Lagrangian analysis method based on least square

Lagrangian analysis method is a method with which the physical variables of each Lagrangian positions are measured to analyze the other physical variables of a material, and then the dynamic mechanical properties of the material can be determined. However, the existing Lagragian analysis method is still inadequate with the strain of a material known. Here, a new Lagrangian analysis method with least square combining the inverse method and self-consistency examination was proposed. The theoretical accuracy of the method could achieve M-order partial derivatives ∂Mσ/∂hM≡0 along the particle line (M is the number of particle lines). And the method satisified the self-consistency examination, the algorithm itself did not cause the distortion of the data processing results, its accuracy depended entirely on the test accuracy and the amount of test data. Test data for a set of concrete under action of impact were processed with the method, the corresponding particle velocity wave, stress wave, and stress-strain curves of the whole process of loading and unloading were calculated, and it was revealed that the elastic-plastic constitutive characteristics of the concrete is related to its strain rate.