Implicit, Incremental Homogenization Method for Periodic Inelastic Solids

Analytical homogenization method for periodic composite materials

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We present an easy-to-implement technique for determining the effective properties of composite materials with peri...

An implicit finite element method for elastic solids in contact

This work focuses on the simulation of mechanical contact between nonlinearly elastic objects such as the components of the human body. The computation of the reaction forces that act on the contact surfaces (contact forces) is the key for designing a reliable contact handling algorithm. In traditional methods, contact forces are often defined as discontinuous functions of deformation, which le...

Periodic Homogenization for Hypoelliptic Diffusions

Abstract We study the long time behavior of an Ornstein–Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian motion whose covariance can be expressed in terms of the solution of a Poisson equation. We also derive upper bounds on the convergence rate in several ...

Incremental homogenization approach for ageing viscoelastic polycrystals

Material fatigue simulation using a periodic time homogenization method

This paper deals with the numerical simulation of combined cycle fatigue (CCF), which is characterized by two periodic loads, whose frequencies are very different one from the other. Rather than using classical fatigue life estimations, a time transient evolution model is solved using a periodic time homogenization method. This latter is based on the assumption that the time scales associated w...