research

The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the Hamilton-Jacobi equation from conservative systems to general Newtonian particle systems involving non-conservative forces, including dissipative ones. A geometric optics approximation leads to a dissipative Schr¨odinger equation, with the expected limiting form when the associated classical force system involves conservative forces.

A direct and time-saving method is presented in a paper published in the Elsevier journal Engineering Fracture Mechanics. The paper is well-written and really read-worthy. The link to it is: 

Direct mixed-mode I&II partitioning in beam-like geometries using Digital Image Correlation and the decomposed 𝐽 -integral by L. Binsfeld, R. Bonato, Z. Pagliaro, N. Murphy, and A. Ivankoviç

Extreme Mechanics Letters is pleased to announce the Recipients of the 2025 EML Young Investigator Award

The Executive Committee of the ASME Applied Mechanics Division is pleased to congratulate the recipients of the 2025 Robert M. and Mary Haythornthwaite Foundation* Research Initiation Grants Awards: Prof. Vatsa Gandhi (University of California at Los Angles), Prof. Chase Hartquist (University of Florida), Prof. Junsoo Kim (Northwestern University), Prof. Emily Sanders (Georgia Institute of Technology), and Prof. Angkur JD Shaikeea (California Institute of Technology).

The Executive Committee of the ASME Applied Mechanics Division is pleased to congratulate the recipients of the 2025 Robert M. and Mary Haythornthwaite Foundation Student Travel Awards: Victor Riera Naranjo (Georgia Institute of Technology), Omar M.

The Executive Committee of the ASME Applied Mechanics Division is pleased to congratulate Professor Ruike Renee Zhao, Department of Mechanical Engineering, Stanford University, as the recipient of the 2026 Thomas J. R. Hughes Young Investigator Award.

The Executive Committee of the ASME Applied Mechanics Division is pleased to congratulate Professor Shaofan Li, Professor of Civil and Environmental Engineering at UC Berkeley, as the recipient of the 2026 Ted Belytschko Applied Mechanics Award.

Authors: Abhishek Arora, Caglar Oskay

It is known that the balance laws of hyperelasticity (Green elasticity), i.e., conservation of mass and balance of linear and angular momenta, can be derived using the first law of thermodynamics and by postulating its invariance under superposed rigid body motions of the Euclidean ambient space---the Green-Naghdi-Rivlin theorem. In the case of a non-Euclidean ambient space, covariance of the energy balance---its invariance under arbitrary time-dependent diffeomorphisms of the ambient space---gives all the balance laws and the Doyle-Ericksen formula---the Marsden-Hughes theorem.