Classical non-relativistic fractons by Prakash, A, Goriely, A, Sondhi, SL

“…We initiate the study of the classical mechanics of nonrelativistic fractons in its simplest setting—that of identical one-dimensional particles with local Hamiltonians characterized by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. …”

Kovalevskaya rods and Kovalevskaya waves by Goriely, A, Nizette, M

“…The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular cross-sections. …”

On the figure of elastic planets I: gravitational collapse and infinitely many equilibria by Jai, F, Kodio, O, Chapman, S, Goriely, A

“…A classic problem of elasticity is to determine the possible equilibria of an elastic planet modelled as a homogeneous compressible spherical elastic body subject to its own gravitational field. …”

The anelastic Ericksen problem: universal deformations and universal eigenstrains in incompressible nonlinear anelasticity by Goodbrake, C, Yavari, A, Goriely, A

“…We characterize explicitly the universal eigenstrains that share the symmetries present in the classical problem, and show that in the presence of eigenstrains, the six known classical families of universal solutions merge into three distinct anelastic families, distinguished by their particular symmetry group. …”

Minimal morphoelastic models of solid tumour spheroids: a tutorial by Walker, BJ, Celora, GL, Goriely, A, Moulton, DE, Byrne, HM

“…Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. …”

Universal solutions in nonlinear anelasticity by Goodbrake, C

“…To this end, we provide a framework under which a wide array of different anelasticity theories can be recast, and use this framework to classify all anelastic universal solutions exhibiting particular symmetries, using known families of universal solutions in classical nonlinear elasticity as a starting point. …”

On the mechanics of thin films and growing surfaces by Holland, M, Kosmata, T, Goriely, A, Kuhl, E

“…Here, we establish a theoretical and computational framework for continua with growing surfaces and demonstrate its application to classical phenomena in plant growth. To allow the surface to grow independently of the bulk, we equip it with its own potential energy and its own surface stress. …”

Instabilities in liquid crystal elastomers by Mihai, LA, Goriely, A

“…Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. …”

A predictive theoretical model for stretch-induced instabilities in liquid crystal elastomers by Mihai, LA, Raistrick, T, Gleeson, HF, Mistry, D, Goriely, A

“…Following the experimental lead, we construct a general mathematical model which, depending on whether the uniaxial scalar order parameter is constant or not, can predict either the classical shear striping instability or the molecular auxetic response and mechanical Fréedericksz transition observed in different liquid crystal elastomers. …”

A brief history of Kovalevskaya exponents and modern developments by Goriely, A

“…Kovalevskaya to prove the single-valuedness of the classical cases of integrability of the rigid body motion. …”

Morpho-elastodynamics: the long-time dynamics of elastic growth. by Vandiver, R, Goriely, A

“…These evolution laws lead to new dynamical systems that can be studied by the classical methods of dynamical systems theory.…”

Dynamics of helical strips by Goriely, A, Shipman, P

“…The dynamics of inertial elastic helical thin rods with noncircular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis, and the dispersion relation for helical strips is derived and analyzed. …”

Dynamics of helical strips by Goriely, A, Shipman, P

“…The dynamics of inertial elastic helical thin rods with noncircular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis, and the dispersion relation for helical strips is derived and analyzed. …”

Spontaneous Cavitation in Growing Elastic Membranes by McMahon, J, Goriely, A

“…These stresses are known to change many of the classical properties of the material and have been studied extensively in the context of volumetric growth in biomechanics. …”

Stress Singularities in Swelling Soft Solids by Goriely, A, Weickenmeier, J, Kuhl, E

“…At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. …”

The surprising dynamics of a chain on a pulley: Lift-off and snapping by Brun, P, Audoly, B, Goriely, A, Vella, D

“…The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. …”

Geometric conditions for the positive definiteness of the second variation in one-dimensional problems by Lessinnes, T, Goriely, A

“…Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. …”

Mechanical basis of morphogenesis and convergent evolution of spiny seashells. by Chirat, R, Moulton, D, Goriely, A

“…Spines in mollusk seashells are classically interpreted as having repeatedly evolved as a defense in response to shell-crushing predators. …”

Controllable deformations of unconstrained ideal nematic elastomers by Mihai, LA, Goriely, A

“…This result generalizes the classical Ericksen’s theorem for nonlinear homogeneous isotropic hyperelastic materials. …”

Soft cells and the geometry of seashells by Domokos, G, Goriely, A, Horváth, ÁG, Regős, K

“…A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. …”