Krishna Kannan
Professor
Mechanical Engineering
Krishna Kannan
Research Areas
Dept of Applied Mechanics and Biomedical Engineering
People
Phd Scholars
Aravind.K - Ph.D. scholar
Sadagopan T.S Ph.D. scholar
Reddipaga Mani - Ph.D. scholar
Rahul Kumar - Ph.D. scholar
MS Scholars
Yagnik Vaidya - MS Scholars
Tammisetti Hari Sai Chaitanya - MS Scholars
Mrunal Kanti Das - MS Scholars
Research
Constitutive modelling of passive arterial tissues
1. Constitutive modelling of passive arterial tissues:
Arterial tissues are collagen fiber-reinforced materials. However, modelling the collagen fibers’ inability to support compression is essential. A popular approach is to use a switching criterion – but this could lead to issues such as discontinuous stresses, dual stretch state, etc. This work develops a novel anisotropic invariant that automatically excludes the contribution from fibers under pure compression. When the fibers are dispersed, the contribution from compressed fibers is discounted appropriately. In addition to precluding the need for a switch criterion, the proposed constitutive relations show a significantly improved ability to emulate the biaxial mechanical data for normal and diseased arterial tissues.
Figure 1. Schematic of the constituents of an artery. (Source- Lauralee Sherwood, 2016)
Constitutive modelling of active arterial tissues
The ability of the vascular smooth muscle cells (VSMCs) to contract in response to chemical and mechanical stimuli necessitates the need for a chemo-mechanical constitutive relation. The concentration of cytoplasmic Ca2+ regulates the contractile state of VSMCs. In this work, the chemical kinetics, governed by the Hai-Murphy relations, are coupled to the mechanical response in a proper thermodynamic setting. The deformation tensor for the cell contraction is averaged according to the cell dispersion, thereby accounting for the observed level of anisotropy. The framework can emulate the observed phenomena like 1) dispersion of the VSMCs, 2) increased hysteresis with contraction, and 3) the presence of an optimal stretch.
Figure 2. Schematic of contraction of VSMCs. (Source- Lacolley et. al, 2017)
Growth & Remodelling of arterial tissues
Growth means an increase in mass achieved locally through increased number or size (hypertrophy) of cells. Remodelling means a change in structure, whether it is intracellular, cellular, or extracellular. This change is achieved by reorganizing existing constituents, such as altering their orientation, cross-linking, or synthesizing new constituents with a different organization. Remodelling may or may not alter the mass density, but it does impact characteristics like stiffness and material symmetry. The primary objective of this work is to develop and apply a constraint mixture model that incorporates the mass transport of various constituents from the endothelial layer to gain insights into the underlying mechanisms of arterial remodelling in hypertension. The primary objective of this work is to develop and apply a constraint mixture model that incorporates the mass transport of various constituents from the endothelial layer to gain insights into the underlying mechanisms of arterial remodelling in hypertension.
Figure 3. Schematic of growth in an abdominal aortic aneurysm. (Source- John Hallett et. al, 2009)
Growth & Remodelling of arterial tissues
Growth means an increase in mass achieved locally through increased number or size (hypertrophy) of cells. Remodelling means a change in structure, whether it is intracellular, cellular, or extracellular. This change is achieved by reorganizing existing constituents, such as altering their orientation, cross-linking, or synthesizing new constituents with a different organization. Remodelling may or may not alter the mass density, but it does impact characteristics like stiffness and material symmetry. The primary objective of this work is to develop and apply a constraint mixture model that incorporates the mass transport of various constituents from the endothelial layer to gain insights into the underlying mechanisms of arterial remodelling in hypertension. The primary objective of this work is to develop and apply a constraint mixture model that incorporates the mass transport of various constituents from the endothelial layer to gain insights into the underlying mechanisms of arterial remodelling in hypertension.
Figure 4. Human brain tissue (Source- Budday et. al, 2017)
Constitutive modelling of myocardial tissue:
The heart is a complex organ that relies on the mechanical properties of the myocardium to maintain normal function. The myocardium is a surrounding muscular tissue composed of a network of collagen and muscle fibers that interact to provide the necessary mechanical properties for cardiac function. To accurately model the anisotropic behavior of the myocardium, it is important to incorporate microstructural information into the constitutive relations. Notwithstanding the dissipative mechanics, the interactions with the surrounding tissue and fluids, the active response, and the growth & remodelling aspects, we take a modest approach and treat the myocardial tissue as an elastic material. Unlike collagen fibers, muscle fibers can withstand some degree of compressive stress due to their relatively large diameter and crosslinking with collagen fibers. The accuracy of the proposed model has important implications for understanding the biomechanics of the heart and developing new treatments for cardiac diseases.
Figure 5. Top- Schematic of the human heart highlighting the myocardium. Bottom- Muscle fibers can sustain some compression, unlike collagen fibers. (Source- Sommer et. al, 2015 & Holzapfel and Ogden, 2009.
Constitutive modelling of liquid crystal elastomers:
Liquid crystal elastomers (LCE) are polymeric materials cross-linked with liquid crystal mesogens. They combine the elastic properties of rubbers and the orientational properties of liquid crystals. This combination results in an entirely new phenomena well beyond liquid crystals of elastomers. There are different types of LCEs such as nematic, cholesteric and smectic etc., and they are responsive to different stimuli like temperature, light, electric and magnetic fields. Nematic elastomers are of particular interest which are LCEs with rod-shaped mesogens. Experiments suggest that the LCEs exhibit anisotropic non-linear viscoelastic behaviour. In the current body of research literature pertaining to LCEs only a few models incorporate viscoelasticity. Even the ones which incorporate viscoelasticity also treat the order parameter like a material parameter determined from experiments. However, one can intuitively expect changes in order parameter due to the deformation since there is a coupling between orientational order and network deformation. Our study attempts to address this issue by considering a mesogen distribution that actively depends on the viscoelastic response of the polymer chains in a thermodynamically consistent manner. Another feature of our framework is that we do not consider a director theory which is commonly used. Instead, we adopt a methodology like order tensor-type theories originally proposed by de Gennes. We incorporate ideas of a structure tensor-based theory typically used in the modelling of biological tissues.
Figure 5. Top- Schematic of the human heart highlighting the myocardium. Bottom- Muscle fibers can sustain some compression, unlike collagen fibers. (Source- Sommer et. al, 2015 & Holzapfel and Ogden, 2009.
Projects
to be added
Facilities
- High performance workstations for performing computations
- Biaxial testing device (to be procured- a part of CSBM facilities)
- SAXS (to be procured- a part of CSBM facilities)
Collaboration
- Dr. Seungik Baek, Associate Professor in the Department of Mechanical Engineering, Head of Cardiovascular and Tissue Mechanics Laboratory, Michigan State University,Michigan, USA.
Publication
- A semi-analytical inverse method to obtain the hyperelastic potential using experimental data V Kulwant, K Arvind, D Prasad, P Sreejith, KV Mohankumar, K Kannan Journal of the Mechanics and Physics of Solids 181, 105431 2023
- A new viscoelastic model for human brain tissue using Lode invariants based rate-type thermodynamic framework D Prasad, P Sreejith, K Kannan Applications in Engineering Science 15, 100130 2023
- An efficient mode-of-deformation dependent rate-type constitutive relation for multi-modal cyclic loading of elastomers K Srikanth, P Sreejith, K Arvind, K Kannan, M Pandey International Journal of Plasticity 163, 103517 2023
- A thermodynamic framework for additive manufacturing of crystallizing polymers, Part II: Simulation of the printing of a stent P Sreejith, K Srikanth, K Kannan, KR Rajagopal International Journal of Engineering Science 184, 103790 2023
- A thermodynamic framework for the additive manufacturing of crystallizing polymers. Part I: A theory that accounts for phase change, shrinkage, warpage and residual stress P Sreejith, K Kannan, KR Rajagopal International Journal of Engineering Science 183, 103789 2023
- On the explicit dynamics implementation and validation of partitioned rate-type constitutive relation for dampers K Srikanth, M Pandey, K Kannan Mechanics of Advanced Materials and Structures 30 (2), 284-302 2023
- A new stabilised curvature computation method using the level set function M Sellam, K Kannan, S Natarajan International Journal of Hydromechatronics 6 (4), 325-341 2023
Social Impact
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Gallery
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