Ravindra Duddu, Sam John Vallier Sutcliffe, Wangcheng Zhang, William Coombs
Modelling cliff collapse and run-out with the material point method
This paper proposes a method for modelling the combined collapse and large deformation run-out of cliffs using the Material Point Method (MPM). An explicit dynamic MPM formulation is derived with features key for simulating ductile–brittle fracture dynamics over varying timescales. An isotropic non-local plastic-damage scheme is presented that may be used to simulate crack initiation and growth leading to brittle collapse of a cliff. The scheme is applicable to both quasi-static and dynamic cases. The behaviour of the proposed plastic-damage model is compared to experimental data utilising numerical shear-box tests. A numerical case study is carried out on a real-world chalk cliff to show the model’s applicability to rock-slope mechanics in both failure initiation and post-failure run-out.
Fracture & Damage Modeling
Ravindra Duddu, Abhinav Gupta, Philip Luke Karuthedath, Rajib Chowdhury
A generalized framework towards continuity and computational efficiency in topology optimization using multi-patch isogeometric methods
This study proposes a generalized framework to establish and maintain a comprehensive continuity and provide computational efficiency for solving topology optimization (TO) problems in structural mechanics by utilizing the technique of multi-patch isogeometric analysis (IGA). The continuity of the solution inside a patch is realized by taking the benefit of IGA to easily discretize the C0 and C1 continuous weak form of second and fourth-order differential equations respectively. The continuity of the solution between patches for fourth-order systems is established through a strong C1 coupling at patch boundaries, where new basis functions are constructed as a linear combination of existing C0 bases at the patch interfaces. A continuous density function (CDF) is then established by linearly combining the design vector and the isogeometric basis functions, providing a continuous smooth distribution of material for the TO in the design domain. Furthermore, an adaptive mesh refinement (AMR) approach is incorporated into the methodology to enhance computational efficiency by significantly reducing the degree’s-of-freedom and CPU time required to achieve the converged solution. Collectively, these integrated methodologies establish a robust and versatile framework capable of addressing a wide spectrum of structural mechanics problems, as demonstrated through numerical examples, with a particular emphasis on the challenges posed by fourth-order systems. The results highlight the continuity-preserving nature of the approach and achieve up to 90 % reduction in degrees of freedom and elements, underscoring its computational efficiency and accuracy.
Computational Mechanics
Ravindra Duddu, Huadong Gao, Lili Ju, Xiao Li
A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion
In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.
Corrosion & Multiphysics Modeling
Ravindra Duddu, Meghana Ranganathan, Alexander A. Robel, Alex Huth
Glacier damage evolution over ice flow timescales
The rate of mass loss from the Antarctic and Greenland ice sheets is controlled in large part by the processes of ice flow and ice fracture. Studies have shown these processes to be coupled: the development of fractured zones weakens the structural integrity of the ice, reducing ice viscosity and enabling more rapid flow. This coupling may have significant implications for the stability of ice shelves and the rate of flow from grounded ice. However, there are challenges with modeling this process, in large part due to the discrepancy in timescales of fracture and flow processes and to uncertainty about the construction of the damage evolution model. This leads to uncertainty about how fracture processes can affect ice viscosity and, therefore, projections of future ice mass loss. Here, we develop a damage evolution model that represents fracture initiation and propagation over ice flow timescales, with the goal of representing solely the effect of damage on flow behavior. We then apply this model to quantify the effect of damage on projections of glacier response to climate forcing. We use the MISMIP+ benchmark glacier configuration with the experiment Ice1r, which represents grounding line retreat due to basal melt forcing. In this model configuration, we find that damage can enhance mass loss from grounded and floating ice by ∼ 13 %–29 % in 100 years. The enhancement of mass loss due to damage is approximately of the same order as increasing the basal melt rate by 50 %. We further show the dependence of these results on uncertain model parameters. These results emphasize the importance of further studying the multiscale processes of damage initiation and growth from an experimental and observational standpoint and of incorporating this coupling into large-scale ice sheet models.
Glaciology & Ice-Sheet Modeling
Ravindra Duddu, Theo Clayton, Tim Hageman, Emilio M. Pañeda
Modeling ice cliff stability using a new Mohr-Coulomb-based phase field fracture model
Full thickness crevasses can transport water from the glacier surface to the bedrock where high water pressures can open kilometre-long cracks along the basal interface, which can accelerate glacier flow. We present a first computational modelling study that describes time-dependent fracture propagation in an idealised glacier causing rapid supraglacial lake drainage. A novel two-scale numerical method is developed to capture the elastic and viscoelastic deformations of ice along with crevasse propagation. The fluid-conserving thermo-hydro-mechanical model incorporates turbulent fluid flow and accounts for melting/refreezing in fractures. Applying this model to observational data from a 2008 rapid lake drainage event indicates that viscous deformation exerts a much stronger control on hydrofracture propagation compared to thermal effects. This finding contradicts the conventional assumption that elastic deformation is adequate to describe fracture propagation in glaciers over short timescales (minutes to several hours) and instead demonstrates that viscous deformation must be considered to reproduce observations of lake drainage rate and local ice surface elevation change. As supraglacial lakes continue expanding inland and as Greenland Ice Sheet temperatures become warmer than -8 degree C, our results suggest rapid lake drainages are likely to occur without refreezing, which has implications for the rate of sea level rise.
Glaciology & Ice-Sheet Modeling
Ravindra Duddu, Tim Hageman, Jessica Mejia, Emilio M. Pañeda
Ice viscosity governs hydraulic fracture that causes rapid drainage of supraglacial lakes
Iceberg calving at glacier termini results in mass loss from ice sheets, but the associated fracture mechanics is often poorly represented using simplistic (empirical or elementary mechanics-based) failure criteria. Here, we propose an advanced Mohr-Coulomb failure criterion that drives cracking based on the visco-elastic stress state in ice. This criterion is implemented in a phase field fracture framework, and finite element simulations are conducted to determine the critical conditions that can trigger ice cliff collapse. Results demonstrate that fast-moving glaciers with negligible basal friction are prone to tensile failure causing crevasse propagation far away from the ice front; whilst slow-moving glaciers with significant basal friction are likely to exhibit shear failure near the ice front. Results also indicate that seawater pressure plays a major role in modulating cliff failure. For land terminating glaciers, full thickness cliff failure is observed if the glacier exceeds a critical height, dependent on cohesive strength τc (H≈120 m for τc=0.5 MPa). For marine-terminating glaciers, ice cliff failure occurs if a critical glacier free-board (H−hw) is exceeded, with ice slumping only observed above the ocean-water height; for τc=0.5 MPa, the model-predicted critical free-board is H−hw≈215 m, which is in good agreement with field observations. While the critical free-board height is larger than that predicted by some previous models, we cannot conclude that marine ice cliff instability is less likely because we do not include other failure processes such as hydrofracture of basal crevasses and plastic necking.
Glaciology & Ice-Sheet Modeling