Isaac Vikram Chenchiah

Vita

1. Lecturer in Applied Mathematics, School of Mathematics, University of Bristol (Since April 2006)

2. Postdoctoral Associate, Max Planck Institute for Mathematics in the Sciences with Stefan Müller (January 2004 - March 2006)

3. Ph.D., California Institute of Technology (January 2004)

   1. Ph.D. Thesis: Energy-minimizing microstructures in multiphase elastic solids

   2. Doctoral advisor: Kaushik Bhattacharya

4. M.S., California Institute of Technology (June 1999)

5. B.Tech., Indian Institute of Technology, Madras (July 1998)

Research Interests

Mathematical problems in solid mechanics, molecular mechanics, materials science and soft-matter physics:

1. Mechanics of the growth of biological materials .

2. Molecular biomechanics, for example, of viruses and DNA.

3. Continuum biomechanics, for example, of plants and skeletal systems.

4. Statics and evolution of microstructures in solids that arise due to phase transitions and damage.

5. Defect motion on surfaces.

These typically involve methods and tools from analysis (especially calculus of variations and partial differential equations) but I have also used some algebraic results (from convex polytope theory, group theory, invariant theory and algebraic geometry).

Current Research

1. Microstructure in multi-phase solids has long been a research interest of mine. Recently Anja Schloemerkemper and I have shown that Monoclinic-I martensite is capable of exhibiting T₃ microstructures (which are infinite-rank laminates). Moreover we show that there is an open set of points for which this is possible. This is the first "real-world" example (we are aware of) of these theoretically much-investigated microstructures. We also show that there are in fact two kinds of Monoclinic-I martensites, group-theoretically indistinguishable but with different convex polytope structures, and thus also different semi-convex hulls/envelopes. Curiously all known Monoclinic-I martensites lie in one of these groups. This work is part of a larger programme to understand the zero-energy states of monoclinic-I martensite and is funded by the Royal Society.

2. Claire Grierson, Tanniemola Liverpool and I are seeking to understand plant uprooting. Antoni Matyjaszkiewicz joined us for three months in summer 2011 as part of his MRes in Complexity Sciences. Will Russell continued some of his work in an undergraduate project in 2011-12. Joshua Scurll joins us this summer.

3. Christopher Larsen and I have recently extended his earlier work with Adriana Garroni on damage from scalar to elastic materials capable of exhibiting multiple damage modes. This research was funded by the Leverhulme Trust.

4. While I'm interested in several aspects of the mechanics of growth of biological materials I am currently focused on investigating continuum limits of discrete growing systems. Some preliminary results were presented at Banff in October 2010. I've had many valuable discussions with Patrick Shipman on these and related matters. Pardeep Bahra joined me over summer 2011 for an undergraduate research project on this topic.

5. Jonathan Robbins and I are interested in vortex motion on curved surfaces. Chiara Liverani joined us for four months in Spring 2011. Nick Jones joins us for six weeks this summer.

6. Tanniemola Liverpool and I working with Neil Burton to help veterinary surgeons correct cranial cruciate ligament failure in dogs.

7. Thomas Blesgen and I have recently made progress on a problem that has interested me for many years: Coarsening in superalloys, which are used in turbine blades. The microstructure of these materials evolves through a elasticity-influenced diffusion. We have recently proposed a two-scale model that attempts to rigourously include both elasticity and diffusion.

8. Paul Weaver's group and I are designing and analysing composite structures that are inspired by the behaviour of biological structures, especially in exploiting subtle interplay between geometry and mechanics. We have prototyped a bistable cylindrical lattice structure that mimics the behaviour of the virus bacteriophage T₄.

Talks

1. 6 November 2012
   Surprises in monoclinic-I martensite
   Institute for Complex Engineered Systems, Carnegie Institute of Technology, Carnegie Mellon University
   
   
2. 8 November 2012
   Quasi-Static Brittle Damage Evolution with Multiple Damaged Elastic States
   Center for Nonlinear Analysis, Department of Mathematical Sciences, Carnegie Mellon University
   
   

Visitors

1. March 2013
   Kaushik Dayal
   Department of Civil and Environmental Engineering, Carnegie Mellon University
   
   

Research Funding

1. 2012-13
   University of Bristol EPSRC Building Global Engagements in Research
   Stress-induced phase fronts and networks in polycrystals
   (with Samantha Daly)

2. 2012-13
   University of Bristol EPSRC Building Global Engagements in Research
   Objective structures
   (with Kaushik Dayal)

3. 2012
   London Mathematical Society Scheme 2 Grant
   To host Friedemann Brock

4. 2011
   ACCIS Innovation Seed Corn Funding
   Bi-stability: From nature to engineering
   (with Paul Weaver, Alberto Pirrera, Xavier Lachenal, Stephen Daynes, Advanced Composites Centre for Innovation and Science (ACCIS) and Department of Aerospace Engineering)

5. 2010-11
   University of Bristol EPSRC Cross-Disciplinary Feasibility Account
   Engineering the substrate elasticity for stem cells differentiation in cartilage tissue: Experimental and mathematical modelling study
   (with Wael Kafienah, School of Cellular and Molecular Medicine and Sameer Rahatekar, Aerospace Engineering)

6. 2010
   The Nuffield Foundation Undergraduate Research Bursary
   Analysis of asymmetric metric and inner product spaces
   (with Rosemary Drummond)

7. 2009-12
   Royal Society International Joint Project
   Symmetrised rank-one convex hull of monoclinic martensite
   (with Anja Schloemerkemper, Institute for Mathematics, University of Würzburg)

   Formulas for Shapes, an article MaxPlanckResearch (the magazine of the Max Planck Society) by Peter Hergersberg has a non-technical introduction to this project and the general area.

8. 2009-10
   Leverhulme Trust Visiting Professorship for Christopher Larsen, Department of Mathematical Sciences, Worcester Polytechnic Institute
   (with Valeriy Slastikov)

Publications

In Preparation

1. Threshold-based quasi-static brittle damage evolution with multiple damaged elastic states
   (with Christopher Larsen)

2. A multistable composite braided tubular structure for morphing applications
   (with Paul Weaver, Alberto Pirrera, Xavier Lachenal, Stephen Daynes)

Preprints

1. An energy-deformation decomposition for morphoelasticity
   (with Patrick Shipman, under review)

2. Cahn-Hilliard equations incorporating elasticity: Analysis and comparison to experiments
   (with Thomas Blesgen, under review, preprint available on request)

Journal Publications

1. Non-laminate microstructures in monoclinic-I martensite (with Mathematica files)
   (with Anja Schloemerkemper)
   Archive for Rational Mechanics and Analysis (Published online)
   (Preprint)

2. A generalised Cahn-Hilliard equation incorporating geometrically linear elasticity
   (with Thomas Blesgen)
   Interfaces and Free Boundaries, 13(1), 1-27, 2011

3. Gradient flows in asymmetric metric spaces
   (with Marc Oliver Rieger and Johannes Zimmer)
   Nonlinear Analysis: Theory, Methods & Applications, 71(11), 5820-34, Dec. 2009
   MathSciNet review
   (Preprint)

4. The relaxation of two-well energies with possibly unequal moduli
   (with Kaushik Bhattacharya)
   Archive for Rational Mechanics and Analysis, 187(3), 409-479, Mar. 2008
   MathSciNet review
   (Preprint)

5. Examples of nonlinear homogenization in plane strain involving degenerate energies. I. Plane strain
   (with Kaushik Bhattacharya)
   Proceedings of the Royal Society A - Mathematical, Physical and Engineering Sciences, 461(2063), 3681 - 3703, Nov. 2005
   (Preprint)

6. Towards the efficient computation of effective properties of microstructured materials
   (with Carl-Friedrich Kreiner and Johannes Zimmer)
   Comptes Rendus Mecanique, 332(3), 169-174, Mar. 2004
   (Preprint)

7. A two variant thermomechanical model for shape memory alloys
   (with Srinivasan M. Sivakumar)
   Mechanics Research Communications, 26(3), 301-307, May-June 1999

Edited Volumes

1. Multiscale and variational methods in material science and quantum theory of solids
   (with Isabelle Catto, Ivan Veselić and Johannes Zimmer)
   Oberwolfach Reports 4(1), 371-416, 2007

Organisation

1. I am the applied mathematics representative for the university's Predictive Life Sciences research theme and a member of the University's "Materials Steering Group".

2. I am involved with the Bristol Centre for Complexity Sciences.

3. I am the Bristol representative on the organising committee of the South West Regional PDE Winter Schools (1, 2).

Teaching

Postgraduate Teaching (for Bristol Centre for Complexity Sciences)

1. 2007-12: Nonlinear Dynamics (with Tanniemola Liverpool)

Undergraduate Teaching

1. 2009-12: MATH M/36203 Applied Analysis (with Valeriy Slastikov)

2. 2008-10: MATH 20901 Multivariable Calculus

3. 2006-10: MATH 20900 Calculus 2

Postgraduate Projects (2010-12)

1. Multi-stable structures: From biology to engineering (for ACCIS, with Paul Weaver and Alberto Pirrera)

2. Uprooting plants (for Bristol Centre for Complexity Sciences, with Claire Grierson and Tanniemola Liverpool)

3. Vortex motion on Riemannian manifolds (with Jonathan Robbins)

Undergraduate Projects (2006-12)

1. Analysis on asymmetric metric spaces
2. Elasticity of helices (with Valeriy Slastikov)
3. Geodesics on surfaces
4. Hyperbolic geometry and hyperbolic convexity
5. Isoperimetric problems
6. Knottedness and elasticity of DNA (with Jonathan Robbins)
7. Microstructure formation in martensitic solids
8. Optimal transport systems
9. Seismology
10. Topology and elasticity of DNA (with Valeriy Slastikov)
11. Uprooting plants (with Tanniemola Liverpool)

Email: Isaac.Chenchiah, Phone: +44 117 928 7984, Room 2.15 Updated: Monday 25 June 2012