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

Eugeniai V. Feklistova, Artur I. Mugatarov, Valeriy E. Wildemann

Author details

Eugeniai V. Feklistova
Perm National Research Polytechnic University, Perm, Russian Federation
Artur I. Mugatarov
Perm National Research Polytechnic University, Perm, Russian Federation
Valeriy E. Wildemann
Perm National Research Polytechnic University, Perm, Russian Federation

https://doi.org/10.15593/perm.mech/2024.4.07

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 condi- tions 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 ele- ments. 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 dam- age 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 charac- teristics of structural elements into account.

Keywords

fracturefinite element methodnumerical modelingstress concentratorstrength properties distribution.

ЧИСЛЕННОЕ ИССЛЕДОВАНИЕ ПРОЦЕССОВ РАЗРУШЕНИЯ ДЕФОРМИРУЕМЫХ ТЕЛ С КОНЦЕНТРАТОРАМИ НАПРЯЖЕНИЙ С УЧЕТОМ СТАТИСТИЧЕСКОГО РАСПРЕДЕЛЕНИЯ ПРОЧНОСТИ СТРУКТУРНЫХ ЭЛЕМЕНТОВ

Решение проблемы обеспечения прочности и безопасности ответственных конструкций требует изучения их механического поведения не только в условиях нормальной эксплуатации, но и при реализации процессов разрушения на структурном уровне. Для численного моделиро- вания процессов разрушения применяются различные методы, одним из широко используемых является подход, связанный с редуцированием жесткости конечных элементов при выполнении критерия разрушения. При данном подходе важным является учет неоднородности распределе- ния прочностных характеристик структурных элементов в объеме тела. В работе проведено численное исследование процессов разрушения тел с концентратора- ми напряжений при учете стохастичности распределения прочностных характеристик структур- ных элементов. Приведена постановка краевой задачи деформирования и разрушения и алго- ритм ее решения методом конечных элементов. На примере решения типовой задачи изучено влияние геометрии концентратора напряжений и характерного размера зоны повреждения на поведение тела на макроуровне, его несущую способность и кинетику процесса накопления повреждений. Отмечена реализация закритической стадии деформирования на макроуровне при высоком значении разброса прочностных характеристик. Выявлено наличие порогового значения дисперсии распределения пределов прочности структурных элементов, по достижении которого концентратор напряжений перестает влиять на процесс разрушения. Отмечена существенная зависимость результатов численного моделирования от характерного размера зоны разрушения и целесообразность подбора данного параметра путем сопоставления полученных результатов с экспериментальными данными. Сделан вывод о рациональности учета неоднородности рас- пределения прочностных характеристик структурных элементов при изучении процессов разру- шения конструкций.

Ключевые слова

разрушениеметод конечных элементовчисленное моделированиеконцентратор напряженийраспределение прочностных характеристик.

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Published: 25 November 2024
Issue date: 25 November 2024
Issue: No. 4 (2024)

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

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