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Biosketch
Non-linear Constitutive Modeling
v I develop robust constitutive models (relations between stress and strain) for various nonlinear soft materials, including rubber, foam, biological tissues, the brain, arteries, etc. Our modeling often involves advanced tensor analysis, sophisticated experiments, as well as machine learning.Mechanics of Residually Stressed Materials
v Residual stress has created a new arena in continuum mechanics. Almost all existing frameworks of continuum mechanics rely on the assumption that the material remains stress-free, before any load is applied. However, residual stress is unavoidably present in almost all real-life mechanical and biological structures, affecting the constitutive relations, mechanical behavior, failure, instabilities, buckling, wrinkling, etc. We are investigating these influences of residual stress on engineering and biological systems, which starts with identifying the appropriate constitutive relations in presence of residual stress.v Our approach to accurately and exactly determine the constitutive relation for residually stressed materials, is not straight-forward, or trivial. It involves inverse analysis of the existing continuum mechanics theories. We have developed the first constitutive relations for residually stressed materials, exhibiting(a) non-linear viscoelasticity,
(c) implicit elasticity, and
(e) We also developed the first failure model for residually stressed soft materials. A generalization of this failure model will be published soon.
(f) Here is a paper on new approaches of changing reference configuration-- to identify the stress-free material from the mechanical behavior of the residually stressed body.
v We are planning to create YouTube videos to explain our residual stress theory to the general audiences. The present publications are accessible via google scholar or researchgate. We will soon report finite element investigations of wrinkling, buckling, bulging etc., using new models of residual stress developed by our team. We have also determined a von Kármán theory for residually stressed plates, and currently pursuing the finite element analysis.Continuum Mechanics
v I am actively working on implicit elasticity, non-linear viscoelasticity, and developing non-linear, or weakly non-linear plate theories. - Research
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