145 citations · 427 across the 25 of their papers we have counts for
25 papers
Dual Variational Principles for Curl Forces
Arash Yavari, Amit Acharya
Curl forces are position-dependent, non-conservative, and non-dissipative forces that, in general, cannot be derived from an ordinary potential energy. Consequently, their equation…
Nonlinear Anisotropic Viscoelasticity
Souhayl Sadik, Arash Yavari
In this paper we revisit the mathematical foundations of nonlinear viscoelasticity. We study the underlying geometry of viscoelastic deformations, and in particular, the intermedia…
Accretion-Ablation Mechanics
Satya Prakash Pradhan, Arash Yavari
In this paper we formulate a geometric nonlinear theory of the mechanics of accreting-ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio and Ya…
Universal Displacements in Inextensible Fiber-Reinforced Linear Elastic Solids
Arash Yavari
For a given class of materials, universal displacements are those displacements that can be maintained for any member of the class by applying only boundary tractions. In this pape…
A Geometric Field Theory of Dislocation Mechanics
Fabio Sozio, Arash Yavari
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deforma…
Nonlinear Mechanics of Remodeling
Aditya Kumar, Arash Yavari
In this paper we present a large-deformation formulation of the mechanics of remodeling. Remodeling is anelasticity with an internal constraint -- material evolutions that are mass…
On the Effective Mass of Mechanical Lattices with Microstructure
Francesco Fedele, Phanish Suryanarayana, Arash Yavari
We present a general formalism for the analysis of mechanical lattices with microstructure using the concept of effective mass. We first revisit a classical case of microstructure…
Geometric Phases of Nonlinear Elastic -Rotors via Cartan's Moving Frames
Francesco Fedele, Arash Yavari
We study the geometric phases of nonlinear elastic -rotors with continuous rotational symmetry. In the Hamiltonian framework, the geometric structure of the phase space is a pri…
Optimal Elastostatic Cloaks
Fabio Sozio, Mostafa Faghih Shojaei, Arash Yavari
An elastic cloak hides a hole or an inhomogeneity from elastic fields. In this paper, a formulation of the optimal design of elastic cloaks based on the adjoint state method, in wh…
Elastodynamic Transformation Cloaking for Non-Centrosymmetric Gradient Solids
Fabio Sozio, Ashkan Golgoon, Arash Yavari
In this paper we investigate the possibility of elastodynamic transformation cloaking in bodies made of non-centrosymmetric gradient solids. The goal of transformation cloaking is…
Transformation Cloaking in Elastic Plates
Ashkan Golgoon, Arash Yavari
In this paper we formulate the problem of elastodynamic transformation cloaking for Kirchhoff-Love plates and elastic plates with both the in-plane and out-of-plane displacements.…
Compatible-Strain Mixed Finite Element Methods for 3D Compressible and Incompressible Nonlinear Elasticity
Mostafa Faghih Shojaei, Arash Yavari
A new family of mixed finite element methodscompatible-strain mixed finite element methods (CSFEMs)are introduced for three-dimensional compressible and incompressible nonlin…
Nonlinear and Linear Elastodynamics Transformation Cloaking
Arash Yavari, Ashkan Golgoon
We formulate the problems of nonlinear and linear elastodynamics transformation cloaking in a geometric framework. It is noted that a cloaking transformation is neither a spatial n…
Line and Point Defects in Nonlinear Anisotropic Solids
Ashkan Golgoon, Arash Yavari
In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with distributed line and point defects. In particular, we determine the s…
Differential Complexes in Continuum Mechanics
Arzhang Angoshtari, Arash Yavari
We study some differential complexes in continuum mechanics that involve both symmetric and non-symmetric second-order tensors. In particular, we show that the tensorial analogue o…
Convergence Analysis of the Wolf Method for Coulombic Interactions
Arzhang Angoshtari, Arash Yavari
A rigorous proof for convergence of the Wolf method for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of…
Effect of External Normal and Parallel Electric Fields on 180^o Ferroelectric Domain Walls in PbTiO_3
Arzhang Angoshtari, Arash Yavari
We impose uniform electric fields both parallel and normal to 180^o ferroelectric domain walls in PbTiO_3 and obtain the equilibrium structures using the method of anharmonic latti…
Atomic Structure of Steps on 180^o Ferroelectric Domain Walls in PbTiO_3
Arzhang Angoshtari, Arash Yavari
Using the method of anharmonic lattice statics, we calculate the equilibrium structure of steps on 180^o ferroelectric domain walls (DW) in PbTiO_3. We consider three different typ…
Structure of Defective Crystals at Finite Temperatures: A Quasi-Harmonic Lattice Dynamics Approach
Arash Yavari, Arzhang Angoshtari
In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it static…
Finite-Temperature Atomic Structure of 180^o Ferroelectric Domain Walls in PbTiO3
Arzhang Angoshtari, Arash Yavari
In this letter we obtain the finite-temperature structure of 180^o domain walls in PbTiO3 using a quasi-harmonic lattice dynamics approach. We obtain the temperature dependence of…
Estimating Terminal Velocity of Rough Cracks in the Framework of Discrete Fractal Fracture Mechanics
Arash Yavari, Hamed Khezrzadeh
In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness…
Effect of strain and oxygen vacancies on the structure of 180^o ferroelectric domain walls in PbTiO_3
Arzhang Angoshtari, Arash Yavari
In this paper we study the effect of normal and shear strains and oxygen vacancies on the structure of 180^o ferroelectric domain walls in PbTiO_3. It is known that oxygen vacancie…
A Geometric Theory of Thermal Stresses
Arkadas Ozakin, Arash Yavari
In this paper we formulate a geometric theory of thermal stresses. Given a temperature distribution, we associate a Riemannian material manifold to the body, with a metric that exp…
A Geometric Theory of Growth Mechanics
Arash Yavari
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric r…