FE–BE Coupling Methods for Elastoplasticity

Non-linear physical systems of infinite extent are conveniently modelled using FE–BE coupling methods. By the combination of both methods, suitable use of the advantages of each one may be obtained. Several possibilities of FEM–BEM coupling and their performance in some practical cases are discussed in this paper. Parallelizable coupling algorithms based on domain decomposition are developed and compared with the most traditional coupling methods.

A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

Elastoplastic consolidation at finite strain. Part 2: finite element implementation and numerical examples

A mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. A two-field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations. The constitutive model for the solid phase is represented by modified Cam—Clay theory formulated in the Kirchhoff principal stress space, and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches. The constitutive model for fluid flow is represented by a generalized Darcy's law formulated with respect to the current configuration. The finite element model is fully amenable to exact linearization. Numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses. The paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability.

A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution

In this paper we present a continuum theory for large strain anisotropic elastoplasticity based on a decomposition of the modified plastic velocity gradient into energetic and dissipative parts. The theory includes the Armstrong and Frederick hardening rule as well as multilayer models as special cases even for large strain anisotropic elastoplasticity. Texture evolution may also be modelled by the formulation, which allows for a meaningful interpretation of the terms of the dissipation equation

A simplified model for evaluation of fatigue damage in frames

Many studies have been developed to analyze the structural seismic behavior through the damage index concept. The evaluation of this index has been employed to quantify the safety of new and existing structures and, also, to establish a framework for seismic retrofitting decision making of structures. Most proposed models are based in a posterthquake evaluation in such a way they uncouple the structural response from the damage evaluation. In this paper, a generalization of the model by Flórez-López (1995) is proposed. The formulation employs irreversible thermodynamics and internal state variable theory applied to the study of beams and frames and it allows and explicit coupling between the degradation and the structural mechanical behavior. A damage index es defined in order to model elastoplasticity coupled with damage and fatigue damage.

Fatigue damage modelling of steel structures

In the present work a constitutive model is developed which permits the simulation of the low cycle fatigue behaviour in steel framed structures. In the elaboration of this model, the concepts of the mechanics of continuum medium are applied on lumped dissipative models. In this type of formulation an explicit coupling between the damage and the structural mechanical behaviour is employed, allowing the possibility of considering as a whole different coupled phenomena. A damage index is defined in order to model elastoplasticity coupled with damage and fatigue damage.