Simulation of Fracture in Deformable Bodies with Stress Concentrators Taking into Account the Statistical Distribution of Ultimate Strength in Structural Elements

To solve the problem of ensuring the strength and safety of critical structures, it is required to study their mechanical behavior at the structural level not only under normal operating conditions but also under destruction. Various methods are used to simulate destruction processes; one of them implies the reduction of the stiffness of finite elements when fulfilling the destruction criterion. When using this approach, it is important to take the heterogeneous distribution of strength characteristics of structural elements in the body’s volume into account. The paper presents a numerical study of the destruction processes of bodies with stress concentrators taking into account the stochasticity of the distribution of strength characteristics of the structural elements. We present the statement of the boundary value problem of deformation and destruction, also its solution algorithm using the finite element method. By solving a typical problem, we study the influence of the stress concentrator geometry and the characteristic size of the damage zone on the behavior of the body at the macrolevel, its bearing capacity and the kinetics of the damage accumulation process. The implementation of the postcritical stage of deformation at the macrolevel with a wide range of strength characteristics is noted. There is a threshold value of the variance of the distribution of the strength limits of structural elements, upon which the stress concentrator ceases to affect the destruction process. A significant dependence of the simulation results on the characteristic size of the destruction zone and the expediency of selecting this parameter by comparing the obtained results with experimental data are noted. When studying structural destructions it is important to take heterogeneity of the distribution of strength characteristics of structural elements into account.