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:
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.
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
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).
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:
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.
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:
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).
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)