). DOI: 10.1021/acs.macromol.4c01360

Currently employed computational methods to simulate materials and their mechanical behavior are based on molecular dynamics (MD) with atomistic force-fields. These methods provide an excellent description of the thermodynamically stable phases of materials with arbitrary chemical and microstructural complexity.

However, simulating the mechanical deformation behavior of materials at the atomistic level, or, in general, the response of a material to an external time-dependent stimulus, has been an open challenge for a long time. The main bottleneck is represented by the inevitably short time scale of integration of the equations of motion (just a few femtoseconds) that atomistic MD methods rely on. This is a necessary step in order to discretize the equations of motion that govern atomic motions and collisions, in order to solve them on a computer.

This limitation makes it impossible to simulate the dynamical deformation of materials on long time scales encountered in experiments, i.e., for deformation rates lower than ~10 to 100 gigahertz. This fundamental time-scale bridging problem is currently unsolved, and prevents the computational prediction of material mechanics in the regimes that are experimentally accessible in standard mechanical tests and rheology.

With my post-doc, Dr. Vinay Vaibhav, and with my long-time collaborator at the US Army Research Lab, Dr. Tim Sirk, I have now developed a computational framework that provides a working solution to this problem, arguably one of the biggest problems in molecular simulations of materials under deformations and external stimuli.

The key idea of our approach is that the mechanical response at the low frequencies (e.g., around the Hertz) is dominated by atomic displacements known as nonaffine displacements. A nonaffine displacement is a swerve in the trajectory of an atom, which thus deviates from the trajectory prescribed by the externally imposed deformation (akin to Epicurus's "clinamen," if you are familiar with Greek philosophy).

The origin of this swerve is the necessity to enforce mechanical equilibrium at every step in the deformation. In other words, at each step, the atom receives forces from its neighbor atoms, which need to be relaxed via an extra motion, the nonaffine swerve.

As my collaborators and I have come to realize over the years, implementing this description of atomic trajectories implies computing the vibrational normal modes of the system, which can be done with modern computational techniques.

This has now allowed us, in a paper published in the journal Macromolecules, to achieve a parameter-free agreement with the viscoelastic moduli of a real complex material, a crosslinked epoxy polymer glass in its amorphous solid state, at frequencies that are about 10 orders of magnitude lower than those that can be achieved by simulating the deformation process in standard molecular dynamic simulations.

The agreement with experimental data from mechanical tests is striking, considering that no adjustable parameters are involved in the comparison.
Our approach can still be refined in future work, e.g., by taking larger snapshots of the material configuration, with an increasing number of atoms, which will improve our predictions and reduce the noise from numerical fluctuations.

An exciting prospect offered by this method is that of being able to single out the atomic and molecular vibrations, and motions, that are mostly responsible for the stiffness and hardness of a given material (or, conversely, for its softness), with plenty of opportunities for the development of new materials with high-performance properties for many technological and engineering applications.
This story is part of Science X Dialog, where researchers can report findings from their published research articles. 

Source: https://tinyurl.com/56aewrtm via Phys.Org