Non-local Damage-Enhanced MFH for Multiscale Simulations of Composites

in Patterson, Eann; Backman, David; Cloud, Gary (Eds.) Composite Materials and Joining Technologies for Composites, Volume 7 (2013)

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix ... [more ▼]

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way. Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient comput0ational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions. [less ▲]

Homogenization of fibre reinforced composite with gradient enhanced damage model

in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November)

Classical finite element simulations face the problems of losing uniqueness and strain localization when the strain softening of materials is involved. Thus, when using continuum damage model or ... [more ▼]

Classical finite element simulations face the problems of losing uniqueness and strain localization when the strain softening of materials is involved. Thus, when using continuum damage model or plasticity softening model, numerical convergence will not be obtained with the refinement of the finite element discretization when strain localization occurs. Gradient-enhanced softening and non-local continua models have been proposed by several researchers in order to solve this problem. In such approaches, high-order spatial gradients of state variables are incorporated in the macroscopic constitutive equations. However, when dealing with complex heterogeneous materials, a direct simulation of the macroscopic structures is unreachable, motivating the development of non-local homogenization schemes. In this work, a non-local homogenization procedure is proposed for fiber reinforced materials. In this approach, the fiber is assumed to remain linear elastic while the matrix material is modeled as elasto-plastic coupled with a damage law described by a non-local constitutive model. Toward this end, the mean-field homogenization is based on the knowledge of the macroscopic deformation tensors, internal variables and their gradients, which are applied to a micro- structural representative volume element (RVE). Macro-stress is then obtained from a homogenization process. [less ▲]

Thermomechanical modeling of metals at finite strains: First and mixed order finite elements

in International Journal of Solids and Structures (2005), 42(21-22), 5615-5655

The aim of this paper is to describe an updated EAS (Enhanced Assumed Strain) finite element formalism developed to model the thermomechanical behavior of metals submitted to large strains. We will also ... [more ▼]

The aim of this paper is to describe an updated EAS (Enhanced Assumed Strain) finite element formalism developed to model the thermomechanical behavior of metals submitted to large strains. We will also expose the use of mixed order elements (first order mechanical elements strongly coupled with quadratic thermal elements) which, as we will show, is of particular interest for modeling fast processes inducing important temperature gradients. The features of this formalism, used jointly with an Updated Lagrangian approach and an hypoelastic anisothermal constitutive formulation, will be described. Three applications involving finite strains and important thermomechanical couplings will be studied. The results obtained will be compared with the results given by the now classical SRI (Selective Reduced Integration) formalism. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲]

Numerical Simulation of Viscoplastic and Frictional Heating during Finite Deformation of Metal. Part II: Applications

in Journal of Engineering Mechanics (2002), Vol. 128

In this paper we will apply the theoretical framework developed in Part I to various metal forming processes. These numerical simulations are exposed showing the capability of the formulation to simulate ... [more ▼]

In this paper we will apply the theoretical framework developed in Part I to various metal forming processes. These numerical simulations are exposed showing the capability of the formulation to simulate finite anisothermal deformation of solids and thermal field evolution due to viscoplastic and frictional heating. [less ▲]

A coupled thermo-viscoplastic formulation at finite strains for the numerical simulation of superplastic forming

in Materials Science Forum (2001), 357-359

This paper is concerned with the numerical simulation of hot metal forming, especially superplastic forming. A complete thermo-viscoplastic formulation at finite strains is derived and a unified stress ... [more ▼]

This paper is concerned with the numerical simulation of hot metal forming, especially superplastic forming. A complete thermo-viscoplastic formulation at finite strains is derived and a unified stress update algorithms for thermo-elastoplastic and thermo-elastoviscoplastic constitutive equations is obtained. The resulting unified implicit algorithm is both efficient and very inexpensive. Finally, numerical simulations of superplastic forming are exposed. [less ▲]