题目：Energy-Inconsistent Objective Stress Rates in ABAQUS, ANSYS, LS-DYNA and Other FE Codes: Magnitude of Errors and How to Correct Them

报告人：Prof. Zdeněk P. Ba?ant

时 间：5月10日（周四）下午3:00-5:00
地 点：力学楼434会议室
主持人：方岱宁（教授）

报告内容摘要：
    The objective stress rates used in most commercial finite element (FE) codes for the incremental (updated Lagrangian or Riks) analysis is the Jaumann rate of Cauchy (true) stress. However, this rate causes an error in energy, due to the fact that it is not work-conjugate to any finite strain tensor except if the material is incompressible. For bifurcation load analysis, most programs use the Jaumann rate of Kirchhoff stress, which is work-conjugate to the Hencky (or logarithmic) stress tensor. Yet this causes another kind of energy error in the case of highly orthotropic structures very soft in shear, requiring the Truesdell stress rate which is work-conjugate to the Green-Lagrangian finite strain tensor. Although these errors were identified long ego, they were generally thought to be negligible. It is now demonstrated by numerical examples that this is not always so.
    First, an example of indentation of a naval-type sandwich plate with a polymeric foam core demonstrates an error of 28.7% in the indentation force and 15.0% in the work on indentation. Similar errors must be expected for all highly compressible materials, such as metallic and ceramic foams, honeycomb, loess, silt, organic soils, pumice, tuff, corral, light wood, osteoporotic bone and various biologic tissues. As a remedy, 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 the lack of work-conjugacy and make the program give the results corresponding to the Jaumann rate of Kirchhoff stress, which is work-conjugate.
    Second, it is shown that, in buckling of compressed highly orthotropic columns or sandwich columns very soft in shear, the use of Jaumann stress rates can cause large errors, as high as 100% of the critical load, even if the strains are small. Another example of a highly orthotropic plate, equivalent to a large rectangular foam-core sandwich plate for the cladding of a steel ribbed hull of a large ship, shows a critical load error of 40%. A similar situation could arise when severe damage such as distributed cracking leads to a highly anisotropic tangential stiffness matrix, or when axial cracks between fibers severely weaken a uniaxial fiber composite. It is demonstrated that if a certain previously derived stress-dependent transformation of the tangential moduli is introduced into the user’s material subroutine in these commercial programs, one can obtain correct results that correspond to Truesdell’s stress rate and are also supported by experiments. Iterations of the bifurcation analysis with updating of the transformation are required to reduce further numerical error.

报告人简介：
    Born and educated in Prague (Ph.D. 1963), Ba?ant joined Northwestern in 1969, where he has been W.P. Murphy Professor since 1990 and simultaneously McCormick Institute Professor since 2002, and Director of Center for Geomaterials (1981-87). He was inducted to Nat. Academy of Sciences, Nat. Academy of Engrg. and Am. Acad. of Arts & Aci., as well as Italian Nat. Acad. (dei Lincei), Austrian Acad. of Sciences, Czech Acad. of Engrg., Spanish Royal Acad. of Eng., Eur. Acad. of Sci. & Arts, and Istituto Lombardo. An ASCE Hon. Member and Illinois Registered Structural Engineer, he received 7 honorary doctorates (Prague, Karlsruhe, Colorado, Milan, Lyon, Vienna, Ohio State), ASME Timoshenko, Warner and Nadai Medals, ASCE von Karman, Newmark, Biot and Croes Medals and Lifetime Achievement Award, SES Prager Medal, RILEM L'Hermite Medal, Torroja Medal, etc. He authored six books: Scaling of Structural Strength, Inelastic Analysis, Fracture and Size Effect, Stability of Structures, Concrete at High Temperatures, and Concrete Creep. With H-index 68 and >21,400 citations (on Google), he is one of the original top 100 ISI Highly Cited Scientists in engineering.