arash_yavari's blog

This paper presents a geometric theory of the mechanics of growing bodies.



This paper is dedicated to the memory of Professor Jim Knowles.



http://lanl.arxiv.org/abs/0911.4671

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 explicitly

depends on the temperature distribution. A change of temperature

corresponds to a change of the material metric. In this sense, a

temperature change is a concrete example of the so-called

referential evolutions. We also make a concrete connection between

our geometric point of view and the multiplicative decomposition

http://arxiv.org/PS_cache/arxiv/pdf/0903/0903.5321v1.pdf



The above article is an April Fool's joke. It reminded me of the recent "discoveries" in the mechanics community regarding stress tensor.



Regards,

Arash

The fractal crack model described here incorporates the essential

features of the fractal view of fracture, the basic concepts of

the LEFM model, the concepts contained within the

Barenblatt-Dugdale cohesive crack model and the quantized

(discrete or finite) fracture mechanics assumptions. The

well-known entities such as the stress intensity factor and the

Barenblatt cohesion modulus, which is a measure of material

toughness, have been re-defined to accommodate the fractal view of

fracture.

This paper revisits continua with microstructure from a geometric point of view. We model a structured continuum as a triplet of Riemannian manifolds: a material manifold, the ambient space manifold of material particles and a director field manifold. Green-Naghdi-Rivlin theorem and its extensions for structured continua are critically reviewed.

This paper studies the invariance of balance of

energy for a system of interacting particles under groups of

transformations. Balance of energy and its invariance is first

examined in Euclidean space. Unlike the case of continuous media,

it is shown that conservation and balance laws do not follow

from the assumption of invariance of balance of energy under

time-dependent isometries of the ambient space. However, the

postulate of invariance of balance of energy under arbitrary

This paper presents a geometric discretization of elasticity when

the ambient space is Euclidean. This theory is built on ideas from

algebraic topology, exterior calculus and the recent developments

of discrete exterior calculus. We first review some geometric

ideas in continuum mechanics and show how constitutive equations

of linearized elasticity, similar to those of electromagnetism,

can be written in terms of a material Hodge star operator. In the

discrete theory presented in this paper, instead of referring to

In this paper we covariantly obtain the governing equations of linearized elasticity. Our motivation is to see if one can make a connection between (global) balance of energy in nonlinear elasticity and its counterpart in linear elasticity. We start by proving a Green-Naghdi-Rivilin theorem for linearized elasticity. We do this by first linearizing energy balance about a given reference motion and then by postulating its invariance under isometries of the Euclidean ambient space.

This paper extends the recently developed theories of fracture
mechanics with finite growth (mainly the work of Pugno and Ruoff, 2004
on quantized fracture mechanics) to fractal cracks. One interesting
result is the prediction of crack roughening for fractal cracks.

This paper presents an anharmonic lattice statics analysis of 180 and 90 domain walls in tetragonal ferroelectric perovskites. We present all the calculations and numerical examples for the technologically important ferroelectric material PbTiO3. We use shell potentials that are fitted to quantum mechanics calculations. Our formulation places no restrictions on the range of the interactions. This formulation of lattice statics is inhomogeneous and accounts for the variation of the force constants near defects.