A simple computational homogenization method for structures made of heterogeneous linear viscoelastic materials

نویسندگان

  • A. B. Tran
  • J. Yvonnet
  • Q.-C. He
  • C. Toulemonde
  • J. Sanahuja
چکیده

In this paper, a numerical multiscale method is proposed for computing the response of structures made of linearly non-aging viscoelastic and highly heterogeneous materials. In contrast with most of the approaches reported in the literature, the present one operates directly in the time domain and avoids both defining macroscopic internal variables and concurrent computations at micro and macro scales. The macroscopic constitutive law takes the form of a convolution integral containing an effective relaxation tensor. To numerically identify this tensor, a representative volume element (RVE) for the microstructure is first chosen. Relaxation tests are then numerically performed on the RVE. Correspondingly, the components of the effective relaxation tensor are determined and stored for different snapshots in time. At the macroscopic scale, a continuous representation of the effective relaxation tensor is obtained in the time domain by interpolating the data with the help of spline functions. The convolution integral characterizing the time-dependent macroscopic stress-strain relation is evaluated numerically. Arbitrary local linear viscoelastic laws and microstructure morphologies can be dealt with. Implicit algorithms are provided to compute the time-dependent response of a structure at the macroscopic scale by the finite element method. Accuracy and efficiency of the proposed approach are demonstrated through 2D and 3D numerical examples and applied to estimate the creep of structures made ICorrespondance to J. Yvonnet Email address: [email protected] () Preprint submitted to Elsevier April 1, 2011 of concrete.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials

In this paper, a numerical multiscale method is proposed for computing the response of structures made of linearly non-aging viscoelastic and highly heterogeneous materials. In contrast with most of the approaches reported in the literature, the present one operates directly in the time domain and avoids both defining macroscopic internal variables and concurrent computations at micro and macro...

متن کامل

A General Boundary Element Formulation for The Analysis of Viscoelastic Problems

The analysis of viscoelastic materials is one of the most important subjects in engineering structures. Several works have been so far made for the integral equation methods to viscoelastic problems. From the basic assumptions of viscoelastic constitutive equations and weighted residual techniques, a simple but effective Boundary Element (BE) formulation is developed for the Kelvin viscoelastic...

متن کامل

Nonlinear Vibration and Stability Analysis of Beam on the Variable Viscoelastic Foundation

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different bou...

متن کامل

An Enhanced Finite Element method for Two Dimensional Linear Viscoelasticity using Complex Fourier Elements

In this paper, the finite element analysis of two-dimensional linear viscoelastic problems is performed using quadrilateral complex Fourier elements and, the results are compared with those obtained by quadrilateral classic Lagrange elements. Complex Fourier shape functions contain a shape parameter which is a constant unknown parameter adopted to enhance approximation’s accuracy. Since the iso...

متن کامل

Incremental layerwise finite element formulation for viscoelastic response of multilayered pavements

This paper provides an incremental layerwise finite element formulation for the viscoelastic analysis of multilayered pavements.  The constitutive behavior of asphalt concrete is represented by the Prony series. Layerwise finite element has been shown to provide an efficient and accurate tool for the numerical simulation of laminated structures. Most of the previous research on numerical simula...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015