Constitutive Parameters Identification Of Heterogeneous Materials Using Virtual Fields Method

Traditional constitutive parameters identification method is the direct method,in which,the electrometry can only collect strain data of the device installation location.Therefore,on the assumption of homogeneity of strain field,all constitutive parameters of complex constitutive model can be identified only through many standard experiments?e.g.,uniaxial tensile test?.With the development of the photometry,full-field measurement?e.g.,Digital image correlation?have provided the possibility to eliminate the assumption of homogeneous strain field,and the inverse identification methods which can deal with heterogeneous strain field data have received more and more attention from the academia,especially of which the Virtual field method?VFM?.The heterogeneity of strain field caused by multiple constitutive parameters of complex constitutive model has been solved by the traditional virtual field method.For heterogeneous materials,the resolution of the heterogeneity of strain field caused by the spatial variation of constitutive parameters needs further improvement of the virtual field method.Owing to the efforts of the researchers,the constitutive parameters identification of heterogeneous material using VFM has a preliminary solution,but there are still two limitations:Firstly,constitutive parameters of one have to be known a priori,then,constitutive parameters of the other can be identified.Secondly,the boundary between different materials must be known.In view of the above limitations,this study selects heterogeneous materials formed by the superposition of two materials as the research object,and takes the plane stress problem of elastic mechanics as an example,and is carried out according to the following contents:?1?Under the condition that constitutive parameters of the two materials are unknown,this study use polynomial and piecewise functions to expand virtual field,and use the special optimized virtual field to choose virtual field automatically.And through the 3-pt bending test,identify all constitutive parameters of the two kinds of material.The weighted relative error does not exceed 1%.At the same time,the reason for the numerical difference in the relative errors of the four constitutive parameters in the constitutive model and the influence of the number of virtual field coefficients on the identification result are analyzed.The weighted relative error of the final identification result of the simulated speckle experiment is 1.14%,which verifies the feasibility and effectiveness of the method.?2?Under the condition that the spatial boundary between two different materials is unknown,Fourier series is used to conduct spatial parameterization of the elastic modulus and trigonometric functions are used to represent the virtual field,then,the spatial distribution of the elastic modulus is identified by uniaxial tensile test.The curve identified after adding noise is basically the same as the curve before adding noise,and the relative error increases by no more than 1%.The relative error of the identification result of the simulated speckle experiment is within 2%,which verifies the feasibility and effectiveness of the method.?3?combining the above methods,when the boundary between the two kinds of different materials is not clear and the constitutive parameters of any material are unknown,firstly,identify the border between two materials through uniaxial tensile test,then,identify all the constitutive parameters of two kinds of material through 3-pt bending test.The results show that even after adding Gaussian white noise with an amplitude of 5×10^-4,the relative error increases but is still less than 2%.At the same time,the weighted relative error of the simulated speckle experiment is 1.33%,which further shows the feasibility and effectiveness of this method in conjunction with the DIC full-field measurement technology in actual experiments.The simulation test results prove the effectiveness of the proposed this identification method for the spatial variation of constitutive parameters of heterogeneous materials,and provide a new idea for the inverse identification method based on heterogeneous strain field data.