Algorithms of through calculation for damage processes

Burago N.G., Nikitin I.S.
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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 the unified rheological relationships taking into account the elastic, viscous and plastic properties of materials and describing the loss of the deformation resistance ability with the accumulation of microdamages is presented. It is shown that the mathematical model under consideration provides a continuous dependence of the solution on input parameters (parameters of the material medium, initial and boundary conditions, discretization parameters) with softening of the material.

Explicit and implicit non-matrix algorithms for calculating the evolution of deformation and fracture development are presented. Non-explicit 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. So, 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. Based on the experience of calculations, recommendations are given for modeling the processes of destruction and ensuring the reliability of numerical solutions.

Keywords: destruction, damage, elasticity, viscosity, plasticity, thermodynamics, constitutive relations, softening, grid methods, through calculations
Citation in English: Burago N.G., Nikitin I.S. Algorithms of through calculation for damage processes // Computer Research and Modeling, 2018, vol. 10, no. 5, pp. 645-666
Citation in English: Burago N.G., Nikitin I.S. Algorithms of through calculation for damage processes // Computer Research and Modeling, 2018, vol. 10, no. 5, pp. 645-666
DOI: 10.20537/2076-7633-2018-10-5-645-666
URL: http://crm-en.ics.org.ru/journal/article/2734/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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