Numerical methods and multi-scale modeling for phase-field fracture - With applications in linear elastic and poro-elastic media
Doctoral thesis, 2023
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
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
fracture
multiphysics
finite element
multiscale
desiccation
solvers
fracking
phase-field
solution techniques
Virtual Development Laboratory, Chalmers
Opponent: Prof. Laura De Lorenzis, Dep. of Mechanical and Process Eng., ETH Zürich, Switzerland
Author
Ritukesh Bharali
Chalmers, Industrial and Materials Science, Material and Computational Mechanics
The need for computer models to predict fracture
Fracture prediction through computer models is a crucial pursuit in various fields, from material science to structural engineering and biomechanics. Imagine you're trying to understand whether your apartment would survive an earthquake, how a bridge might respond to heavy loads, or how the oil and natural gas powering your vehicle is extracted from deep under the ground – these models provide invaluable insights.
At its core, fracture prediction involves simulating the behaviour of materials or structures when subjected to different forces, pressures, impacts, or environmental effects. Materials differ in their composition. For instance, the rocks and soil that need to be fractured to extract oil and natural gas comprise of grains, water and air, in varying proportions. Therefore, computer models predicting fracture are required to include as much detail as possible about the underlying material. To simulate a real-world scenario, computer models utilize complex mathematical methods and simulation techniques to predict how cracks or fractures might initiate or propagate within a material. In this thesis, the focus lies on developing these methods such that computational power is used in an efficient way.
Why is this so important? Well, for starters, it enhances safety. In the extraction of oil and natural gas, one is able to predict if the fractures would lead to groundwater contamination. In industries like aerospace, automotive, or construction, the prediction of fracture patterns would help engineers design safer and more durable components. By understanding how materials break under stress, they can create stronger, more resilient structures that can withstand various conditions. For instance, you would be able to know whether your apartment would survive an earthquake.
Moreover, computer models can save time and resources. Instead of relying solely on physical prototypes and experiments, which can be time-consuming and costly, computer models allow researchers to simulate numerous scenarios rapidly. This accelerates the design process and facilitates the identification of potential weaknesses before the actual production and usage of materials and structures.
Fracture prediction through computer models is a crucial pursuit in various fields, from material science to structural engineering and biomechanics. Imagine you're trying to understand whether your apartment would survive an earthquake, how a bridge might respond to heavy loads, or how the oil and natural gas powering your vehicle is extracted from deep under the ground – these models provide invaluable insights.
At its core, fracture prediction involves simulating the behaviour of materials or structures when subjected to different forces, pressures, impacts, or environmental effects. Materials differ in their composition. For instance, the rocks and soil that need to be fractured to extract oil and natural gas comprise of grains, water and air, in varying proportions. Therefore, computer models predicting fracture are required to include as much detail as possible about the underlying material. To simulate a real-world scenario, computer models utilize complex mathematical methods and simulation techniques to predict how cracks or fractures might initiate or propagate within a material. In this thesis, the focus lies on developing these methods such that computational power is used in an efficient way.
Why is this so important? Well, for starters, it enhances safety. In the extraction of oil and natural gas, one is able to predict if the fractures would lead to groundwater contamination. In industries like aerospace, automotive, or construction, the prediction of fracture patterns would help engineers design safer and more durable components. By understanding how materials break under stress, they can create stronger, more resilient structures that can withstand various conditions. For instance, you would be able to know whether your apartment would survive an earthquake.
Moreover, computer models can save time and resources. Instead of relying solely on physical prototypes and experiments, which can be time-consuming and costly, computer models allow researchers to simulate numerous scenarios rapidly. This accelerates the design process and facilitates the identification of potential weaknesses before the actual production and usage of materials and structures.
Modeling and calculation based homogenization of a porous medium with fluid transport in a network of propagating fractures
Swedish Research Council (VR) (2017-05192), 2018-01-01 -- 2022-12-31.
Modeling of desiccation cracking in soils due to climate change
Formas (2018-01249), 2019-01-01 -- 2022-12-31.
Subject Categories
Applied Mechanics
Fluid Mechanics and Acoustics
Geosciences, Multidisciplinary
ISBN
978-91-7905-975-0
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5441
Publisher
Chalmers
Virtual Development Laboratory, Chalmers
Opponent: Prof. Laura De Lorenzis, Dep. of Mechanical and Process Eng., ETH Zürich, Switzerland
Related datasets
falcon - A C++ Finite Element Analysis software based on the Jem-Jive library [dataset]
URI: https://github.com/ritukeshbharali/falcon