| 1. |
- Bharali, Ritukesh, 1991, et al.
(author)
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A micromorphic phase-field model for brittle and quasi-brittle fracture
- 2024
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In: Computational Mechanics. - 1432-0924 .- 0178-7675. ; 73:3, s. 579-598
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Journal article (peer-reviewed)abstract
- In this manuscript, a robust and variationally consistent technique is proposed for local treatment of the phase-field fracture irreversibility. This technique involves an extension of the phase-field fracture energy functional through a micromorphic approach. Consequently, the phase-field is transformed into a local variable, while a micromorphic variable regularizes the problem. The local nature of the phase-field variable enables an easier implementation of its irreversibility using a pointwise 'max' with system level precision. Unlike the popular history variable approach, which also enforces local fracture irreversibility, the micromorphic approach yields a variationally consistent framework. The efficacy of the micromorphic approach in phase-field fracture modelling is demonstrated in this work with numerical experiments on benchmark brittle and quasi-brittle fracture problems in linear elastic media. Furthermore, the extensibility of the micromorphic phase-field fracture model toward smultiphysics problems is demonstrated. To that end, a theoretical extension is carried out for modelling hydraulic fracture, and relevant numerical experiments exhibiting crack merging are presented. The source code as well as the data set accompanying this work would be made available on GitHub (https://github.com/ritukeshbharali/ falcon).
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| 2. |
- Bharali, Ritukesh, 1991, et al.
(author)
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A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation
- 2022
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In: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 394
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Journal article (peer-reviewed)abstract
- The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton–Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adopts a fracture energy-based arc-length method and an adaptive under-relaxation scheme. The arc-length method enables the simulation to overcome critical points (snap-back, snap-through instabilities) during the loading of a specimen. The use of an under-relaxation scheme stabilizes the solver by preventing the divergence due to an ill-behaving stiffness matrix. The efficiency of the proposed solver is further amplified with an adaptive mesh refinement scheme based on PHT-splines within the framework of isogeometric analysis. The numerical experiments presented in the manuscript demonstrate the efficacy of the solver. All the codes and data-sets accompanying this work will be made available on GitHub (https://github.com/rbharali/IGAFrac).
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| 3. |
- Bharali, Ritukesh, 1991, et al.
(author)
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Computational aspects of the weak micro‐periodicity saddle point problem
- 2021
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In: Proceedings in Applied Mathematics and Mechanics. - : Wiley. - 1617-7061. ; 20:1
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Journal article (peer-reviewed)abstract
- The finite element implementation of the weak micro-periodicity problem in computational homogenisation requires special preconditioning techniques owing to the saddle point formulation. The saddle point nature arises from enforcing periodicity constraints using Lagrange multipliers. This manuscript addresses the solution techniques and preconditioning options for the aforementioned problem in a monolithic setting. Furthermore, an alternative technique is proposed, based on a linear multi-point constraints strategy. The latter approach eliminates the Lagrange multiplier Degrees of Freedom (DOFs), thereby preventing the break-down of conventional incomplete LU (ILU) variants and multi-grid method based preconditioners.
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| 4. |
- Bharali, Ritukesh, 1991
(author)
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Computational homogenisation and solution strategies for phase-field fracture
- 2021
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Licentiate thesis (other academic/artistic)abstract
- The computational modelling of fracture not only provides a deep insight into the underlying mechanisms that trigger a fracture but also offers information on the post-fracture behaviour (e.g., residual strength) of engineering materials and structures. In this context, the phase-field model for fracture is a popular approach, due to its ability to operate on fixed meshes without the need for explicit tracking of the fracture path, and the straight-forward handling of complex fracture topology. Nevertheless, the model does have its set of computational challenges viz., non-convexity of the energy functional, variational inequality due to fracture irreversibility, and the need for extremely fine meshes to resolve the fracture zone. In the first part of this thesis, two novel methods are proposed to tackle the fracture irreversibility, (i) a micromorphic approach that results in local irreversibile evolution of the phase-field, and (ii) a slack variable approach that replaces the fracture irreversibility inequality constraint with an equivalent equality constraint. Benchmark problems are solved using a monolithic Newton-Raphson solution technique to demonstrate the efficiency of both methods. The second aspect addressed in this thesis concerns multi-scale problems. In such problems, features such as the micro-cracks are extremely small (several orders of magnitude) compared to the structure itself. Resolving these features may result in a prohibitively computationally expensive problem. In order to address this issue, a computational homogenisation framework for the phase-field fracture is developed. The framework allows the computational of macro (engineering)-scale quantities using different homogenising (averaging) approaches over a microstructure. It is demonstrated that, based on the choice of the homogenisation approaches, local and non-local macro-scale material behaviour is obtained.
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| 5. |
- Bharali, Ritukesh, 1991, et al.
(author)
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Computational homogenisation of phase-field fracture
- 2021
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In: European Journal of Mechanics, A/Solids. - : Elsevier BV. - 0997-7538. ; 88
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Journal article (peer-reviewed)abstract
- In this manuscript, the computational homogenisation of phase-field fractures is addressed. To this end, a variationally consistent two-scale phase-field fracture framework is developed, which formulates the coupled momentum balance and phase-field evolution equations at the macro-scale as well as at the Representative Volume Element (RVE) scale. The phase-field variable represent fractures at the RVE scale, however, at the macro-scale, it is treated as an auxiliary variable. The latter interpretation follows from the homogenisation of the phase-field through volume or a surface-average. For either homogenisation choices, the set of macro-scale and sub-scale equations, and the pertinent macro-homogeneity satisfying boundary conditions are established. As a special case, the concept of selective homogenisation is introduced, where the phase-field is chosen to live only in the RVE domain, thereby eliminating the macro-scale phase-field evolution equation. Numerical experiments demonstrate the local macro-scale material behaviour of the selective homogenisation based two-scale phase-field fracture model, while its non-selective counterpart yields a non-local macro-scale material behaviour.
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| 6. |
- Bharali, Ritukesh, 1991, et al.
(author)
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Multi-scale phase-field fracture model: Selective homogenization and macroscopic bounds
- 2021
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Conference paper (other academic/artistic)abstract
- In this work, a multi-scale phase-field model for fracture is developed from the fully resolved phasefield model using the variationally consistent homogenization technique. The concept of selective homogenization is applied to the phase-field variable. Allowing the phase-field variable to live only on the sub-scale yields a conventional local damage model at the macro-scale, as the phase-field becomes an internal variable.
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| 7. |
- Bharali, Ritukesh, 1991
(author)
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Numerical methods and multi-scale modeling for phase-field fracture - With applications in linear elastic and poro-elastic media
- 2023
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Doctoral thesis (other academic/artistic)abstract
- This thesis presents novel numerical methods and a multi-scale modelling framework tailored for advancing the phase-field fracture model with applications in linear elastic and poro-elastic media. In the realm of the numerical methods, the focus lies on devising computationally efficient and robust monolithic solution techniques. These techniques aim to solve non-convex fracture problems, while ensuring the irreversibility of fracture in a variationally consistent way. The multi-scale modelling framework seeks to incorporate microstructural heterogeneities (such as material constituents, voids, and defects) and fractures to derive engineering-scale mechanical responses. Within the range of monolithic solution techniques proposed in this thesis, the fracture energy-based arc-length method and the Hessian scaling method stand out for their demonstrated computational efficiency and robustness on benchmark mechanical problems. Furthermore, to ensure the irreversibility of fracture in a variational context, a micromorphic variant of the phase-field fracture model is presented. The micromorphic variant not only allows a point-wise treatment of the fracture irreversibility constraint, but also demonstrates compatibility with the aforementioned arc-length method. Based on the computational efficiency and robustness proven by the arc-length method, this thesis presents a time-step computing variant of the method for hydraulic fracturing problems. Furthermore, in the context of multiphysics fracture problems, a novel energy functional is proposed for soil desiccation cracking. The energy functional incorporates the part of the water pressure propagating into the solid skeleton in the fracture driving energy. Numerical experiments that utilize the integration point Hessian scaling method showcase the model’s ability to capture experimentally observed phenomenon. Finally, a hierarchical multi-scale phase-field fracture framework is developed using the variationally consistent homogenization technique. The framework allows the selective upscaling of micro-structural information to the engineering scale. The numerical multi-scale ‘finite element squared’ (FE2 ) experiment conducted in this thesis successfully demonstrates the solvability of the engineering and fine-scale governing equations in a nested sequence. The culmination of the novel numerical methods and the multi-scale framework represents a significant step towards robust, computationally efficient, and accurate modelling of fractures in engineering materials and structures
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