Jaumann率型一维大变形本构关系的双曲线模型

Hyperbolic model for one-dimensional large strain constitutive relations of Jaumann rate-type

鉴于 Jaumann 率型本构关系难以得到应力应变全量之间的严格解析形式,采用有限元法研究了一维大变形过程中Kirchhoff 应力和 Green 应变之间的变化规律。首先,基于虚功原理推导了完全拉格朗日描述的大变形有限元方程,然后提出了模拟大变形本构关系的双曲线模型和割线模量处理方法。算例分析结果表明,双曲线模型能够较好地拟合大变形本构关系。大变形计算本构关系应当考虑初始孔隙比的影响。

The exact analytical solution to the constitutive relation of Jaumann rate-type has not yet been found in the magnitudes of stress and strain.The variation of Kirchhoff stress with Green strain for one-dimensional large strain problems was studied using finite-element method.Based on the principle of virtual work,the large strain FEM was formulated in terms of total Lagrangian description.A new hyperbolic model for simulating the large strain constitutive relations was put forward along with the rearrangement method of secant modulus.The results of numerical simulation show that the presented hyperbolic model can fit the large strain constitutive relation nicely.The initial void ratio has considerable influence on the computational large strain constitutive relations.