Program
The research program
How mechanics, multiscale simulation, design and error control became one argument about trustworthy computation.
There is one question underneath all of it: what must a model keep in order to be trusted, and where is it worth spending computation?
That question has two halves, and the work alternates between them. The mechanics half asks which physics controls a failure: matrix cracking against interface debonding against particle fracture, contact against adhesion, a material reorganizing under an applied field. The computation half asks what an approximation costs you: not error in the abstract, but error in the quantity a decision depends on.
Neither half comes first. Mechanics supplies the regimes where approximation breaks down; error control decides what has to be resolved or measured before a conclusion is accepted.
How it developed
- 2010–2016
Formulation and coarse graining
Monolithic compressible fluid–structure interaction at IISc with Chandrashekhar S. Jog, where the nonlinear continuum mechanics and finite element method came from, then doctoral work with Kaushik Dayal on coarse graining long-range electrostatic interactions. The habit set here, mechanics then mathematics then implementation, runs through everything after it.
- 2016–2019
Nonlocal fracture foundations
With Robert Lipton at LSU: well-posedness of nonlocal models, convergence to their local limits, discretization error, state-based damage. Finite-element and later nodal-FE work tied that mathematical structure to solvers that run.
- 2019–2023
Prediction under model and data uncertainty
With the late J. Tinsley Oden at the Oden Institute: Bayesian calibration, model-error estimation, goal-oriented methods, optimal experimental design, and mixed-dimensional tumor models. The turn here is the one that matters: computational savings have to preserve the quantity you are actually asking about.
- 2021–
Fracture-capable particles, reusable software
PeriDEM turns the nonlocal-fracture work into granular mechanics: particles that deform and break, with contact resolved at the peridynamic discretization. The JOSS paper establishes that capability as software; the NSF ERI award supports building the criterion for spending high fidelity selectively rather than resolving every particle identically.
- 2023–
Reliable surrogates, and design
Bayesian residual correction, then a single-author general corrector operator, a neural-operator review, and a book chapter, all developing residual-correction and error-control strategies for repeated-query workflows. MatTO and the hMSM work connect that to material and structural design; adhesion extends the mechanics question.
Where it stands now
The research index- Mechanics and design of field-responsive materials How electric and magnetic fields interact with microstructure, interfaces and geometry, and how those interactions determine actuation, adhesion and degradation in soft composites.
- Fracture and failure in heterogeneous materials How matrix cracking, interface debonding, particle fracture and contact interactions compete to control strength, toughness, localization and residual load capacity.
- Reliable scientific AI for mechanics, discovery and design How residuals, error estimates and targeted high-fidelity solves can determine when a reduced or learned model is accurate enough for inference, optimization or design.