Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it

被引:31
作者
Bazant, Zdenek P. [1 ]
Gattu, Mahendra [1 ]
Vorel, Jan [1 ]
机构
[1] Northwestern Univ, Dept Civil & Environm Engn, CEE, Evanston, IL 60208 USA
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2012年 / 468卷 / 2146期
关键词
objective stress rate; finite strain; energy error; updated Lagrangian method; incremental analysis; compressible materials; SANDWICH; INDENTATION; FAILURE; STRAIN; SHEAR; FOAMS; MODEL; SOFT;
D O I
10.1098/rspa.2012.0167
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Most commercial finite-element programs use the Jaumann (or co-rotational) rate of Cauchy stress in their incremental (Riks) updated Lagrangian loading procedure. This rate was shown long ago not to be work-conjugate with the Hencky (logarithmic) finite strain tensor used in these programs, nor with any other finite strain tensor. The lack of work-conjugacy has been either overlooked or believed to cause only negligible errors. Presented are examples of indentation of a naval-type sandwich plate with a polymeric foam core, in which the error can reach 28.8 per cent in the load and 15.3 per cent in the work of load (relative to uncorrected results). Generally, similar errors must be expected for all highly compressible materials, such as metallic and ceramic foams, honeycomb, loess, silt, organic soils, pumice, tuff, osteoporotic bone, light wood, carton and various biological tissues. It is shown that a previously derived equation relating the tangential moduli tensors associated with the Jaumann rates of Cauchy and Kirchhoff stresses can be used in the user's material subroutine of a black-box commercial program to cancel the error due to the lack of work-conjugacy and make the program perform exactly as if the Jaumann rate of Kirchhoff stress, which is work-conjugate, were used.
引用
收藏
页码:3047 / 3058
页数:12
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