Accelerated computational micromechanics and its application to polydomain liquid crystal elastomers

Abstract

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Approximation of periodic Green's operator in real space using numerical integration and its use in fast Fourier transform‐based micromechanical models

“…Therefore, we conclude that the results are dependent on the reference stiffness. A larger reference stiffness better enforces strain compatibility, while a lower one better enforces stress equilibrium 43 . Therefore, changing the reference stiffness leads to changes in the errors of stress equilibrium and strain compatibility.…”

“…A larger reference stiffness better enforces strain compatibility, while a lower one better enforces stress equilibrium. 43 Therefore, changing the reference stiffness leads to changes in the errors of stress equilibrium and strain compatibility. It appears that for 𝛤 per,real this leads to different results and further investigation is necessary.…”

A Programmable Liquid Crystal Elastomer Metamaterials With Soft Elasticity

“…While sophisticated continuum constitutive models (Zhang et al, 2019) and computational micromechanics simulations (Zhou and Bhattacharya, 2021) for nematic LCEs have been proposed recently, we shall proceed with the simple phenomenological description of LCE with free energy density function in Eq. 7.…”

Multiscale modeling of materials: Computing, data science,uncertainty and goal-oriented optimization

“…Consequently, they can provide enormous computational power if the calculations are carefully arranged to meet the limitations of the architecture. This section describes how accelerators like graphical processing units (GPUs) can be effectively used in rapidly solving such problems drawing from Zhou and Bhattacharya [98].…”

“…This raises the first question: Can we use accelerators to efficiently and rapidly solve models at the individual scales? Section 2 reviews recent work of Zhou and Bhattacharya [98] that describes how such accelerators can be effectively used in the solution of problems of micromechanics. A key idea in this work is to note that nonlinear partial differential equations that describe micromechanical phenomena come about through a composition of universal laws of physics (kinematic compatibility and balance of mass, momenta, energy etc.)…”