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 |
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01.12.2024
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| ISSN: | 0178-7675, 1432-0924 |
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| Abstract | 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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| AbstractList | 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. |
| Audience | Academic |
| Author | Mobasher, Mostafa E. Saji, Roshan Philip Pantidis, Panos |
| Author_xml | – sequence: 1 givenname: Roshan Philip surname: Saji fullname: Saji, Roshan Philip organization: Mechanical Engineering Department, Tandon School of Engineering, New York University, Mechanical Engineering Department, New York University Abu Dhabi – sequence: 2 givenname: Panos surname: Pantidis fullname: Pantidis, Panos organization: Civil and Urban Engineering Department, New York University Abu Dhabi – sequence: 3 givenname: Mostafa E. orcidid: 0000-0002-5108-4713 surname: Mobasher fullname: Mobasher, Mostafa E. email: mostafa.mobasher@nyu.edu organization: Mechanical Engineering Department, Tandon School of Engineering, New York University, Civil and Urban Engineering Department, New York University Abu Dhabi |
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| Keywords | Arc-length Damage Material non-linearity Efficiency Snap-back Newton–Raphson |
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| SubjectTerms | 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 |
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| Title | A new unified arc-length method for damage mechanics problems |
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