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.

We study particle dynamics under curl forces. These forces are a class of non-conservative, non-dissipative, position-dependent forces that cannot be expressed as the gradient of a potential function. We show that the fundamental quantity of particle dynamics under curl forces is a work 1-form. By using the Darboux classification of differential 1-forms on R² and R³, we establish that any curl force in two dimensions has at most two generalized potentials, while in three dimensions, it has at most three.

Uditnarayan Kouskiya          Robert L. Pego        Amit Acharya

We look for traveling waves of the semi-discrete conservation law $4 \dot{u}_j + u_{j+1}^2 - u_{j-1}^2 = 0$, using variational principles related to concepts of ``hidden convexity'' appearing in recent studies of various PDE (partial differential equations). We analyze and numerically compute with two variational formulations related to dual convex optimization problems constrained by either the differential-difference equation (DDE) or nonlinear integral equation (NIE) that wave profiles should satisfy. We prove existence theorems conditional on the existence of extrema that satisfy a strict convexity criterion, and numerically exhibit a variety of localized, periodic and non-periodic wave phenomena.

Previous studies have reported fracture localization within the inclusions of 3D-printed staggered composites, despite their significantly higher strength compared to the matrix – a seemingly counterintuitive phenomenon. In this letter, we investigate whether material failure is governed by the volumetric energy of fracture rather than the maximum stress criterion. We perform experiments on the constituent phases of 3D-printed staggered composites to evaluate the validity of energy-based failure criteria.

The Curie brothers, Pierre and Jacques, discovered the piezoelectric effect in 1880. The phenomenon has been exploited in many useful applications, such as for the pickup on the gramophone that registers the sound when it follows the winding groove in the vinyl record surface. It is also used in lighters that ignite a gas when the voltage gap between different locations exceeds the limit to produce a spark. When things are made smaller and smaller, passing mm's, microns down to nano scales, the piezoelectric effect is surpassed by the flexoelectric effect.

I have an opening PhD Position at my Chair of Computational Mechanics, Otto von Guericke University Magdeburg (Germany).
The candidate should work on a research project including physics-based modeling of wafer-to-wafer bonding.
The application is open until 24^th of April.

Please follow the link for the application: Apply here

``UNIFIED MICROMECHANICS THEORY of Composites” by Buryachenko has been created (see https:// arxiv.org/abs/2503.14529,  89pp, 514refs) for analyses of composites of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures with either local, weakly nonlocal (strain gradient and stress gradient), strongly nonlocal (strain-type and displacement-type, peridynamics) or multiphysics phase properties and any unpredefined surrogate (effective) nonlocal operators.

A PhD position will be available at University of Pavia in Italy starting November 2025. 

Interested candidates are encouraged to contact Prof. Giulia Scalet (giulia.scalet [at] unipv.it).

The candidate will work on new computational approaches for the simulation of smart polymers and hydrogels and their application to mechanobiology studies.