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【期刊论文】A MESH TRANSFORMATION METHOD FOR COMPUTING MICROSTRUCTURES
李治平, ZHIPING LI
,-0001,():
-1年11月30日
A numerical method is established to solve the problem of minimizing a nonquasiconvex potential energy. Convergence of the method is proved both in the case on its own and in the case when it is combined with a weak boundary condition. Numerical examples are given to show that the method, especially when applied together with a continuation method and some other numerical techniques, is not only successful and e
Key words and phrases., nonquasiconvex,, microstructure,, minimizing sequence,, mesh transformation,, finite element solutions,, convergence.,
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【期刊论文】MULTI-ATOMIC YOUNG MEASURE AND ARTIFICIAL BOUNDARY IN APPROXIMATION OF MICROMAGNETICS
李治平, ZHIPING LI XIAONAN WU
,-0001,():
-1年11月30日
Some micromagnetic phenomena can be modelled by a minimization problem of a nonconvex energy. A numerical method to compute the micromagnetic field, which gives rise to a finite dimensional unconstrained minimization problem, is given and analyzed. In our method, the Maxwell's equation defined on the whole space is solved by a finite element method using artificial boundary, and the highly oscillatory magnetization structure is approximated by an element-wise constant Young measure supported on a finite number of unknown points on the unit sphere. Numerical experiments on some uniaxial and cubic anisotropic energy densities show that the method is e
Key words and phrases., non-convex energy minimization,, micromagnetic,, microstructure,, Young measure,, unbounded domain,, artificial boundary,, finite element method.,
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【期刊论文】Numerical Computation of Stress Induced Microstructure
李治平, ZHIPING LI
SCIENCEIN CHINA (Seriies A), 2003: 1-10,-0001,():
-1年11月30日
The mesh transformation method is applied on a two dimensional elastic crystal model to study the formation of laminated microstructure in austenitemartensite phase transition when certain external loads are applied. Numerical experiments show that simple laminated microstructures with various volume fractions and twin width can be obtained by varying the loads. Numerical experiments also show that second order laminated microstructure with branched peedle-like laminates can also be obtained by oertain loads.
nonconvex energy minimization,, mesh transformation,, stress induced phase transition,, laminated microstructure.,
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【期刊论文】MULTISCALE MODELLING AND COMPUTATION OF MICROSTRUCTURES IN MULTI-WELL PROBLEMS
李治平, ZHIPING LI
,-0001,():
-1年11月30日
A multiscale model and numerical method for computing microstructures with large and inhomogeneous deformation is established, in which the microscopic and macroscopic information is recovered by coupling the finite order rank-one convex envelope and the finite element method. The method is capable of computing microstructures which are locally finite order laminates. Numerical experiments on a double well problem show that plenty of stress free large deformations can be achieved by microstructures consisting of piecewise simple twin laminates.
Key words and phrases., multiscale modelling,, multi-well problem,, energy minimization,, laminated microstructure,, stress free large deformation.,
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【期刊论文】COMPUTATIONS OF NEEDLE-LIKE MICROSTRUCTURES
李治平, ZHIPING LI
,-0001,():
-1年11月30日
We report some numerical results on the computation of needlelike microstructrues at mesoscopic scale obtained by applying the mesh transformation method, which basically includes a mesh optimization into the finite element approximations, on a nonquasiconvex elastic crystal model. Numerical experiments show that the branched needle-like microstructures can be well resolved near the interfaces between twinned layers of martensite and a single variant of martensite, which are in good qualitative agreement with the physical experiments.
Key words and phrases., nonquasiconvex,, mesh transformation,, twinned layers,, branch,, needle-like microstructure,, interface,, metastable state.,
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