Multi-scale analysis in elasto-viscoplasticity coupled with damage

Kruch, Serge; Chaboche, Jean–Louis

doi:10.1016/j.ijplas.2011.03.007

Cited by 47 publications

(18 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To bridge the evolution of microscopic strain localization toward macroscopic material failure, different two-scale approaches for damage have been presented in the last years. In the so-called concurrent models, the most critical macroscale zones are locally enriched by a detailed microstructural description, which permits to capture damage initiation and evolution in a realistic manner, see, for example, [15][16][17][18][19][20][21]. Generally, the enhancement zone needs to be known a priori, and these approaches are usually more suitable for a moderate scale separation.…”

Section: Introductionmentioning

confidence: 82%

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM

Bosco¹,

Kouznetsova²,

Geers

2015

Numerical Meth Engineering

View full text Add to dashboard Cite

The aim of this paper is to propose a continuous-discontinuous computational homogenization-localization framework to upscale microscale localization toward the onset and propagation of a cohesive discontinuity at the macroscale. The major novelty of this contribution is the development of a fully coupled micromacro solution strategy, where the solution procedure for the macroscopic domain is based on the extended finite element method. The proposed approach departs from classical computational homogenization, which allows to derive the effective stress-strain response before the onset of localization. Upon strain localization, the microscale is characterized by a strain localization band where damage grows and by two adjacent unloading bulk regions at each side of the localization zone. The microscale localization band is lumped into a macroscopic cohesive crack, accommodated through discontinuity enriched macroscale kinematics. The governing response of the continuum with a discontinuity is obtained numerically based on proper scale transition relations in terms of the traction-separation law and the stress-strain description of the continuous surrounding material at both sides of the discontinuity. The potential of the method is demonstrated with a numerical example, which illustrates the onset and propagation of a macroscale cohesive crack emerging from microstructural damage within the underlying microstructure. Dedicated to the memory of Professor Ted BelytschkoAs one of the world leaders in computational mechanics, Ted Belytschko greatly influenced the scientific community. Many of his contributions to the field were groundbreaking, thereby initiating novel routes which inspired many researchers, young and old. Moreover, Ted Belytschko always showed a great interest in the work of others. Among the various subjects, he had a great interest for multi-scale approaches addressing damage and fracture. Based on his outspoken interest for our work on this topic, this paper presents our latest developments in computational homogenizationlocalization to an X-FEM enriched macroscale continuum. He was one of the founding fathers of X-FEM, and this paper is therefore our scientific contribution to pay tribute to the memory of professor Ted Belytschko.an intrinsic limitation of the classical embedded discontinuity technique emerges: the displacement field enrichment is performed at the element level only, which does not allow to describe a compatible displacement field across element boundaries. The assumptions made on the strain field are relaxed in [38], where the macrostructural kinematics allows for the description of a discontinuous displacement field together with a non-uniform deformation field across the discontinuity. Consistent scale transitions are formulated to couple the discontinuous macroscale fields to the continuous kinematics at the microstructural level. The effective microscale response is recovered consisting of the effective stress tensors at each side of the discontinuity (while preserving tract...

show abstract

Section: Introductionmentioning

confidence: 82%

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM

Bosco¹,

Kouznetsova²,

Geers

2015

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Formulation of the damage mechanics with respect to the Zener parameter provides enough flexibility to formulate a rate and temperature-dependent damage theory [74][75][76][77], = 9{T)Zn'' (33) where ||(/)|| = J2(j) : ^ is the effective shear damage and 6{T) introduces the temperature dependency in the damage evolution, which is represented by the Arrhenius function of temperature; Z is the Zener parameter and n'' represents the direction of the damage flow. The proposed damage theory utilizes the same concept as viscous stresses in plasticity theory.…”

Section: Cyclic Updatesmentioning

confidence: 99%

Cyclic Viscoplastic-Viscodamage Analysis of Shape Memory Polymers Fibers With Application to Self-Healing Smart Materials

Shojaei

Voyiadjis

2012

Journal of Applied Mechanics

View full text Add to dashboard Cite

The cold-drawn, programmed shape memory polymer (SMP) fibers show excellent stress recovery property, which promotes their application as mechanical actuators in smart material systems. A full understanding of the thermomechanical-damage responses of these fibers is crucial to minimize the trial-and-error manufacturing processes of these material systems. In this work, a multiscale viscoplastic-viscodamage theory is developed to predict the cyclic mechanical responses of SMP fibers. The proposed viscoplastic theory is based on the governing relations for each of the individual microconstituents and establishes the microscale state of the stress and strain in each of the subphases. These microscale fields are then averaged through the micromechanics framework to demonstrate the macroscale constitutive mechanical behavior. The cyclic loss in the functionality of the SMP fibers is interpreted as the damage process herein, and this cyclic loss of stress recovery property is calibrated to identify the state of the damage. The continuum damage mechanics (CDMj together with a thermodynamic consistent viscodamage theory is incorporated to simulate the damage process. The developed coupled viscoplastic-viscodamage theory provides an excellent correlation between the experimental and simulation results. The cyclic loading-damage analysis in this work relies on the underlying physical facts and accounts for the microstructural changes in each of the micro constituents. The established framework provides a well-structured method to capture the cyclic responses of the SMP fibers, which is of utmost importance for designing the SMP fiber-based smart material systems.

show abstract

“…The developed framework should be equipped with fully coupled thermo-mechanical homogenization equations and the FE 2 computational scheme. Considering the pure mechanical response of composites, numerous multiscale models for nonlinear materials have been proposed in the literature Suquet (1987); Ponte-Castañeda (1991); Terada and Kikuchi (2001); Meraghni et al (2002); Yu and Fish (2002); Aboudi et al (2003); Aboudi (2004); Chaboche et al (2005); Asada and Ohno (2007); Mercier and Molinari (2009); Khatam and Pindera (2010); Kruch and Chaboche (2011) ;Brenner and Suquet (2013); Mercier et al (2012) ;Chatzigeorgiou et al (2015); Charalambakis et al (2018). In the study of periodic composite materials, the FE 2 technique appears to be an appropriate solution strategy to identify the macroscopic response of the structure, accounting for all the mechanisms observed in the heterogeneous microstructure (Feyel and Chaboche, 2000;Nezamabadi et al, 2010;Asada and Ohno, 2007;Tikarrouchine et al, 2018;Xu et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Fully coupled thermo-viscoplastic analysis of composite structures by means of multi-scale three-dimensional finite element computations

Tikarrouchine

Chatzigeorgiou

Chemisky

et al. 2019

International Journal of Solids and Structures

View full text Add to dashboard Cite

The current paper presents a two scale Finite Element approach (FE 2 ), adopting the periodic homogenization method, for fully coupled thermomechanical processes. The aim of this work is to predict the overall response of rate-dependent, non-linear, thermo-mechanically coupled problems of 3D A C C E P T E D M A N U S C R I P T nite element framework is applied to simulate thermoelastic-viscoplastic materials of complex 3D composite structures, and its capabilities are demonstrated with proper numerical examples. It is worth mentioning that the proposed computational strategy can be applied for any kind of 3D periodic microstructure and non-linear constitutive law.

show abstract

Multi-scale analysis in elasto-viscoplasticity coupled with damage

Cited by 47 publications

References 32 publications

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM

Cyclic Viscoplastic-Viscodamage Analysis of Shape Memory Polymers Fibers With Application to Self-Healing Smart Materials

Fully coupled thermo-viscoplastic analysis of composite structures by means of multi-scale three-dimensional finite element computations

Contact Info

Product

Resources

About