ZHAO Xue-chuan, LEI Yong-jun, ZHOU Jian-ping. Strain Analysis of Nonlocal Viscoelastic Kelvin Bar in Tension[J]. Applied Mathematics and Mechanics, 2008, 29(1): 62-68.
 Citation: ZHAO Xue-chuan, LEI Yong-jun, ZHOU Jian-ping. Strain Analysis of Nonlocal Viscoelastic Kelvin Bar in Tension[J]. Applied Mathematics and Mechanics, 2008, 29(1): 62-68.

# Strain Analysis of Nonlocal Viscoelastic Kelvin Bar in Tension

• Rev Recd Date: 2007-11-19
• Publish Date: 2008-01-15
• Based on viscoelastic Kelvin model and nonlocal relationship of strain and stress, a nonlocal constitutive relationship of viscoelasticity was obtained and the strain response of a bar in tension was studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the close form solution of strain field of the bar was obtained. The creep process of the bar is presented. When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity.
•  [1] Eringen A C,Speziale C G,Kim B S.Crack-tip problem in nonlocal elasticity[J].Journal of Mechanic Physics Solids,1977,25(1):339-355. [2] Eringen A C.On continuous distributions of dislocations in nonlocal elasticity[J].International Journal of Applied Physics,1984,56(10):2675-2680. doi: 10.1063/1.333787 [3] 戴天民.广义连续统场论在中国的进展[J].辽宁大学学报(自然科学版)，1999，26(1):1-11. [4] 戴天民.广义连续统场论在中国的进展(续篇)[J].辽宁大学学报(自然科学版)，1999，31(4):295-301. [5] 黄再兴.关于非局部理论的几个新观点及其在断裂力学中的应用(Ⅱ)——重论非线性非局部热弹性本构方程[J].应用数学和力学,1999,20(7):713-720. [6] 黄再兴.关于非局部理论的几个新观点及其在断裂力学中的应用(Ⅲ)——重论线性非局部弹性理论[J].应用数学和力学,1999,20(11):1193-1197. [7] 周振功,王彪.采用新方法研究非局部理论中Ⅰ型裂纹的断裂问题[J].应用力学和数学,1999,20(10):1025-1032. [8] 周振功,王彪.双Ⅰ型裂纹断裂动力学问题的非局部理论解[J].应用力学和数学,2001,22(7):682-690. [9] Pisano A A,Fuschi P.Closed form solution for a nonlocal elastic bar in tension[J].International Journal of Solids and Structures,2003,40(1):13-23. [10] Weckner O,Abeyaratne R.The effect of long-range forces on the dynamics of a bar[J].International Journal of Solids and Structures,2005,53(3):705-728. [11] Lei Y J,Friswell M I,Adhikari S.A Galerkin method for distributed systems with nonlocal damping[J].International Journal of Solids and Structures,2006,43(11/12):3381-3400. [12] Adhikai S,Lei Y J,Friswell M I.Dynamics of non-viscously damped distributed parameter systems[R]. AIAA-2005-1951,2005. [13] Ahmadi G. Linear theory non-local viscoelasticity[J].International Journal of Nonlinear Mechanics,1975,10(6):253-258. [14] Nowinski J L.On the non-local aspects of stress in a viscoelastic medium[J].International Journal of Nonlinear Mechanics,1986,21(6):439-446. [15] 张义同.热粘弹性理论[M].天津:天津大学出版社,2002,4-10. [16] Polizzotto C.Nonlocal elasticity and related variational principles[J].International Journal of Solids and Structures,2001,38(42/43):7359-7380. [17] Polizzotto C,Fuschi P,Pisano A A. A strain-difference-based nonlocal elasticity model[J].International Journal of Solids and Structures,2004,41(9/10):2383-2401.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142