Ye Lu¹, Hengyang Li¹, Sourav Saha², Satyajit Mojumder², Abdullah Al Amin¹, Derick Suarez¹, Yingjian Liu³, Dong Qian³, Wing Kam Liu^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1351-1371, 2021, DOI:10.32604/cmes.2021.017719

Abstract This paper presents the concept of reduced order machine learning finite element (FE) method. In particular, we propose an example of such method, the proper generalized decomposition (PGD) reduced hierarchical deeplearning neural networks (HiDeNN), called HiDeNN-PGD. We described first the HiDeNN interface seamlessly with the current commercial and open source FE codes. The proposed reduced order method can reduce significantly the degrees of freedom for machine learning and physics based modeling and is able to deal with high dimensional problems. This method is found more accurate than conventional finite element methods with a small portion of degrees of freedom. Different… More >

Yan Wang¹, Weina Li¹, Jorg Weissmoller^2,3, Huiling Duan¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.18, No.4, pp. 117-118, 2011, DOI:10.3970/icces.2011.018.117

Abstract Surface stress plays a very important role in surface morphology evolution [1-3]. Since the bonding configurations of the atoms at surfaces become different when adsorbates are situated on the surfaces, surface stress can be altered by the presence of adsorbates. Moreover, unless experiments are carried out on high quality single crystals, the surface will typically exhibit corrugation or roughness even when it is nominally planar. We have analyzed this kind of problem and pointed out that stress can be quite significantly affected by surface roughness when the microstructure scale reaches the nanometer range [4].

Therefore, we first build a… More >

T. Hasebe¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 145-156, 2006, DOI:10.3970/cmes.2006.011.145

Abstract This paper presents recent achievements in field theoretical approach toward substantial linkage among key hieratical scales dominating polycrystalline plasticity of metals and alloys. Major ingredients of the theory are briefly shown first, which is followed by several overwhelming results and some implications including key factors for dislocation cell structure evolution, key features of polycrystalline plasticity and their rational modeling in crystal plasticity-based constitutive equation. More >