A Tangent Stiffness MLPG Method for Atom/Continuum Multiscale Simulation
نویسندگان
چکیده
The main objective of this paper is to develop a multiscale method for the static analysis of a nano-system, based on a combination of molecular mechanics and MLPG methods. The tangent-stiffness formulations are given for this multiscale method, as well as a pure molecular mechanics method. This method is also shown to naturally link the continuum local balance equation with molecular mechanics, directly, based on the stress or force. Numerical results show that this multiscale method quite accurate. The tangent-stiffness MLPG method is very effective and stable in multiscale simulations. This multiscale method dramatically reduces the computational cost, but it still can provide reasonable accuracy in some regions of the model. keyword: Molecular mechanics, Multiscale method, continuum mechanics, MLPG.
منابع مشابه
Multiscale Simulation Based on The Meshless Local Petrov-Galerkin (MLPG) Method
A multiscale simulation technique based on the MLPG methods, and finite deformation mechanics, is developed, implemented, and tested. Several alternate time-dependent interfacial conditions, between the atomistic and continuum regions, are systematically studied, for the seamless multiscale simulation, by decomposing the displacement of atoms in the equivalentcontinuum region into long and shor...
متن کاملPrediction of Dislocation Nucleation During Nanoindentation by the Orbital-Free Density Functional Theory Local Quasi-continuum Method
We introduce the orbital-free density functional theory local quasi-continuum (OFDFT-LQC) method: a first-principles-based multiscale material model that embeds OFDFT unit cells at the subgrid level of a finite element computation. Although this method cannot address intermediate length scales such as grain boundary evolution or microtexture, it is well suited to study material phenomena such a...
متن کاملGlobal Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates
This paper studies mathematical models of biopolymer supramolecular aggregates that are formed by the self-assembly of single monomers. We develop a new multiscale numerical approach to model the structural properties of such aggregates. This theoretical approach establishes micro-macro relations between the geometrical and mechanical properties of the monomers and supramolecular aggregates. Mo...
متن کاملMultiscale Analysis of Transverse Cracking in Cross-Ply Laminated Beams Using the Layerwise Theory
A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numeric...
متن کاملNonlinear inelastic static analysis of plane frames with numerically generated tangent stiffness matrices
For the nonlinear analysis of structures using the well known Newton-Raphson Method, the tangent stiffness matrices of the elements must be constructed in each iteration. Due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the Newton-Raphson method to reduce the cost and time required by the analysis. In this paper, a ...
متن کامل