AkashJain

Elasticity is a branch of mechanics that describes how solid materials respond to static or time-independent deformations. It defines the fundamental relationship between stress and strain and introduces key material properties—such as elastic moduli—that determine stiffness and resilience. By contrast, the theory of viscoelasticity extends this framework to include time-dependent effects, capturing how materials gradually recover their shape or continue to deform under sustained stress, reflecting both elastic and viscous behavior.

Viscoelasticity is conventionally formulated using the shape field, which characterizes the deformation of a solid as a function of space and time. In a striking development, Grozdanov et al. (2018) showed that viscoelasticity in two spatial dimensions can alternatively be understood as a form of hydrodynamics endowed with a novel symmetry known as a generalized global symmetry. (See here for more on generalized global symmetries.) This reformulation offers distinct advantages over the traditional approach. All the degrees of freedom in this framework are directly tied to conserved quantities, allowing the theory to be expressed more systematically. It also provides a cleaner foundation for tackling initial value problems in numerical simulations of viscoelastic systems.

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