AKASH KUMAR BEHERA

Publications

A phase-field model for thermo-mechanical fracture

In this article, we propose a thermodynamically consistent phase-field model for thermo-mechanical fracture and provide an open-source implementation of the proposed model using a recently developed finite element toolbox, Gridap in Julia. Here, we have derived the balance equations for the thermo-mechanical fracture by invoking the virtual power principle and determined the constitutive relations for the thermodynamic fluxes based on the satisfaction of the thermodynamic laws. Our proposed formulation provides an equation of temperature evolution that can easily accommodate dissipative effects such as viscous damping. We provide very compact and user-friendly open-source codes for implementing the proposed model using Gridap in Julia that requires very low memory usage and gives a high degree of flexibility to the users in defining weak forms of the governing partial differential equations (PDEs). We have validated the proposed model and its implementation against such standard results available in the literature as crack propagation in the cruciform shape material, single edge notched plate, bi-material beam, and a quenching test.

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A phase-field model for electro-mechanical fracture with an open-source implementation of it using Gridap in Julia

In this paper, we propose a phase-field model for electro-mechanical fracture in brittle materials and provide an open-source implementation of the proposed model using a newly developed finite element (FE) toolbox, Gridap in Julia. Here, we have considered electric potential as an additional kinematic descriptor along with the displacement and phase-field variable. Using the virtual power principle, we have derived force balances for the electro-mechanical forces and a force balance associated with the damage. To incorporate the strong electro-mechanical coupling effect into the model, we have considered the Helmholtz free energy as a function of the electric field vector, strain tensor, phase-field variable, and the gradient of the phase-field variable. The proposed model ensures that the constitutive relations of the thermodynamic fluxes are on the satisfaction of the thermodynamic laws and can readily accommodate dissipative energy effects whenever needed. The proposed model provides complex crack paths as a solution to the governing partial differential equations (PDEs), and thus bypasses the need for re-meshing, enrichment of FE shape functions, and an explicit tracking of the crack surfaces. The use of Gridap makes the FE implementation of the proposed model exceedingly compact and user-friendly requiring very low memory usage and providing a high degree of flexibility to the users in defining weak forms of the governing PDEs. We have validated the proposed model and its implementation against a compact tension test on a single edge notched plate and a set of three-point bending tests on a notched beam made of lead zirconium titanate (PZT)-4 piezoelectric ceramics.

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Combined diffused material interface and hybrid phase-field model for brittle fracture in heterogeneous composites

In this article, we propose a novel approach for modeling brittle fracture in heterogeneous composites using a combined diffused material interface method and a hybrid phase-field model (PFM). We have used the diffused material interface method to derive analytical expressions for the regularized material properties across the material interfaces that are treated as an input to the PFM for the simulation of brittle fractures in composites. The use of diffused material interface method regularizes the material properties in such a way that one can avoid the discontinuity in stress across the material interface and thus bypass the requirement of explicit tracking of material interfaces for finite element implementation of the hybrid PFM. We have implemented the proposed combined model using a recently developed open-source finite element toolbox, Gridap in Julia. We have considered tests on a single circular fiber inclusion under tension, a bi-material rectangular plate under tension, single square inclusion under tensile loading, a notched composite beam with a central notch under symmetric three-point bending, and a rectangular plate with multiple fibers under tensile loading to show how the proposed combined model can be used to simulate brittle fracture in composites.

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Thermodynamically consistent volumetric–deviatoric decomposition-based phase-field model for thermo-electro-mechanical fracture

Using a volumetric–deviatoric decomposition of strain, we propose a novel phase-field model for thermo-electro-mechanical fracture and provide an open-source finite element implementation of the proposed model. Considering displacement, electric potential, temperature field, and phase-field variable, we have obtained the governing partial differential equations (PDEs), by utilizing the virtual power principle. We have obtained the constitutive relations for the necessary thermodynamic fluxes on satisfying the first and second laws of thermodynamics. The proposed model can accommodate any dissipative effect, such as viscous damping, whenever necessary, in a thermodynamically consistent manner. We have developed open-source finite element codes for the proposed model using the Gridap package in Julia. Here, we have used the proposed model for fracture simulation in transversely isotropic material and functionally graded material for compact tension and three-point bending tests. We have considered variations in thermal and electrical loading conditions and investigated the corresponding changes in the structural responses. For the functionally graded specimens, we have also considered the variation in the material property gradation directions, along with the thermal and electrical boundary conditions to evaluate their effect on the structural responses of specimens.

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Two different micro-polar phase-field models for brittle fracture and their open-source finite element implementation

Realizing the limitations of classical phase-field fracture models and the need for the development of non-local phase-field models that can capture the experimentally observed size effects in brittle and quasi-brittle materials, we propose thermodynamically consistent volumetric-deviatoric and spectral decomposition-based phase-field models (PFMs) for brittle fracture in micro-polar continua. For developing the proposed models, we have considered the micro-rotation as an additional kinematic descriptor, and have derived the balance equations by invoking the virtual power principle. On satisfying the thermodynamic laws, we have determined the constitutive relations for the thermodynamic fluxes and demonstrated that any dissipative effect can easily be incorporated into the proposed models. We have provided an open-source finite element (FE) implementation of the micro-polar PFMs using Gridap in Julia. The implementation includes various benchmark problems to illustrate how the responses in a specimen change with the variations in micro-polar material parameters. Through a series of numerical examples with different values of micro-polar material parameters, we have showcased both the capabilities and limitations of the proposed volumetric-deviatoric and spectral decomposition-based micro-polar PFMs.

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A residual stress-dependent mixed-mode phase-field model: Application to assessing the role of tailored residual stresses on the mechanical performance of ceramic laminates

Ceramics offer several attractive properties of industrial relevance, e.g. high strength and hardness, low thermal conductivity, and chemical inertness in critical environments. There is thus interest among researchers to improve the fracture toughness of ceramics, which is generally low and considered a major drawback. Numerous experimental studies in the literature report on the enhancement of mechanical performance of ceramic laminates, especially fracture toughness, by tailoring the residual stress, resulting in crack deflection or bifurcation. However, there is a dearth of computational models that can reliably predict the crack path and accurately quantify the improved fracture toughness. In this article, we propose a residual stress-dependent mixed-mode phase-field model within a small deformation set-up. The proposed model is efficient in including any energy dissipation effect in a consistent manner. The model can be exploited as a tool to study the effect of tailored residual stresses on the fracture toughness of ceramic laminates. We have validated our proposal by reproducing the results for a few problems that require the incorporation of residual stresses within the formulation.

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A phase-field length scale insensitive mode-dependent fracture model for brittle failure

This article presents a consistent phase-field length scale insensitive mode-dependent fracture model for brittle failure by proposing mode-factor dependent degradation functions that incorporate the effect of two additional fracture parameters, namely the mode-II critical energy release rate and mode-II fracture strength, on the overall mechanical response. Using the proposed mode-factor dependent degradation functions and employing a recently proposed modified strain decomposition scheme, we provide analytical expressions for the mode-I and mode-II fracture strengths corresponding to the mode-dependent parts of the elastic energy. Adopting a modified Benzeggagh–Kenane (B–K) criteria, we propose mode-dependent driving forces by deriving expressions for the critical energy release rate corresponding to individual fracture modes. The proposed model provides a consistent coupling between the different fracture modes and can thus predict fracture for all possible mode-mixity ratios. A parametric study is carried out to unravel the effect of mixed-mode fracture parameters on the mechanical response of isotropic materials by considering a few representative numerical examples. The numerical results from the proposed model show an excellent agreement with experimental results reported in the literature.

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Experience

Education

Skills

• Julia
• Matlab
• Mathematica
• Python
• Abaqus
• Ansys
• COMSOL
• STAAD.pro
• MS Office
• LaTeX

Interests

I have a deep passion for travel and exploring new places, which fuels my love for hiking and outdoor adventures. Badminton is one of my favorite ways to stay active, and I find joy in both the challenge and camaraderie of the sport. Music is a constant companion in my life, providing inspiration and relaxation in equal measure.

I’m an avid reader, with a particular fondness for books that transport me to other worlds, especially in the sci-fi and fantasy genres. My love for storytelling extends to the screen, where I enjoy immersing myself in sci-fi and fantasy movies and television shows.In addition to these interests, I’m also an aspiring chef, always eager to experiment with new recipes and flavors in the kitchen. Cooking is a creative outlet for me, and I find it both rewarding and enjoyable.

Achievements & Certifications

• Presented on "Anisotropic phase-field modeling of brittle fracture under thermo-mechanical loading" at 9th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2024, Lisbob, Portugal.
• Presented on "A finite-deformation phase-field model for fracture in ceramic laminates under residual stress field" at 9th International Congress on Computational Mechanics and Simulation, IIT Gandhinagar.
• Presented on "A thermodynamically consistent phase-field model for electro-mechanical fracture" 8th International Congress on Computational Mechanics and Simulation, IIT Indore.
• Completed short-term certificate-based course on Bridge design and construction organized by Indian Concrete Institute (ICI), Chennai (11th and 12th October 2018).
• Presented a seminar on "Utilizing GFRG Panels in Construction" during the M. Tech program at NIT Calicut.