A new unified arc-length method for damage mechanics problems

The numerical solution of continuum damage mechanics (CDM) problems suffers from convergence-related challenges during the material softening stage, and consequently existing iterative solvers are subject to a trade-off between computational expense and solution accuracy. In this work, we present a...

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Vydáno v:Computational mechanics Ročník 74; číslo 6; s. 1197 - 1228
Hlavní autoři: Saji, Roshan Philip, Pantidis, Panos, Mobasher, Mostafa E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024
Springer
Springer Nature B.V
Témata:
Algorithms
Boundary conditions
Classical and Continuum Physics
Computational Science and Engineering
Continuum damage mechanics
Crack initiation
Engineering
Equilibrium
Independent variables
Iterative methods
Mechanical engineering
Mechanics
Methods
Optimization techniques
Original Paper
Solvers
Theoretical and Applied Mechanics
Arc-length
Damage
Material non-linearity
Efficiency
Snap-back
Newton–Raphson
ISSN:0178-7675, 1432-0924
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Shrnutí:The numerical solution of continuum damage mechanics (CDM) problems suffers from convergence-related challenges during the material softening stage, and consequently existing iterative solvers are subject to a trade-off between computational expense and solution accuracy. In this work, we present a novel unified arc-length (UAL) method, and we derive the formulation of the analytical tangent matrix and governing system of equations for both local and non-local gradient damage problems. Unlike existing versions of arc-length solvers that monolithically scale the external force vector, the proposed method treats the latter as an independent variable and determines the position of the system on the equilibrium path based on all the nodal variations of the external force vector. This approach renders the proposed solver substantially more efficient and robust than existing solvers used in CDM problems. We demonstrate the considerable advantages of the proposed algorithm through several benchmark 1D problems with sharp snap-backs and 2D examples under various boundary conditions and loading scenarios. The proposed UAL approach exhibits a superior ability of overcoming critical increments along the equilibrium path. Moreover, in the presented examples, the proposed UAL method is 1–2 orders of magnitude faster than force-controlled arc-length and monolithic Newton–Raphson solvers.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-024-02473-5