Projects and key publications

• A unified theory for fracture

The project started with a goal to develop a unified theory of nucleation and propagation of fracture in elastomers that can describe and predict some famed, but heretofore unexplained, experiments in natural and silicone rubber (related to a phenomenon called cavitation).

This work provided unexpected motivation to revisit the nucleation of fracture in brittle materials at large, not just elastomers, and led to a general model for nucleation and propagation of brittle fracture. More recently, it has provided motivation to revisit ductile fracture and cast it also in the same generalized framework.

Key publications:

1.  Fracture and healing of elastomers: A phase-transition theory and numerical implementation 

•  Aditya Kumar, Gilles A Francfort, Oscar Lopez-Pamies

•  Journal of Mechanics and Physics of Solids, 2018 (pdf)

2.  Revisiting nucleation in the phase-field approach to brittle fracture

•  Aditya Kumar, Blaise Bourdin, Gilles A Francfort, Oscar Lopez-Pamies

•  Journal of Mechanics and Physics of Solids, 2020 (pdf)

3.  The poker-chip experiments of Gent and Lindley (1959) explained 

•  Aditya Kumar, Oscar Lopez-Pamies

•  Journal of Mechanics and Physics of Solids, 2021 (pdf)

4.  The strength of the Brazilian fracture test  

•  Aditya Kumar, Yangyuanchen Liu, John Dolbow, Oscar Lopez-Pamies

•  Journal of Mechanics and Physics of Solids, 2023 (pdf)

5.  Emergence of tension-compression asymmetry in the complete phase-field approach to brittle fracture

•  Chang Liu, Aditya Kumar

•  Under Review (Preprint)

• Mechanics of growth, remodeling and aging in biological tissues

The mechanics of how biological tissues respond to mechanical forces and adapt, grow and evolve is not well understood. The goal is to constitutively define these evolutions in a suitable mechanics framework. Along with colleague Prof. Arash Yavari, we have proposed a new variational approach to explain of remodeling of collagen fibers in soft tissues. More recently, we are working on understanding arterial growth with the same variational framework.

Key publications:

1.  Nonlinear mechanics of remodeling

•  Aditya Kumar, Arash Yavari

•  Journal of Mechanics and Physics of Solids, 2023 (pdf)

• Viscoelastic behavior of elastomeric composites

The goal is to describe the macroscopic viscoelastic behavior of polymeric composites directly in terms of the behavior of its microscopic constituents. As a first step, we developed a two-potential framework for nonlinear viscoelasticity to unify various constitutive models in the literature. A model coming out of this framework is now widely used. The viscoelasticity framework is also being used now to investigate fracture in ultra-soft materials like hydrogels and biological tissues, supported by NSF.

Key publications:

1.  On the two-potential constitutive modelling of rubber viscoelastic materials 

•  Aditya Kumar, Oscar Lopez-Pamies

•  Comptes Rendus Mecanique, 2016 (pdf)

2.  The nonlinear viscoelastic response of suspensions of rigid inclusions in rubber: I — Gaussian rubber with constant viscosity 

•  Kamalendu Ghosh, Bhavesh Shrimali, Aditya Kumar, Oscar Lopez-Pamies

•  Journal of Mechanics and Physics of Solids, 2021 (pdf)

• Frontal polymerization and applications to 3D printing and patterning

Front polymerization is an energy- and time-efficient way of curing polymers and polymeric composites that has opened up new avenues into advanced manufacturing. The goal of this project is to develop rigorous non-linear multi-physics models and supporting theory that can aid the manufacturing process.

Key publications:

1.  Surface pattern formation induced by oscillatory loading of frontally polymerized gels

•  Aditya Kumar, Leon M Dean, Mostafa Yourdkhani, Allen Guo, Cole BenVau, Nancy R Sottos, Philippe H Geubelle

•  Journal of Mechanics and Physics of Solids, 2022 (pdf)

2.  A thermo-chemo-mechanical model for the material extrusion of frontally polymerizing thermoset polymers. 

•  Aditya Kumar, Michael J Zakoworotny, Jia En Aw, Javier Balta, Sameh H Tawfick, Nancy R Sottos, Philippe H Geubelle

•  Additive Manufacturing, 2024 (pdf)