Several issues connected with bridging methods for atomistic-to-continuum(AtC)coupling are examined.Different coupling approaches using various energy blending models are studied as well as the influence that model pa...Several issues connected with bridging methods for atomistic-to-continuum(AtC)coupling are examined.Different coupling approaches using various energy blending models are studied as well as the influence that model parameters,blending functions,and grids have on simulation results.We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region.We also show that continuum models are not appropriate for dealing with problems with singular loads,whereas AtC bridging methods yield correct results,thus justifying the need for a multiscale method.We investigate models that involve multiple-neighbor interactions in the atomistic region,particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.展开更多
We study the effect of ＂ghost forces＂ for a quasicontinuum method in three dimension with a planar interface. ＂Ghost forces＂ are the inconsistency of the quasicontinuum method across the interface between the atom...We study the effect of ＂ghost forces＂ for a quasicontinuum method in three dimension with a planar interface. ＂Ghost forces＂ are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region. Numerical results suggest that ＂ghost forces＂ may lead to a negilible error on the solution, while lead to a finite size error on the gradient of the solution. The error has a layer-like profile, and the interfacial layer width is of O（ε）. The error in certain component of the displacement gradient decays algebraically from O（1） to O（ε） away from the interface. A surrogate model is proposed and analyzed, which suggests the same scenario for the effect of ＂ghost forces＂. Our analysis is based on the explicit solution of the surrogate model.展开更多
In this paper,we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum(a/c)coupling with finite range interactions in two dimensions.W...In this paper,we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum(a/c)coupling with finite range interactions in two dimensions.We have systematically derived a new explicitly computable stress tensor formula for finite range in-teractions.In particular,we use the geometric reconstruction based consistent atomistic/continuum(GRAC)coupling scheme,which is quasi-optimal if the continuum model is discretized by P1 finite elements.The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.展开更多
基金This work was supported by the Department of Energy under grant number DE-FG02-05ER25698.
文摘Several issues connected with bridging methods for atomistic-to-continuum(AtC)coupling are examined.Different coupling approaches using various energy blending models are studied as well as the influence that model parameters,blending functions,and grids have on simulation results.We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region.We also show that continuum models are not appropriate for dealing with problems with singular loads,whereas AtC bridging methods yield correct results,thus justifying the need for a multiscale method.We investigate models that involve multiple-neighbor interactions in the atomistic region,particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.
基金supported by National Natural Science Foundation of China(Grant Nos.1093201191230203 and 11021101)
文摘We study the effect of ＂ghost forces＂ for a quasicontinuum method in three dimension with a planar interface. ＂Ghost forces＂ are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region. Numerical results suggest that ＂ghost forces＂ may lead to a negilible error on the solution, while lead to a finite size error on the gradient of the solution. The error has a layer-like profile, and the interfacial layer width is of O（ε）. The error in certain component of the displacement gradient decays algebraically from O（1） to O（ε） away from the interface. A surrogate model is proposed and analyzed, which suggests the same scenario for the effect of ＂ghost forces＂. Our analysis is based on the explicit solution of the surrogate model.
基金supported by National Natural Science Foundation of China grant 11861131004,11771040,91430106supported by Natural Science Foundation of China grant 11871339,11861131004,11571314,11471214 and the One Thousand Plan of China for young scientists.
文摘In this paper,we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum(a/c)coupling with finite range interactions in two dimensions.We have systematically derived a new explicitly computable stress tensor formula for finite range in-teractions.In particular,we use the geometric reconstruction based consistent atomistic/continuum(GRAC)coupling scheme,which is quasi-optimal if the continuum model is discretized by P1 finite elements.The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.
