Conjugate Stress/Strain Pair Approach for Anisotropic Materials

2018 ◽  
Author(s):  
VEYSEL EREL ◽  
MINGLIANG JIANG ◽  
ALAN D. FREED
Keyword(s):  
Anisotropic Materials ◽  
Stress Strain ◽  
Strain Pair ◽  
Conjugate Stress

An optimized constitutive model for reproducing flow stress–strain relationships of anisotropic materials

2018 ◽  
Vol 233 (4) ◽  
pp. 1357-1368 ◽  
Author(s):  
Yanli Lin ◽  
Guannan Chu ◽  
Caiyuan Lin ◽  
Yongda Yan
Keyword(s):  
Flow Stress ◽  
Fourth Order ◽  
Anisotropic Materials ◽  
Second Order ◽  
Least Square ◽  
Experimental Stress ◽  
Function Model ◽  
Stress Strain ◽  
Order Function ◽  
Ordinary Least Square

Due to the strong anisotropic property of the advanced metal materials used in automobile, aviation, and aerospace, experimental flow stress–strain relations including different stress states are necessary to provide the information of anisotropic hardening and plastic flow for constructing a constitutive model. Therefore, reasonably reproducing the experimental stress–strain relations is the most fundamental work to substitute adequate flow stress–strain curves into the constitutive equation at the same time. However, accurate and stable regression results are difficult to obtain through the current regression models such as power exponent, second-order function model, fourth-order function model, and so forth. In this paper, an optimized model named as a least square quadratic regression model (ordinary least square model) was proposed based on the most useful second-order function model. The significant difference is that all experimental points are used to reproduce the experimental stress–strain relations in ordinary least square model in place of only three experimental points adopted in second-order function model, which results in good regression accuracy. Through comparison, it is found that the regression results by power function are poor with regard to some experimental results, and the results reproduced by second-order function model or fourth-order function model are very sensitive to the experimental points selected to do the regression. The sum of squares for error (SSE) increases sharply when the selected points are unreasonable. In addition, for second-order function and fourth-order function models, only limited experimental points are adopted to do the regression, the best regression accuracy cannot be obtained even if the selected points are reasonable. In contrast, SSE of the regression curve by ordinary least square model reduces to less than 50% of the best regressed result by second-order function model, the yielding behavior and variable strain increment ratio of the anisotropic materials can be reflected more accurately. This is very important for accurately describing the plastic flow behaviors of anisotropic materials.

Stress/strain basis pairs for anisotropic materials

2017 ◽  
Vol 120 ◽  
pp. 152-158 ◽  
Author(s):  
Veysel Erel ◽  
Alan D. Freed
Keyword(s):  
Anisotropic Materials ◽  
Stress Strain

Anisotropic conjugate stress/strain base pair approach for laminates undergoing large deformations

Materialia ◽  
2019 ◽  
Vol 6 ◽  
pp. 100318
Author(s):  
Veysel Erel ◽  
Mingliang Jiang ◽  
Michael R. Moreno ◽  
Alan D. Freed
Keyword(s):  
Base Pair ◽  
Large Deformations ◽  
Stress Strain ◽  
Conjugate Stress

Long Destruction of Structurally Damaged Composite Pipe

2013 ◽  
Vol 3 (1) ◽  
pp. 37-47
Author(s):  
Akhundov Mohammed B. ◽  
Sadayev Azber Sh.
Keyword(s):  
Composite Materials ◽  
Anisotropic Materials ◽  
Important Class ◽  
Stress Strain ◽  
Structural Criterion ◽  
Composite Pipe ◽  
The Given

Composite materials represent the important class of anisotropic materials. Unlike the previous works of authors in which estimations of long durability of an anisotropic pipe are given within the bounds of criterion of the destruction being generalization of the first theory of durability on the maximal stretching or compressing strain on the account of the process of damageability, in the given work the estimation of long durability is given within the bounds of the structural criterion of durability offered in work of one of the authors. According to him, destruction of a material is defined by the greatest level of the accumulated volume of damageability on some of proper stress-strain states. A problem in revealing stages of scattered destruction of an anisotropic pipe with the use of the simplified variant of criterion of durability, has been solved in the given work.

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