非经典大变形弹塑性本构方程及其算法研究

本文介绍了作者提出的非经典大变形弹塑性木构方程的增量形式，发展了相应的有限元分析方法。由于不采用屈服面的概念及相应的流动规律与加载准则，与传统的算法相比，本文提出的算法不仅简化了计算过程，而且改善了收敛速度和计算精度。作为验证和应用的例子，分析了圆柱试件的大变形拉伸颈缩过程和短圆柱的镦粗过程。与实验结果的比较证明了所发展方法的有效性。

Nonclassical Constitutive Equation for LargeElastoplastic Deformation and Its FEM Algorithm

One of the essential premises of classical mathematical theory of plasticity is the assumption of apriori existence of a yield surface. Although it has, and will still have,a contribution to solve differ-ent kinds of engineering problems,to the extent that this assumption is mostly an idealization and,inmany cases,leads to many difficulties in application and numerical analysis, one could be in a goodposition to develop theories alternative to classical plasticity,which does not make use of this idealiza-tion a priori and can easily be applled to the structural analysis.The incremental form of the nonclassical constitutive equation for large elastoplastic deformation,which was recently obtained by the authors through a thermomechanically consistent mechanical mod-el, is firsdy introduced. Based on that the elastoplastic matrix is proposed and then iniplemented intotangent stiffness,finite element approach for the analysis of the stnictures subjected to large elastoplas-tic deformation is develolied. The main features of this work are: (a) the materinl behavior from elas-ticity to pfasticity is assumed to be transient and smooth,thus no yield surface and the correspondingflow rule and loading/unloading criterion is adopted,which greatly simplifies the numerical process ofstructural analysis; and (b).the adopted incremental form of the constitutive eqiiation circumvents themathematical difficulties caused by the weak singularity or highly decaying properties of the nonclassi-cal plastic constitutive equation, which may induce considerable error and even deteriorate conver-gence in numerical process, and greatly reduces the sensitivity of the nunlerical approach to theamount of incremental loading , which was once a serious problem in the numerical anaiysis when theincremental form of the constitutive equation is obtained directiy from the differential one. These ad-vantages greatiy inlproved the computational accuracy and convergence. The developed approach iscritically verified by the comparison between the ealculated and experimental results of circular cylin-ders subjected to necking and, upsetting. Compared with the algorithm based on the classical theory ofplasticity and that based on the original incremental form of nonclassical constitutive equation, thepresent algorithm seems more powerful in structural analysis.