Earlier Lectures (2021)

Adventures in nonlinear structural mechanics (Lecture 21 - August 2021)

Speaker: Dr. Ramsharan Rangarajan (Indian Institute of Science, India)

Abstract of the lecture For many engineers, structural mechanics stops at Euler buckling. For others, it starts after. Indeed, an emerging paradigm in mechanics considers geometric nonlinearity and buckling phenomena as features to be exploited rather than as modes of failure. The principles underlying this emerging field enjoy two distinctive features- dependence on aspect ratios rather than absolute length scales and near independence from the material constitution. Hence, these principles promise to be useful, say, in examining the mechanics of graphene nanostructures, designing flexible electronic devices, or even deploying structures in space. At the talk, I will discuss two examples from my group’s work on studying the mechanics of slender elastic structures. The first concerns how flexible structures can function like robots.

The second example concerns various aspects of modeling and experimenting elastic ribbons. I hope that these examples will highlight the multi-faceted nature of challenges in the field as well as opportunities for designing novel engineering applications.

Stability analysis of highly deformable electroelastic and magnetoelastic structures (Lecture 20 - July 2021)

Speaker: Dr. Prashant Saxena (University of Glasgow, UK)

Abstract of the lecture In recent years, highly deformable electroelastic and magnetoelastic composite materials have been developed that can undergo significant deformation in the presence of electromagnetic fields. Large deformation in structures are often accompanied by material and structural instabilities that have traditionally been a source of structural failure. In these novel soft materials, “reversible” instabilities can be exploited as a design feature to develop multifunctional components.

In this presentation, I will first discuss the mathematical models currently used to describe nonlinear electro-mechanical and magneto-mechanical coupling in soft elastomers. I will then discuss the fundamental techniques to model instabilities based on variational principles and on the tension field theory. Finally, I will present some recent results on modelling limit point, wrinkling, and symmetry-breaking instabilities in the inflation of thin electroelastic and magnetoelastic membranes.

Related publications

Reddy, N. H., & Saxena, P. (2017). “Limit points in the free inflation of a magnetoelastic toroidal membrane,” International Journal of Non-Linear Mechanics, 95, 248–263.
Reddy, N. H., & Saxena, P. (2018). “Instabilities in the axisymmetric magnetoelastic deformation of a cylindrical membrane,” International Journal of Solids and Structures, 136–137, 203–219.
Liu, Z., McBride, A.T., Sharma, B.L., Steinmann, P., Saxena, P. (2021) “Coupled electro-elastic deformation and instabilities of a toroidal membrane”, Journal of the Mechanics and Physics of Solids, doi: 10.1016/j.jmps.2020.104221

All publications are open to access at this webpage.

Biological growth: Mathematical modeling and FEM implementation (Lecture 19 - July 2021)

Speaker: Dr. Meisam Soleimani (Leibniz University Hannover, Germany)

Abstract of the lecture Growth phenomena usually occur in living tissues under different mechanobiological stimuli. In this lecture, a mathematical model for the growth driven by nutrient diffusion is extensively presented in a “continuum mechanics” framework. Besides, the practical considerations for FEM implementation in the context of a multiphysics ANSYS User Element are discussed. Several numerical examples are presented to demonstrate the applicability and versatility of the proposed model for reproducing biofilm growth in confined geometries; overgrowth of the arteries walls as a result of inflammation; tumor growth within the brain in the avascular stage; and bone ingrowth in the vicinity of a rough implant surface. It will be shown that all these processes share the same spirit from a “modeling” point of view.

Related publications

M. Soleimani, N. Muthyala, M. Marino, P. Wriggers, “A novel stress-induced anisotropic growth model driven by nutrient diffusion: Theory, FEM implementation and applications in bio-mechanical problems,” Journal of the Mechanics and Physics of Solids, v. 144, pp. 104097 (2020)
M. Soleimani, “Finite strain visco-elastic growth driven by nutrient diffusion: theory, FEM implementation and an application to the biofilm growth,” Computational Mechanics, v. 64, pp. 1289–1301 (2019)

Scalable asynchronous computing method for solving PDE’s at extreme scale (Lecture 18 - June 2021)

Speaker: Dr. Konduri Aditya (Indian Institute of Science, India)

Abstract of the lecture Recent advances in computing technology have made numerical simulations an indispensable research tool in understanding fluid flow phenomena in complex conditions at a great detail. Due to the nonlinear nature of the governing Navier-Stokes equations, simulations of high Reynolds number turbulent flows are computationally very expensive and demand extreme levels of parallelism. The current state-of-the-art turbulent flow simulations are routinely being performed on hundreds of thousands of processing elements (PEs). At this extreme scale, communication and synchronization between PEs significantly affect the scalability of solvers. Indeed, communication and data synchronization pose a bottleneck in scalability as simulations advance towards exascale computing.In this talk, we present an overview of a novel approach based on widely used finite-difference schemes in which computations are carried out in an asynchronous fashion, i.e. synchronization of data among processing elements is not enforced and computations proceed regardless of the status of communication. This drastically reduces the CPU idle time and results in much larger computation rates and scalability. We show that while standard schemes are able to remain stable and consistent, their accuracy is significantly reduced. New asynchrony-tolerant schemes, which can maintain accuracy under relaxed synchronization conditions, are introduced. We present computational performance results on homogeneous and heterogeneous architectures. Also, we briefly illustrate the extension of this approach to the discontinuous Galerkin (DG) method.

Computational mechanics for design of energy technologies (Lecture 17 - May 2021)

Speaker: Dr. Saumik Dana

Abstract of the lecture

As with most other sciences, computational mechanics has to reconcile with the reality of the new energy and climate mitigation technologies like enhanced geothermal systems and carbon capture and storage. The intellectual capital built up on solving problems in the defense and aerospace sector in the realm of computational mechanics can be put to good use as guiding protocols for the design of these technologies. The talk will focus on specific concepts in computational geometry and fluid structure interaction to enable the solution of large scale carbon capture problems. The second part of the talk will focus on the leverage of deep learning to resolve fundamental physics to later enable the use of data-driven methods.

Fluid Mechanics as a tool in respiratory disease mitigation (Lecture 16 - Feb 2021)

Speaker: Prof. Saikat Basu

Abstract of the lecture

In this webinar, Prof. Saikat will discuss his long-term research program goals to promote fluid mechanics-based analysis as a planning tool that can be readily accessed by physicians to reach personalized clinical decisions for each patient, especially for pathologies related to flow-based transport. In this talk, he will present his research vision on applying tools from theory and computations to answer specific translational questions arising in clinical therapeutics and mitigation, with the current focus being mostly on respiratory physiology. The next 20-30 years will see great activity in how we can use concepts from mechanics and applied physics to answer open questions in clinical domains, through transdisciplinary collaborations between physicians, engineers, applied mathematicians, and pharmacologists.

Related publications

S Basu, Computational characterization of inhaled droplet transport in the upper airway leading to SARS-CoV-2cinfection. medRxiv: the preprint server for health sciences, Cold Spring Harbor Laboratory Press, October 2020. DOI: https://doi.org/10.1101/2020.07.27.20162362
S Basu, LT Holbrook, K Kudlaty, O Fasanmade, J Wu, A Burke, BW Langworthy, M Mamdani, Z Farzal, WD Bennett, JP Fine, BA Senior, AM Zanation, CS Ebert Jr., A Kimple, B Thorp, DO Frank-Ito, GJM Garcia, and JS Kimbell, Numerical evaluation of spray position for improved nasal drug delivery. Scientific Reports, Volume 10, Article number 10568, 2020

Phase field fatigue fracture (Lecture 15 - Jan 2021)

Speaker: Dr. Fadi Aldakheel

Abstract of the lecture

In this webinar, the phase-field PF approach to fracture is extended to model fatigue failure in the high and low cyclic regime. Fatigue is the primary failure mode for more than 90 % of mechanical failures. It occurs when a structure is subjected to repeated loading at stress levels that are below the yield stress of the material. On the modeling side, a local energy accumulation variable which takes the loading history of a structure into account is introduced within the PF formulation. This is inserted into a fatigue degradation function which degrades the fracture material properties. To this end, only one additional parameter is proposed, that enables the reproduction of main material fatigue features.

Related publications

Aldakheel, F.; Schreiber, C.; Müller, R.; Wriggers, P.: Phase-field modeling of fatigue crack propagation in brittle materials. A part of a new Book submitted to Springer (2021).
Seles, K.; Aldakheel, F.; Tonković, Z.; Sorić, J.; Wriggers, P.: A General Phase-Field Model for Fatigue Failure in Brittle and Ductile Solids. Submitted to Computational Mechanics (minor-revision) (2021).
F.; Schreiber, C.; Müller, Aldakheel, F.: Phase Field Modeling of Fatigue Fracture. A part of a new Book submitted to Springer (2021).
Wriggers, P.; Aldakheel, F.; Lohaus, L.; Heist, M.: Water-induced damage mechanisms of cyclically loaded High-performance concretes. Bauingenieur 95 (4), 126–132 (2020).