13 papers
On Physical Components of Tensors in Elasticity and Inelasticity
Souhayl Sadik, Arash Yavari
Widely used in mechanics and mathematical physics, physical components remove the inherent coordinate-dependent scaling in curvilinear coordinates, yielding components of consisten…
Rational Mechanics of Material Strength in Brittle Solids
Arash Yavari, Aditya Kumar
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite…
First-Order Compatible-Strain Mixed Quadrilateral Finite Elements for 2D Nonlinear Elasticity
Mohsen Jahanshahi, Damiano Pasini, Arash Yavari
Compatible-strain mixed finite elements (CSMFEs) use the differential complex of nonlinear elasticity to construct discretizations that preserve the underlying topological structur…
Nonlinear Anisotropic Visco-Anelasticity
Souhayl Sadik, Arash Yavari
We formulate a nonlinear geometric theory of visco-anelasticity that unifies viscoelastic and anelastic responses within a single thermodynamic framework. At each material point, t…
Universal deformations and universal residual stresses in incompressible isotropic Cauchy elasticity
Arash Yavari
We study universal deformations in incompressible isotropic Cauchy elastic solids with residual stress, without assuming any specific origin for the residual stress. Starting from…
Universal Displacements in Linear Strain-Gradient Elasticity
Dimitris Sfyris, Arash Yavari
We study universal displacement fields in three-dimensional linear strain-gradient elasticity within the Toupin-Mindlin first strain-gradient theory. Building on the approach of Ya…