Sergio Oller

A plastic-damage model for concrete

In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects. Onset and amount of cracking can be studied by a simple postprocessing of the finite-element plasticity solution. The accuracy of the model is checked with some examples of application.

Coupled plastic-damaged model

Abstract A constitutive model that couples plasticity and damage is presented. The model is thermodynamically consistent and comes from a generalization of classical plasticity theory and isotropic damage theory of Kachanov. Coupling between plasticity and damage is achieved through a simultaneous solution of the plastic and the damage problem. After a description of the model, a numerical algorithm for the integration of the resulting constitutive equations is presented. It is an Euler Backward type of algorithm that is particularly suitable to solve plain stress non-linear problems with a 2D finite element program. The consistent stiffness matrix is also derived. The paper is completed with some application examples that show that the model presented accurately reproduces the behaviour of elastic-plastic-damaged materials.

Finite element nonlinear analysis of concrete structures using a “plastic-damage model”

Abstract In this paper a plastic damage model for nonlinear finite element analysis of concrete is presented. The model is based on standard plasticity theory for frictional materials. Details of the expressions of a new yield function proposed and of the evolution laws of the model parameters are given. The model allows to include elastic and plastic stiffness degradation effects. This is also discussed in the paper together with the problem of mesh objectivity, and the a posteriori determination of cracks. Finally, one example of application which shows the accuracy of the model is also given.

A plasticity model for simulation of industrial powder compaction processes

A constitutive model, based on large strain plasticity, for simulation of industrial powder compaction processes is presented. The elastic response is stated in terms of a hyperelastic model based on a hookean elastic free energy. Plastic response is defined in terms of a two parameter yield surface that evolves in terms of the relative density. Two different flow rules are considered and tested in front of some available experimental results. Application to the simulation of an actual powder-metallurgy compaction process is also shown.

An anisotropic elastoplastic constitutive model for large strain analysis of fiber reinforced composite materials

In this work a generalized anisotropic elastoplastic constitutive model for the large strain analysis of fiber-reinforced composite materials in the frame of the mixing theory and the finite element method is presented. The isotropic equivalent formulation proposed assumes the existence of a fictitious isotropic space where a mapped fictitious problem is solved. Both real anisotropic and fictitious spaces are related by means of linear fourth-order transformation tensors that contain the complete information about the real anisotropic material. Details of the numerical implementation of the model into a non-linear or large strain finite element solution scheme are provided. Application examples showing the performance of the model for analysis of fiber reinforced composite materials are given.

VISCOUS DAMAGE MODEL FOR TIMOSHENKO BEAM STRUCTURES

Abstract A local damage constitutive model based on Kachanovs theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one of them compares results obtained by using the proposed model with results of a laboratory test.

A general framework for continuum damage models. I. Infinitesimal plastic damage models in stress space

We identify in this paper a general framework for the development of continuum damage models in their fully coupled plastic damage form. The focus of this paper is directed to the general formulation of infinitesimal models defined by yield and damage surfaces in stress space. The main feature of the proposed formulation is the direct and independent consideration of the damage mechanisms (isotropic damage, cracking, etc.) degrading the stiffness of the material, thus allowing for a complete physical characterization of these effects. This modular structure is accomplished by a kinematic decomposition of the strains in an elastic, plastic and multiple damage parts, as belonging to each activated damage mechanism. An additive decomposition in the infinitesimal range of interest is considered. Based on this decomposition, the constitutive characterization alluded to above for each damage mechanism is carried out in a complete thermodynamically consistent framework. One of the virtues of the considered framework is the fact that it includes many of the diverse damage models existing in the literature as particular cases. In this way, the developments presented herein furnish a unified framework for the formulation of continuum damage models, including isotropic damage, compliance based formulations, effective stress anisotropic models, smeared crack models and the related formulations of cracking and damage based on strong discontinuities. Besides the clear physical significance added to these existing formulations, the proposed framework also defines a very convenient context for the efficient numerical integration of the resulting models. This aspect is explored in Part II of this work, as it is the application of the framework proposed herein to the numerical simulation of porous metals.

A plastic damage constitutive model for composite materials

In this paper a generalized elasto-plastic damage model for the analysis of multiphase frictional composite materials is presented. Details of the derivation of the secant and tangent constitutive equations are given. Mixing theory is used to insert the basic constitutive expressions for each substance on the multiphase composite solid. Details of the numerical implementation of the model into a general non-linear finite element solution scheme are presented. Some examples of linear and non-linear behaviour of composites are given.

Definition of a general implicit orthotropic yield criterion

The definition of an orthotropic yield criterion presents a serious challenge in the formulation of constitutive models based on such theories as elastoplasticity, viscoplasticity, damage, etc. The need to model the behavior of a real orthotropic material requires the formulation of orthotropic yield criteria, and these may be difficult to obtain. For metals, orthotropic yield functions have been formulated by Hill [Proc. Roy. Soc. Lon. Ser. A 193 (1948) 281; J. Mech. Phys. Solids 38(3) (1990) 200], Barlat [Int. J. Plasticity 5 (1989) 51; 7 (1991) 693], Chu [NUMISHEET 93 (1993) 199] and Dutko et al. [Comput. Methods Appl. Mech. Engrg. 109 (1993) 73], but in many cases these functions do not describe the true behavior of the metal. The situation is worse when one attempts to represent a nonmetal such as a polymer, ceramic or composite. In this paper, we present a general definition of an explicit orthotropic yield criterion together with a general method for defining implicit orthotropic yield functions. The latter formulation is based on the transformed-tensor method, whose principal advantage lies in the possibility of adjusting an arbitrary isotropic yield criterion to the behavior of an anisotropic material. As example we choose the adjustment to the Hill, Hoffman [J. Comp. Materials 1 (1967) 200] and Tsai–Wu [J. Comp. Materials 5 (1971) 58] criteria, but these particular cases serve to establish the methodology for achieving the desired function adjustment for any other well-known criterion or experimental set of data obtained from laboratory.

A directional damage model

A directional damage model for initially isotropic metals and geomaterials is presented in this paper. The model is based on a space transformation using an analogy with the theory of finite strains. As a result, damage is defined by a second order damage tensor. The basic equations of the model are derived from the thermodynamics of irreversible processes. A return-mapping algorithm is developed for the numerical integration of the model. Applications examples presented show that the model is able to reproduce damage-induced anisotropy, with directional stiffness degradation and hardening, under general loading conditions.