Blog posts

I am teaching Advanced Elasticity again.  Thermodynamics is involved in nontrivial ways in several topics, such as entropic elasticity and swelling hydrogels.

Two PhD students will be engaged in a research project of National Science Centre (NCN) carried out in the Institute of Fundamental Technological Research PAS, Poland on 'Intelligent design of 2D nanostructures based on molybdenum'.  The materials with a 2D atomic structure (flat, one layer) have drawn attention of researchers for years. The practical applications of graphene sheets, nanotubes can be observed in many areas from electronic industry up to civil engineering (e.g. concrete with nanotubes fillers).

Chiqun Zhang            Amit Acharya            Saurabh Puri

A generalized disclination (g.disclination) theory [AF15] has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of treating the kinematics and dynamics of terminating lines of elastic strain and rotation discontinuities. In this work, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of a single disclination, a single dislocation treated as a disclination dipole, a tilt grain boundary, a misfitting grain boundary with disconnections, a through twin boundary, a terminating twin boundary, a through grain boundary, a star disclination/penta-twin, a disclination loop (with twist and wedge segments), and a plate, a lenticular, and a needle inclusion are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclination-dipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. Our work also represents one systematic way of studying the interaction of (g.)disclinations and dislocations as topological defects, a subject of considerable subtlety and conceptual importance [Mer79, AMK17].

This paper presents a new Feedback-Accelerated Picard Iteration method for solving long-term orbit propagation problems and perturbed Lambert’s problems. This method is developed by combining the collocation method and the variational iteration method over large-time-steps. The resulting iterative formulae are explicitly derived so that they can be directly adopted to solve problems in orbital mechanics. Several typical orbit regimes incorporating high-order gravity and air drag force are used to demonstrate the application of the proposed method in orbit propagation.