Research

Some naturally occurring materials such as piezoelectric ceramics and manufactured composites such magnetorheological elastomers (MREs) and electro-active polymers (EAPs) exhibit coupling of mechanical effects with electromagnetic fields. MREs and EAPs are typically made with a soft elastomer base that is capable of undergoing large deformation with a nonlinear coupling of fields. We develop constitutive models to better understand and predict the response of such materials at various length scales. We also develop computational techniques to uncover the exciting new underlying physical phenomena due to this coupling.

Representative papers:

• Variational principles of nonlinear magnetoelastostatics and their correspondences (open access) (2021)
  Basant Lal Sharma, Prashant Saxena
  Mathematics and Mechanics of solids, doi: 10.1177/1081286520975808 [arxiv]

• Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure (2015)
  Prashant Saxena, Jean-Paul Pelteret, Paul Steinmann
  European Journal of Mechanics - A/Solids, vol. 50, pp. 132-151 [pdf]

• Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers (2014)
  Prashant Saxena, Mokarram Hossain, Paul Steinmann
  Proceedings of the Royal Society A, vol. 470, 20140082

• On rate-dependent dissipation effects in electro-elasticity (2014)
  Prashant Saxena, Duc Khoi Vu, Paul Steinmann
  International Journal of Non-Linear Mechanics, vol. 62, pp. 1-11 [pdf]

Soft tissues are extremely complex heterogeneous materials that can undertake significant deformation under moderate loads. We have developed models to study their anisotropic nonlinear response and applied them to analyse pattern formation due to biological growth and the resulting mechanical stresses.

Representative papers:

• Growth induced instabilities in a circular hyperelastic plate (2021)
  Sumit Mehta, Gangadharan Raju, Prashant Saxena
  International Journal of Solids and Structures, doi: 10.1016/j.ijsolstr.2021.03.013 [arxiv]

• Buckling of chiral rods due to coupled axial and rotational growth (2021)
  Satya Prakash Pradhan, Prashant Saxena
  Mathematics and Mechanics of Solids, doi: 10.1177/1081286521999704 [arxiv]

Large deformation is often accompanied by material or structural instabilities. Traditionally instability was associated with material failure. However, with soft solids, instabilities can be exploited as a design feature to create next generation actuators. Furthermore, multi-physics coupling gives multiple buckling parameters resulting in an entire phase-space of critical points.

Representative papers:

• Coupled electro-elastic deformation and instabilities of a toroidal membrane (2021)
  Zhaowei Liu, Andrew McBride, Basant Lal Sharma, Paul Steinmann, Prashant Saxena
  Journal of the Mechanics and Physics of Solids, 151: 104221 [arxiv]

• Buckling of chiral rods due to coupled axial and rotational growth (2021)
  Satya Prakash Pradhan, Prashant Saxena
  Mathematics and Mechanics of Solids, doi: 10.1177/1081286521999704 [arxiv]

• Growth induced instabilities in a circular hyperelastic plate (2021)
  Sumit Mehta, Gangadharan Raju, Prashant Saxena
  International Journal of Solids and Structures, doi: 10.1016/j.ijsolstr.2021.03.013 [arxiv]

• Magnetoelastic deformation of a circular membrane: Wrinkling and limit point instabilities (2019)
  P. Saxena, N. H. Reddy, S. P. Pradhan
  International Journal of Non-Linear Mechanics, vol. 116, pp. 250-261 [pdf]

Rod, plate, shell, and membrane models can very accurately approximate a large variety of naturally occurring and artificially manufactured structures. Even after decades of work in this area, computation-friendly models of slender structures accounting for nonlinear multi-physics deformation are not readily available. Furthermore, slender structures are very susceptible to structural instabilities resulting in interesting mechanics phenomena. Our aim is to both develop such models for new complex soft solids and to study the new physics that is possible by performing accurate and efficient computations.

Representative papers:

• Buckling of chiral rods due to coupled axial and rotational growth (2021)
  Satya Prakash Pradhan, Prashant Saxena
  Mathematics and Mechanics of Solids, doi: 10.1177/1081286521999704 [arxiv]

• Growth induced instabilities in a circular hyperelastic plate (2021)
  Sumit Mehta, Gangadharan Raju, Prashant Saxena
  International Journal of Solids and Structures, doi: 10.1016/j.ijsolstr.2021.03.013 [arxiv]

• Coupled electro-elastic deformation and instabilities of a toroidal membrane (2021)
  Zhaowei Liu, Andrew McBride, Basant Lal Sharma, Paul Steinmann, Prashant Saxena
  Journal of the Mechanics and Physics of Solids, doi: 10.1016/j.jmps.2020.104221 [arxiv]

• Assessment of an Isogeometric Approach with Catmull-Clark Subdivision Surfaces using the Laplace-Beltrami Problems (open access) (2020)
  Zhaowei Liu, Andrew McBride, Prashant Saxena, Paul Steinmann
  Computational Mechanics, vol. 66, pp. 851-876 [pdf]

The highly nonlinear differential equations derived from the above research themes are solved using bespoke numerical methods. Our recent work includes development of methods to solve PDEs with C1 continuity on shells and to solve ODEs with rapidly varying solutions.

Representative papers:

• Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces (2021)
  Zhaowei Liu, Andrew McBride, Prashant Saxena, Luca Heltai, Yilin Qu, Paul Steinmann [arxiv]

• Assessment of an Isogeometric Approach with Catmull-Clark Subdivision Surfaces using the Laplace-Beltrami Problems (open access) (2020)
  Zhaowei Liu, Andrew McBride, Prashant Saxena, Paul Steinmann
  Computational Mechanics, vol. 66, pp. 851-876 [pdf]

• Growth induced instabilities in a circular hyperelastic plate (2021)
  Sumit Mehta, Gangadharan Raju, Prashant Saxena
  International Journal of Solids and Structures, doi: 10.1016/j.ijsolstr.2021.03.013 [arxiv]

• Instabilities in the axisymmetric magnetoelastic deformation of a cylindrical membrane (2018)
  Narravula Harshavardhan Reddy, Prashant Saxena
  International Journal of Solids and Structures, vol. 136-137, pp. 203-219 [pdf]