| Deformation description is the basis of mechanical analysis.Only when the description of deformation strain field is perfect,can the material properties be accurately studied.Because the process of large deformation is too complicated and contains a lot of nonlinearity,it is very important to describe it correctly.In the theoretical framework of small deformation,when the size of deformed body is very small,rotational deformation can be considered to solve the problem that is difficult to be solved by classical elastic theory.This shows that in some cases,consideration of rotational deformation is necessary,and the stress tensor is asymmetric due to the action of a couple.However,when the deformation is more complex,there are a lot of assumptions in the theory of small deformation,leading to a lot of problems in the theory,and the analysis of large deformation theory is needed.In existing large deformation theory,it is generally believed the distortion when stretching and rotating of the need to be considered at the same time,the description of stretch enough to cope with most of the questions,but for the description of the rotation is always inadequate,its consideration of rotation only stop at the corner,but no further calculation of curvature,and the existing theory of large deformation stress tensor are symmetrical,But obviously if rotational deformation is added,the stress tensor should be asymmetric.In addition,there are many strain measurement methods,and the geometric meaning and configuration of various strains are not uniform,which brings inconvenience to both engineering and academic.Therefore,it is necessary to find a strain measurement with obvious geometric meaning to achieve an accurate description of the deformation field.Therefore,a new large deformation measurement method is proposed in this paper,and a set of large deformation measurement and analysis device is designed around this method.This paper first introduces the description of deformation by continuum mechanics theory and generalized linear elasticity theory,and discusses their existing problems.Therefore,in order to perfect the description of deformation,this paper proposes a new large deformation measurement method including rotational deformation.This method not only adds the description of rotation to the original theory,but also adopts a more reasonable strain measurement method and considers the asymmetry of stress.The deformation description method is as follows: Using the polar decomposition theorem,the deformation gradient is decomposed to obtain the elongation tensor and the orthogonal tensor.Logarithmic strain and Angle tensor can be obtained by taking the logarithm of the two,and the curvature can be calculated by the gradient operation of the diagonal tensor.In order to emphasize the necessity of the new theory for the description of rotational deformation,several examples of the size effect of the rotational deformation of elastic bodies are introduced.It is shown that considering the rotational deformation can solve some problems difficult to be solved by the original theory under small deformation.In order to further verify the theory,it is necessary to accurately measure the full-field strain of deformed body.Firstly,several strain measurement methods are compared,and the non-contact measurement method is selected.Drawing on the principle and technology of digital image correlation(DIC)method,this paper designed and built a set of large deformation measurement device based on monocular vision digital image,and elaborated the design index of the device,as well as the specific structure and working mechanism of each module.Since hyperelastic materials are prone to large deformation,the device measures around them.Considering that rubber material is a kind of material that is easy to obtain,three kinds of tensile measurements are carried out on rubber with the constructed device in this paper,and the displacement field of rubber material at the marking point in the large deformation experiment is obtained.The feasibility of the device is verified by the first test,and the rationality of the logarithmic strain measurement method is further illustrated.The subsequent tests combined with the data,analyzed the tensile and rotational deformation of the line element in the deformation state,obtained the strain and curvature of the rubber specimen in the large deformation state,and improved the measurement of the large deformation. |
