【作者】 程莉；

【导师】 黄克智；

【作者基本信息】 清华大学 ， 固体力学， 1988， 博士

【摘要】 大变形弹塑性理论是国际力学界令人瞩目的问题。在这个领域里有许多问题甚至是基本的问题还没有解决。本文的目的在于针对一系列的基本问题加以探讨和解决。在对现有的最有影响的几种塑性理论加以分析、比较和评判中加以发展和完善。 本文分为三部分: 第一部分研究大变形弹性理论。把建立在刚性标架转换的基础上的Noll定理(或Green-Naghdi-Rivlin定理)推广到任意非刚性的标架,从而把大变形弹性本构关系建立在能量平衡原理不变性的基础上,为大变形弹性本构关系提供了一个新的理论框架。 第二部分研究大变形塑性理论。论证了变形梯度的乘法分解与应变张量加法分解的统一性。提出了弹性与塑性变形率定义必须满足客观性和(?)-不变性这两个条件。提出了弹性与塑性变形率更为广泛的新的定义。把Simo牙Ortiz的塑性理论推广到一般变温的情况,并论证了这一理论成立的条件。导出了Hill与Rice的塑性理论在即时构形中进行更多还原

【Abstract】 Elastic-plastic constitutive theory is currently attracting much attention in academic circles of solid mechanics . There still exist some, even fundamental , problems which are yet unsolved. This thesis aims at investigating and attempting to clarify these problems. Some of the most influential constitutive elastic-plastic theories are analyzed and compared . And in the course of critical review of the existing theories , Some attempts are made for their refinement .The thesis is divided into three parts :The first part is devoted to the study of constitutive elastic theory with finite deformation . The Noll’s Theorem (or Green-Naghdi- Rivlin’s Theorem) is extended to the case of arbitrary deformable frame transformation , and hence the constitutive elastic relations can be founded on the basis of the principle of invariance of energy balance.In the second part the constitutive elastic-plastic theory is Studied The consistency of the multiplication decomposition of deformation gradient and the addition decomposition of strain tensor is demonstrated . Two conditions are explicitly elucidated for correct definition of elastic and plastic strain rate tensors , namely , the condition of objectivity with respect to the frame transformation ( called the condition of Q-objectivity) and the condition of invariance. with respect +o -the rotation of iV mediate configuration ( called the condition of Q-invariance. ) ? A "new general definition of elastic and plastic strain rate -tensors is suggested . The theory of Stmo and Ortiz is extended to the thermal case , and the condition of validity of the theory is demonstrated . Constitutive relations in rate "form in current configuration are derived for the theories of Hill and Rice , and of Mandel as well , with the internal variables being any scajars > vectors or tensors .The -third part is engaged \n the s+udy of spins used for co-rata-tional objective derivatives of tensors . The expression for the spin of Strain-rate frame is derived , and the spin is used in solving the simple shear problem by -the constitutive model of Prager and Ziegler . The results show that this spin is a suitable canditate for the use \n constitutive, relations.更多还原