Abstract
We consider gradient flows of surface energies which depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously.
Abstract
In this paper, we revisit the mathematical foundations of nonlinear viscoelasticity. We study the underlying geometry of viscoelastic deformations, and in particular, the intermediate configuration. Starting from the direct multiplicative decomposition of the deformation gradient $\mathbf{F}=\mathbf{F_e}\mathbf{F_v}\,$, into elastic and viscous distortions $\mathbf{F_e}$ and $\mathbf{F_v}\,$, respectively, we point out that $\mathbf{F_v}$ can be either a material tensor ($\mathbf{F_e}$ is a two-point tensor) or a two-point tensor ($\mathbf{F_e}$ is a spatial tensor).
Abstract
Following on Part I of this work series on local kirigami mechanics, we present a study of a discretely creased mechanism as a model to investigate the mechanics of the basic geometric building block of kirigami--the e-cone.
Abstract
Over the past decade, kirigami—the Japanese art of paper cutting—has been playing an increasing role in the emerging field of mechanical metamatertials and a myriad of other mechanical applications. Nonetheless, a deep understanding of the mathematics and mechanics of kirigami structures is yet to be achieved in order to unlock their full potential to pioneer more advanced applications in the field.
Abstract
In this paper, we formulate a theory for the coupling of accretion mechanics and thermoelasticity. We present an analytical formulation of the thermoelastic accretion of an infinite cylinder and of a two-dimensional block.
Abstract
In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions.
Abstract
In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric.
Abstract
Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time.
Abstract
Eigenstrains are created as a result of anelastic effects such as defects, temperature changes, bulk growth, etc., and strongly affect the overall response of solids. In this paper, we study the residual stress and deformation fields of an incompressible, isotropic, infinite wedge due to a circumferentially symmetric distribution of finite eigenstrains.
Abstract
The objective of this short note is to trace back the major contributions that led to the multiplicative decomposition of the deformation gradient in finite plasticity, nonlinear thermoelasticity, and growth mechanics.