I am happy to share our recent paper published in Cell Reports Physical Science: Inhomogeneous substrate strain-driven long-range cellular patterning

Amit Acharya        Janusz Ginster

A scheme for generating a family of convex variational principles is developed, the Euler-Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary differential equations (ODE) in a well-defined sense. The scheme is applied to the Quadratic-Quadratic Regulator problem for which an explicit form of the functional is derived, and existence of minimizers of the variational principle is rigorously shown. It is shown that the Linear-Quadratic Regulator problem with time-dependent forcing can be solved within the formalism without requiring any nonlinear considerations, in contrast to the use of a Riccati system in the classical methodology.

Our work demonstrates a pathway for solving nonlinear control problems via convex optimization.

Dissipative models for the quasi-static and dynamic response due to slip in an elastic body containing a single slip plane of vanishing thickness are developed. Discrete dislocations with continuously distributed cores can glide on this plane, and the models are developed as special cases of a fully three-dimensional theory of plasticity induced by dislocation motion. The reduced models are compared and contrasted with the augmented Peierls model of dislocation dynamics. A primary distinguishing feature of the reduced models is the a-priori accounting of space-time conservation of Burgers vector during dislocation evolution. A physical shortcoming of the developed models as well as the Peierls model with regard to a dependence on the choice of a distinguished, coherent reference configuration is discussed, and a testable model without such dependence is also proposed.

Smart soft materials have gained increasing attention in recent years because of their adaptive behaviors to external multi-physics stimuli, enabling diverse applications across multiple fields. Here, we show programmable wrinkling morphological patterns on liquid crystal network (LCN) bilayers bonded to compliant substrates under thermal load, by tuning the orientation of directors between LCN bilayers. We propose a solid-shell formulation that merges enhanced and natural assumed strain approaches to investigate the pattern formation and morphological transition of LCN bilayers.

Liquid crystal elastomers (LCEs), as a unique class of smart soft materials combining the properties of liquid crystals and hyperelasticity, are capable of rapid, anisotropic, and reversible deformations in response to mechanical, thermal or optical stimuli. Here, we report a hitherto unknown stretching-induced twisting behavior of LCE bilayer strips. Under uniaxial stretching, we reveal that due to the spontaneous mismatch strain arising from interlayer anisotropy, the bilayer strips exhibit notable twisting deformations.

Monthly Webinar. TTA-Uncertainty Quantification and Probabilistic Modeling.

February 13; 3 pm - 4pm EST

Speaker: Alireza Doostan, University of Colorado, Boulder

Title: Uncertainty Quantification and Generative Modeling Using Multi-fidelity Strategies

The Computational Mechanics and Methods (CM3) Group in the Department of Mechanical and Aerospace Engineering at the University of Kentucky is seeking highly self-motivated individuals who have great interest in the broad research areas of computational solid mechanics and methods, beginning Fall 2025. Interested individuals should send a detailed CV and official transcripts to Dr.