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Aleksandr Dmitrievich Nikitin http://orcid.org/0000-0002-2916-758X Nikolay G. Burago http://orcid.org/0000-0002-1806-9386 Ilia S. Nikitin http://orcid.org/0000-0003-3499-6910 Boris A. Stratula

Abstract

The paper reviews the existing approaches to calculating the destruction of solids. The main attention is paid to algorithms using a unified approach to the calculation of deformation both for nondestructive and for the destroyed states of the material. The thermodynamic derivation of constitutive relations for solids with elastic, viscous and plastic properties accounting possible destruction is presented. Explicit and implicit non-matrix algorithms for calculating the evolution of deformation and fracture development are presented. Implicit schemes are implemented using iterations of the conjugate gradient method, with the calculation of each iteration exactly coinciding with the calculation of the time step for two-layer explicit schemes. Therefore the solution algorithms are very simple. The results of solving typical problems of destruction of solid deformable bodies for slow (quasistatic) and fast (dynamic) deformation processes are presented. Recommendations are given for modeling the processes of destruction and ensuring the reliability of numerical solutions.

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Section
SI: Russian mechanics contributions for Structural Integrity

How to Cite

Nikitin, A. D., Burago, N. G., Nikitin, I. S. and Stratula, B. A. (2019) “Algorithms for calculation damage processes”, Frattura ed Integrità Strutturale, 13(49), pp. 212-224. doi: 10.3221/IGF-ESIS.49.22.