review on the research of mechanical problems with different moduli in tension and compression

다국어 초록 (Multilingual Abstract)

Most materials exhibit different tensile and compressive strains given the same stress applied in tension or compression. These materials are known as bimodular materials. An important model of bimodular materials is the criterion of positive-negative signs of principal stress proposed by Ambartsumyan. This model is mainly applicable to isotropic materials and deals with the principal stress state in a point. However, due to the inherent complexity of the constitutive relation, FEM based on iterative strategy and analytical methods based on a simplified mechanical model are required. In this paper, we review the basic assumptions of this model and its development, several innovative computational methods, and some important engineering applications. We also discuss the sequent key problems in this field.

참고문헌 (Reference)

1 N. Kamiya, "Transverse shear effect in a bimodulus plat" 32 (32): 351-357, 1975

2 C. W. Bert, "Transverse effects in bimodular composite laminates," 17 (17): 282-298, 1983

3 D. Z. Zhao, "The shape optimization of suspended insulator" 8 (8): 313-318, 1991

4 L. Y. Li, "The rationalism theory and its finite element analysis method of shell structures" 11 (11): 395-402, 1990

5 C. Gao, "The plate and shell of structural dynamic analysis with different elastic moduli of material" 18 (18): 81-85, 2001

6 W. J. Yao, "The analytical and numerical solution of retaining wall based on elastic theory of different modulus" 38 (38): 1022-1027, 2004

7 X. T. He, "Symmetry in elastic structural analysis based on different elastic moduli in tension and compression" 31 (31): 735-739, 2008

8 R. M. Jones, "Stress-strain relations for materials with different moduli in tension and compressi" 15 (15): 16-23, 1977

9 K. Vijayakumar, "Stress-strain relation for composites with different stiffnesses in tension and compression: a new model," 1 (1): 167-175, 1987

10 Y. P. Tseng, "Stress analysis of bimodulus laminates using hybrid stress plate elements" 35 (35): 2025-2028, 1998

11 H. T. Yang, "Solving elasticity problems with bi-modulus via a smoothing technique," 23 (23): 19-23, 2006

12 H. T. Yang, "Solution to problem of dual extension-compression elastic modulus with initial stress method" 32 (32): 35-39, 1992

13 H. T. Yang, "Solution of 3-D elastic dual extension-compression modulus problems using initial stress technique," 39 (39): 478-482, 1999

14 D. Z. Zhao,, "Shape optimization of suspended insulator with dual elastic modulus," 34 (34): 10-16, 1994

15 Z. M. Ye, "Progresses in elasticity theory with different modulus in tension and compression and related FEM," 26 (26): 9-14, 2004

16 Y. Z. Zhang, "Numerical method of bimodulus problem under condition of θ≠0 and error analysis of supposing θ=0" 34 (34): 641-645, 1994

17 J. N. Reddy, "Nonlinear bending of bimodular- material plates" 19 (19): 229-237, 1983

18 D. Bruno, "Nonlinear analysis of bimodular composite plates under compression" 14 (14): 28-37, 1994

19 X. B. Liu, "Modulus of elasticity in shear and accelerate convergence of different extension-compression elastic modulus finite element method" 40 (40): 526-530, 2000

20 C. W. Bert, "Models for fibrous composites with different properties in tension and compression" 99 (99): 344-349, 1977

21 Y. Z. Zhang, "Mechanical influences of insulator due to different moduli of material" 14 (14): 36-39, 1992

22 N. Kamiya, "Large deflection of a different modulus circular plate," 97 (97): 52-56, 1975

23 R. S. Srinivasan, "Large deflection analysis of bimodulus annular and circular plates using finite elements" 31 (31): 681-691, 1989

24 Hi Seak Yoon, "In-situ Crack Propagation Observation of a Particle Reinforced Polymer Composite Using the Double Cleavage Drilled Compression Specimens" 대한기계학회 20 (20): 310-318, 2006

25 F. Greco, "Homogenized mechanical behavior of composite micro-structures including micro-cracking and contact evolution" 76 (76): 182-208, 2009

26 Y. Z. Zhang, "Finite element method of elasticity problem with different tension and compression moduli," 6 (6): 236-245, 1989

27 Z. Y. Luo, "Expansion of cylindrical cavities in strain-softening material with different elastic moduli in tension and compression" 21 (21): 40-45, 2004

28 X. N. Gong,, "Expansion of circular cavities with different elastic moduli in tension and compression," 11 (11): 127-132, 1994

29 S. A. Ambartsumyan, "Elasticity theory of different modulus," China Railway Press 1986

30 X. T. He,, "Elasticity solution of simple beams with different modulus under uniformly distributed load," 24 (24): 51-56, 2007

31 R. Zinno, "Damage evolution in bimodular laminated composites under cyclic loading" 53 (53): 381-402, 2001

32 X. T. He, "Convergence analysis of a finite element method based on different moduli in tension and compression" 46 (46): 3834-3740, 2009

33 L. S. Cai, "Constitutive relation of elastic materials with different elastic moduli in tension and compression," 29 (29): 17-21, 2009

34 R. F. Wu, "Computation of 3- D axisymmetric structures with different modulus theory of elasticity" 6 (6): 94-98, 1989

35 X. P. Zhou, "Closed-form analytical solution for beam on elastic foundation with different tension and compression modulus" 30 (30): 78-82, 2007

36 X. T. He, "Approximate elasticity solution of bending-compression column with different tension-compression modul" 31 (31): 339-343, 2008

37 X. T. He, "Applying the equivalent section method to solve beam subjected lateral force and bending-compression column with different moduli," 49 (49): 919-924, 2007

38 S. Q. Guan, "Application on rubber water stop in water conservancy strobe using FEM based on large deformation and different tension-compression moduli" 11 : 127-132, 1994

39 R. M. Jones, "Apparent flexural modulus and strength of multimodulus materials" 10 (10): 342-354, 1976

40 Z. D. Zhu, "Analytical solution to elastic theory on surrounding rocks in tunnels with different compressive and tensile moduli." 31 (31): 21-24, 2003

41 W. J. Yao, "Analytical solution of bendingcompression column using different tension-compression modulus" 25 (25): 983-993, 2004

42 W. J. Yao, "Analytical solution for bending beam subject to lateral force with different modulus" 25 (25): 1107-1117, 2004

43 C. Gao, "Analysis on thin-shell structures based on bimoduli theory" 17 (17): 7-15, 2000

44 X. B. Liu, "Analysis of the dam’s stress and shift using finite element method with different elastic moduli" 23 (23): 39-42, 2001

45 C. Gao, "Analysis for the plate with the theory of different extension-compression moduli" 15 (15): 449-455, 1998

46 C. Gao, "Analysis for the canopy of plane with the theory of extension-compression elastic modulus" 37 (37): 13-20, 1997

47 N. Kamiya, "An energy method applied to large deflection of a thin plate of bimodulus material" 3 (3): 317-329, 1974

48 H. T. Yang, "An analysis of longitudinal vibration of bimodular rod via smoothing function approach" 317 (317): 419-431, 2008

49 Y. Z. Zhang, "Algorithm for frames of bimodulus materials," 29 (29): 23-32, 1989

50 G. Medri, "A nonlinear elastic model for isotropic materials with different behavior in tension and compression" 104 (104): 26-28, 1982

51 Z. M. Ye,, "A new finite formulation for planar elastic de formation" 14 (14): 2579-2592, 1997

52 Z. M. Ye, "A new elasticity and finite element formulation for different Young’s modulus when tension and compression loading" 5 (5): 89-92, 2001

53 K. J. Yang, "A high-precision finite-element for shells of bimodulus materials," 12 (12): 167-174, 1991

54 Z. M. Ye, "A finite element formulation for different Young´s modulus when tension and compression loading," Pohang University of Science and Technology, South Korea 2001