ALLDMD Dissipation Energy Analysis by the Method Extended Finite Elements of a 2D Cracked Structure of an Elastic Linear Isotropic Homogeneous Material

Abstract

The analysis of the crack parameters of a material is an important effect for characterizing the state of stress. Nowadays, materials occupy a very necessary place in modern industry for the study of the life of such structure. This article deals numerically the evolution of (ALLDMD) dissipation energy for an initial rectilinear crack of α=0°. Furthermore, the second case study is based on a crack inclined by the orientation angle α=15°, 30°, and 45°. The X-FEM extended finite element method was used. In addition, the linear elastic isotropic homogeneous material was applied. Thus, the 4-node quadratic CPS4R elements were used. The crack is then modeled numerically using the ABAQUS finite element calculation code. Characterization parameters such as ALLDMD dissipation energy and von Mises stress were calculated. In addition, the results obtained concerning the numerical simulation were compared and discussed between the different mesh approximate total size TGA=1, 2 and 3mm. A good correspondence was obtained between the different comparison results concerning the evolution of the Von Mises stress in all the modeling cases of our work.