Maximiliano Larrain Silva               Amit Acharya

A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete knowledge of constitutive behavior. The scheme is demonstrated in the context of the rate-dependent, elastoplastic response of a bar, resulting in a nonlinear problem of constrained optimization. Both closed form and computational results are developed. The computational solutions utilize a sequence of convex optimization problems, and are shown to be accurate. In the example considered, the approach is shown to automatically correct an (intentionally) faulty constitutive specification, resulting in the solution to be in accord with the fundamental postulates of continuum mechanics.

Context:

Arash Yavari         Amit Acharya

Curl forces are position-dependent, non-conservative, and non-dissipative forces that, in general, cannot be derived from an ordinary potential energy. Consequently, their equations of motion do not, in general, follow from a standard variational principle. In this paper, we present a dual variational formulation for particle dynamics under curl forces. By introducing variables dual to position and velocity and an auxiliary function, we construct a pre-dual action in which the equations of motion act as constraints. Stationarity with respect to the primal variables defines a dual-to-primal mapping, whose substitution into the pre-dual action gives an action expressed entirely in terms of the dual variables. The Euler–Lagrange equations of the dual action recover both the original equations of motion and their prescribed initial conditions. We also introduce an auxiliary dual Hamiltonian that is conserved along stationary dual trajectories, although it does not represent the physical energy. The formulation is illustrated using two nonlinear curl force fields in two and three dimensions and the classical Ziegler column. These examples demonstrate that non-conservative curl-force dynamics can admit variational descriptions even in the absence of an ordinary potential energy or a conventional Lagrangian.

4th August 2026, 2:00 PM -3:00 PM (EDT)

Meeting ID: 824 6447 8256 | Passcode: 003801

Simulating Contact-Rich Fluid-Structure Interaction Problems

Teo Lara, Undergraduate (BS Mathematics& Physics), Massachusetts Institute of Technology

Abstract

31st July 2026, 1:00 PM - 2:00 PM (CDT)

Meeting ID: 824 6447 8256 | Passcode: 003801

Physical Mechanisms of Blast-induced Large Deformations in Brain-like Soft Matter

Dr. Enze Chen, Postdoctoral Researcher in Mechanical Engineering, University of Wisconsin-Madison

Abstract

The 𝗲𝘅𝘁𝗲𝗻𝗱𝗲𝗱 𝗮𝗯𝘀𝘁𝗿𝗮𝗰𝘁 𝘀𝘂𝗯𝗺𝗶𝘀𝘀𝗶𝗼𝗻 𝗱𝗲𝗮𝗱𝗹𝗶𝗻𝗲 𝗶𝘀 𝗮𝗽𝗽𝗿𝗼𝗮𝗰𝗵𝗶𝗻𝗴!

We are pleased to invite researchers to contribute to our symposium at 𝗜𝗖𝗡𝗔𝗔𝗠 𝟮𝟬𝟮𝟲 (𝟭𝟱–𝟮𝟭 𝗦𝗲𝗽𝘁𝗲𝗺𝗯𝗲𝗿 𝟮𝟬𝟮𝟲, 𝗛𝗲𝗿𝗮𝗸𝗹𝗶𝗼𝗻, 𝗚𝗿𝗲𝗲𝗰𝗲):

𝗣𝗵𝘆𝘀𝗶𝗰𝘀-𝗜𝗻𝗳𝗼𝗿𝗺𝗲𝗱 𝗠𝗮𝗰𝗵𝗶𝗻𝗲 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗳𝗼𝗿 𝗡𝘂𝗺𝗲𝗿𝗶𝗰𝗮𝗹 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 𝗼𝗳 𝗠𝗲𝗰𝗵𝗮𝗻𝗶𝗰𝗮𝗹 𝗮𝗻𝗱 𝗠𝘂𝗹𝘁𝗶𝗽𝗵𝘆𝘀𝗶𝗰𝘀 𝗦𝘆𝘀𝘁𝗲𝗺𝘀

This symposium aims to bring together researchers working at the intersection of 𝘀𝗰𝗶𝗲𝗻𝘁𝗶𝗳𝗶𝗰 𝗺𝗮𝗰𝗵𝗶𝗻𝗲 𝗹𝗲𝗮𝗿𝗻𝗶𝗻𝗴 and 𝗰𝗼𝗺𝗽𝘂𝘁𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝗺𝗲𝗰𝗵𝗮𝗻𝗶𝗰𝘀, with particular emphasis on the development and application of data-driven methods for solving engineering and multiphysics problems.

Our latest paper is now freely accessible for the next 50 days from this link: https://authors.elsevier.com/a/1nUCG3In-v8hqF 

I am seeking a Postdoctoral Fellow to work on origami metamaterials in the Architected Metamaterials Group at McGill University (https://pasinigroup.mcgill.ca/).

The Daedalus Lab at the Georgia Institute of Technology (D. Guggenheim School of Aerospace Engineering) is recruiting a PhD student for Spring 2027.

Our group works at the intersection of fracture mechanics, experimental mechanics, computational modeling, and artificial intelligence. Current research directions include:

Someone asked how "Thermodynamic state index in the Unified Mechanics Theory relates, conceptually or mathematically, to conditional phase-space entropy in finite Hamiltonian systems." I posed the question to Gemini AI. Here is its answer in the attached file.