Lagrangian analysis method is re-analyzed, which by measuring the physical variables of each Lagrangian positions to analyze the other physical variables of the material, and then the dynamic mechanical properties of materials can be determined. However, the existing Lagragian analysis methods are still inadequate when the strain is known. In this paper, a new Lagrangian analysis method with least squares which combine inverse method and self-consistency examination was proposed. The theoretical accuracy of the method can achieve -order partial derivatives, which along the particle line, are equal to zero ( is the number of particle line). And the method to meet the self-consistency examination, algorithm itself does not cause distortion for the data processing results; its accuracy depends entirely on test accuracy and the amount of test data. A set of concrete under the impact of experimental data were processed with the method, the corresponding particle velocity wave, stress wave, and stress – strain relations of the whole process of loading and unloading were calculated, and thus the strain rate dependent elastic – plastic constitutive characteristics of the concrete is revealed.
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