Elasto-viscoplastic Problems Research Articles

Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods

In spite of some drawbacks, finite element methods based on nodal rather than Gaussian integration present major advantages, especially in the context of elastoplastic or elastoviscoplastic problems—notably the elimination of locking problems due the plastic or viscoplastic incompressibility condition, and the reduction of computation and storage requirements pertaining to internal variables. This paper investigates another potential advantage of such methods, namely the possibility to account exactly—instead of approximately like with Gaussian integration—for conditions of prescribed traction on external surfaces, and continuity of the traction-vector across internal interfaces separating different materials. The technique proposed is somewhat similar to that classically used to satisfy plane stress conditions in 2D elastoplastic problems: it consists, when using the constitutive law to evaluate the stresses from the strains, in adjusting the out-of-plane components of the strain, so as to enforce either identity of the traction-vector and its prescribed value on external surfaces, or identity of the traction-vectors on both sides of internal interfaces. The examples provided for both traction-free boundaries and interfaces between materials evidence the efficiency of the technique.

Optimal Control of Elastoviscoplastic Macro-Hybrid Mixed Variational Problems

Optimal control of quasistatic elastoviscoplastic macro-hybrid mixed set-valued variational problems are studied. Composition duality methods are the basis of their analysis, in evolution reflexive Banach field spaces. Macro-hybrid set-valued variational formulations, in terms of nonoverlapping multidomains, are the strategy for multi-physics as well as parallel computing. Perturbation conjugate duality results recently established by the author, provide dual macro-hybrid mixed optimality conditions, to which two- and three-field proximal penalty-duality algorithms are further established and analyzed.

Reduced order variational multiscale enrichment method for elasto-viscoplastic problems

This manuscript presents the formulation and implementation of a novel reduced order variational multiscale enrichment (ROVME) method for elasto-viscoplastic problems. This method provides a hierarchical model order reduction technique based on the eigenstrain concept to approximate the fine scale response resolved at subdomains of interest. By eliminating the requirement of direct fine scale discretization, the computational effort associated with the variational multiscale enrichment (VME) method is significantly reduced. The model order reduction is achieved in the scale-coupled inelastic problem by automatically satisfying the microscale equilibrium state through the eigenstrain concept and coarse discretization of inelastic strain fields within the microscale domain. The inelastic material behavior is idealized with coupled Perzyna type viscoplasticity and flow stress evolution based on the Johnson–Cook model. Numerical verifications are performed to assess the capabilities of the proposed methodology, against the direct VME method with detailed fine scale resolutions. The verification results demonstrate high accuracy and computational efficiency of the reduced order VME framework for elasto-viscoplastic problems with material heterogeneity.

Performance of an elasto-viscoplastic model in some benchmark problems

A recent elasto-viscoplastic thixotropic model proposed by (de Souza Mendes in J. Non-Newton. Fluid Mech. 164:66–75, 2009; de Souza Mendes in Soft Matter 7:2471–2483, 2011) is applied to five benchmark problems: the flow in a lid cavity, the flow through an expansion followed by a contraction, the flow over a flat plate, the channel entry flow, and the flow around a cylinder confined between parallel plates. One of the main advantages of this approach is its ability to recover a model for elasto-viscoplastic materials in a smooth fashion, i.e., in the limit where the characteristic thixotropic time tends to zero. These problems are numerically solved using the finite element method, with a four-field GLS-type formulation. While the simplified version is applied to the first three problems, the full model including thixotropy is applied to the channel entry flow and the flow around the cylinder. The elasto-viscoplastic problems analyzed show that, in general, elasticity tends to inhibit yielding and is more concentrated in unyielded regions. The thixotropic effects analyzed show that the delay in the microstructure response of the material significantly alters the problem when compared to the pure elasto-viscoplastic counterpart.

Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity

We propose an a posteriori estimator of the error of hyper-reduced predictions for elastoviscoplastic problems. For a given fixed mesh, this error estimator aims to forecast the validity domain in the parameter space, of hyper-reduction approximations. This error estimator evaluates if the simulation outputs generated by the hyper-reduced model represent a convenient approximation of the outputs that the finite element simulation would have predicted. We do not account for the approximation error related to the finite element approximation upon which the hyper-reduction approximation is introduced. We restrict our attention to generalized standard materials. Upon use of incremental variational principles, we propose an error in constitutive relation. This error is split into three terms including a tailored norm of the hyper-reduction approximation error. This error norm is defined by using the convexity of an incremental potential introduced to state the constitutive equations. The second term of the a posteriori error is related to the stress recovery technique that generates stresses fulfilling the finite element equilibrium equations. The last term is a coupling term between the hyper-reduction approximation error at each time step and the errors committed before this time step. Unfortunately, this last term prevents error certification. In this paper, we restrict our attention to outputs extracted by a Lipschitz function of the displacements. In the proposed numerical examples, we show very good preliminary results in predicting the validity domain of hyper-reduction approximations. The average computational time of the predictions obtained by hyper reduction, is accelerated by a factor of 6 compared to that of finite element simulations. This speed-up incorporates the computational time devoted to the error estimation. The numerical implementation of the proposed error estimator is straightforward. It does not require the computation of the incremental potential. In the numerical results, the estimated validity domain of hyper-reduced approximations is inside the reference validity domain. This paper is a first attempt for a posteriori error estimation of hyper-reduction approximations.

Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problems

This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global---local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson---Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.

Composition duality methods for quasistatic evolution elastoviscoplastic variational problems

Composition duality methods for dual quasistatic evolution elastoviscoplastic variational problems are studied. Dual evolution mixed analysis is performed, as well as corresponding primal static mixed analysis. For multi-constitutive modeling and parallel computing, macro-hybrid variational formulations are further considered at the continuous level.

Multi-level A Priori Hyper-Reduction of mechanical models involving internal variables

This paper concerns the adaptation of reduced-order models during simulations of series of elastoviscoplastic problems. In continuation with previous works, this paper aimed at extending the A Priori Hyper-Reduction method (APHR method) for nonlinear thermal problems to nonlinear mechanical problems involving internal variables. This method is an a priori approach because full incremental responses of detailed models are not forecasted in order to build reduced-order models. The recent extension of the Hyper-Reduction method to reduction of mechanical models involving internal variables makes possible the reduction of degrees of freedom and the reduction of integration points. A multi-level formulation is introduced to focus on the capability of the method to perform efficient parallel computations to adapt reduced-order models.

Ductile damage and fracture finite element modelling of elasto-viscoplastic voided materials

Micro-structure void volume fraction is taken into account with finite element models developed for high strain rate elasto-viscoplastic problems. Void nucleation rate depends on matrix effective strain rate, void growth on material strain rate and elasto-viscoplastic potential proposed for porous material, void coalescence on matrix effective plastic strain rate and ductile fracture on critical void volume fraction. A radial return algorithm is proposed for the implementation into explicit finite element frameworks. Reference finite element modelling of ductile damage increases and fracture occurrence is performed for high-speed upsetting of steel multi-tubular.

A mixed hybrid FE formulation for solution of elasto-viscoplastic problems

A mixed/hybrid FE formulation for the solution of elasto-viscoplastic problems under dynamic loading conditions is presented. The constitutive equations under considerations are those of Chaboche. The spatially semi-discretized system of ordinary differential equations is numerically integrated in time by means of a midpoint type algorithm. A layer-model is developed which enables the application of the proposed methods in shell or plate theory. Numerical examples demonstrate the efficiency of the proposed method.

Finite element crack growth algorithm for dynamic fracture

A new finite element crack growth algorithm has been developed to simulate dynamic fracture. In this algorithm, pseudo elements with very high initial density are placed below the crack plane and the density is reduced to zero in a gradual manner as the crack passes the element. A number of linear elastic and elasto-viscoplastic problems have been carried out to test the new algorithm. The results are compared with some of the existing crack growth models.

A mixed/hybrid FE formulation for solution of elasto-viscoplastic problems

A mixed/hybrid FE formulation for solution of elasto-viscoplastic problems

Method for Solving Inverse Elastoviscoplastic Problems

The solution of transient inverse elastoviscoplastic deformation problems is the topic of this paper. The inverse problems described here involve solving for boundary tractions and displacements given only approximate measurements of displacements at internal points to the body. A finite element formulation for the solution of these inverse problems, in conjunction with the regularization and future‐time methods, is presented here. Several one‐dimensional examples are given to demonstrate the method and to investigate the effect of various parameters on the solution.

Implicit-explicit time integration in quasistatic elastoviscoplasticity using finite and infinite elements

An implicit-explicit time integration technique is employed to obtain economic solutions for quasistatic elastoviscoplastic problems in which the multimaterial domain defines regions of very different permissible time step lengths. Such situations arise currently in composite material analysis and soil-structure interaction problems. Geotechnical applications of the finite element method also involve, very often, unbounded domains where the far regions are commonly truncated in the process of mesh definition. Infinite and finite elements are associated here for an accurate and realistic modelling of such boundary conditions.

Strain hardening representation for implicit quasistatic elasto-viscoplastic algorithms

Time integration processes for the solution of elasto-viscoplastic problems are briefly reviewed. For materials which strain harden, additional terms which arise from the variation in yield level occurring during a time increment are included in the expression of the viscoplastic strain rate. The influence of these additional terms is discussed and illustrated by the solution of numerical examples.