Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold  

作　　者：Yoshihiro Kanno 

机构地区：[1]Mathematics and Informatics Center,The University of Tokyo,Hongo 7-3-1,Tokyo 113-8656,Japan

出　　处：《Theoretical & Applied Mechanics Letters》2021年第5期260-265,共6页力学快报（英文版）

基　　金：supported by Research Grant from the Kajima Foundation,JST CREST Grant No.JPMJCR1911,Japan;JSPS KAKENHI(Nos.17K06633,21K04351).

摘　　要：Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.

关 键 词：Alternating minimization Regularized least-squares Kernel method Manifold learning Data-driven computing 

分 类 号：O302[理学—力学]