RESEARCH

Nonclassical Solid Mechanics

  • Classical elasticity models (Truesdell & Noll) are scale-invariant with no memory across time or length.

  • My research is focused on modeling & simulating constitutive models obtained via relaxation of the assumptions in classical theories.

  • This allows exploring phenomena like nonlocality, hereditariness, surface effects, etc. in the context of structural response.

  • Used in developing equivalent multiscale models for complex structures (see Fig. (c)), designing vibration isolators & tunable waveguides (Mecc.(2021); Wave Mot.,86, 91-109 (2019) ).

  • My research explored and established fractional-order constitutive models for modeling multiscale interactions within solids (see Fig. (a); IJMS, 189, 105992 (2021)).

  • We also analyzed anomalous increase in stiffness at low-dimensions attributed to length-scale effects using strain-gradient and surface elasticity theories (Acta Mech.,229 (9), 3813-3831 (2018)).


Reference Publications:

  1. S Sidhardh, S Patnaik, F Semperlotti. Thermodynamics of fractional-order nonlocal continua and its application to the thermoelastic response of beams. European Journal of Mechanics-A/Solids 88, 104238 (2021). Preprint available on Arxiv.

  2. S Sidhardh, MC Ray. Inclusion problem for a generalized strain gradient elastic continuum. Acta Mechanica 229 (9), 3813-3831 (2018).





Figure: (a) Schematic illustration of nonlocal connections in a lattice structure. These nonlocal connections are assumed to be absent by classical theories of elasticity. (b) Schematic of a crystal lattice to demonstrate the cause of length-scale effects at low-dimensions. (c) Fractional-order homogeneous beam equivalent of a periodic beam developed for wave-propagation analysis. From Mecc. (2021).

Nonlinear Solid Mechanics

  • Linearity is just an assumption we make to simplify the modeling. Every problem is nonlinear.

  • My research analyzes the effect of nonlinearities over structural response, with particular interest over structural stability.

  • Our research on energy-based framework for stability and post-critical (bifurcation) analysis of nonlocal solids resolved the inconsistent observations in literature (IJMS, 201, 106443 (2021)).

  • Combining geometric features like curvature with geometric nonlinearities presents 'bistability' (see figure). My research is focused on controlling the multistable behavior to achieve targeted structural response.


Reference Publications

  1. S Sidhardh, S Patnaik, F Semperlotti. Analysis of the Postbuckling Response of Nonlocal Plates Via Fractional-Order Continuum Theory. Journal of Applied Mechanics 88 (4), 041013 (2021).

  2. S Patnaik, S Sidhardh, F Semperlotti. Nonlinear thermoelastic fractional-order model of nonlocal plates: Application to postbuckling and bending response. Thin-Walled Structures 164, 107809 (2021).







Figure: (Top) Postbuckled shape of nonlocal plate under thermo-mechanical loading depicting a transition in buckled mode. from TWST, 164, 107809 (2021). (Bottom) Snapback buckling response of cylindrical shell depicting bistablity.

Computational Methods

  • Most commercial finite element (FE) packages lack the capability to include complexities introduced by the multiscale constitutive models.

  • My research involves developing state-of-art computational methods and packages for nonlinear, multiscale and multi-physics studies.

  • We developed 'fractional-Finite Element Method' (f-FEM) for fractional-order governing equations (IJSS, 202, 398-417 (2020)).

  • Existing methods like classical FE, nonlocal FE and meshfree methods have also been extensively utilized to develop in-house packages.


Reference Publications:

  1. S Patnaik, S Sidhardh, F Semperlotti. A Ritz-based finite element method for a fractional-order boundary value problem of nonlocal elasticity. International Journal of Solids and Structures 202, 398-417 (2020). Preprint available on Arxiv.

  2. S Sidhardh, MC Ray. Element-free Galerkin model of nano-beams considering strain gradient elasticity. Acta Mechanica 229 (7), 2765-2786 (2018).

Figure: Increasing band of system matrices developed via f-FEM demonstrates nonlocal connections. This results in higher computational demands. from CNSNS, 95, 105601 (2021)

Smart/Multi-physics Structures

  • Typically involves coupling of elastic response with the thermal, electrical and magnetic fields.

  • Opportunities in applications like sensors, actuators and energy-harvesters.

  • My work deals with proposing and developing constitutive models for multi-physics couplings and analyzing their performance in common structural elements.

  • My research proposed & developed constitutive model for flexomagnetism, a novel magneto-elastic coupling (JAP, 124 (24), 244101 (2018)).

  • Further, proposed composites for enhancing flexoelectricity-based multi-field coupling coefficients (Mat. Today Comm., 17, 114-123 (2018)). This required employing micromechanical models for the homogenization of smart composites.


Reference Publications:

  1. S Sidhardh, MC Ray. Exact solutions for flexoelectric response in elastic dielectric nanobeams considering generalized constitutive gradient theories. International Journal of Mechanics and Materials in Design 15 (3), 427-446 (2019).

  2. S Sidhardh, MC Ray. Flexomagnetic response of nanostructures. Journal of Applied Physics 124 (24), 244101 (2018).

Figure: (Top) Net polarization via flexoelectricity in a centrosymmetric crystalline structure. (Bottom) Proposed composite designs for tailoring flexoelectric coefficients. From Mat. Today Comm., 17, 114-123 (2018)