D. Perić

Design of simple low order finite elements for large strain analysis of nearly incompressible solids

A simple four-node quadrilateral and an eight-node hexahedron for large strain analysis of nearly incompressible solids are proposed. Based on the concept of deviatoric/volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart, the formulation developed is applicable to arbitrary material models. The closed form of the corresponding exact tangent stiffnesses, which have a particularly simple structure, is derived. It ensures asymptotically quadratic rates of convergence of the Newton-Raphson scheme employed in the solution of the implicit finite element equilibrium equations. From a practical point of view, the incorporation of the proposed elements into existing codes is straightforward. It requires only small changes in the routines of the standard displacement based 4-node quadrilateral and 8-node brick. A comprehensive set of numerical examples, involving hyperelasticity as well as multiplicative elasto-plasticity, is provided. It illustrates the performance of the proposed elements over a wide range of applications, including strain localisation problems, metal forming simulation and adaptive analysis.

Continuum modelling and numerical simulation of material damage at finite strains

SummaryThis paper describes in detail a general framework for the continuum modelling and numerical simulation of internal damage in finitely deformed solids. The development of constitutive models for material deterioration is addressed within the context of Continuum Damage Mechanics. Links between micromechanical aspects of damage and phenomenological modelling within continuum thermodynamics are discussed and a brief historical review of Continuum Damage Mechanics is presented. On the computational side, an up-to-date approach to the finite element solution of large strain problems involving dissipative materials is adopted. It relies on an implicit finite element discretization set on the spatial configuration in conjunction with the full Newton-Raphson scheme for the iterative solution of the corresponding non-linear systems of equations. Issues related to the numerical integration of the path dependent damage constitutive equations are discussed in detail and particular emphasis is placed on the consistent linearization of associated algorithms. A model for elastic damage in polymers and finite strain extensions to Lemaitres and Gursons models for ductile damage in metals are formulated within the described framework. The adequacy of the constitutive-numerical framework for the simulation of damage in large scale industrial problems is demonstrated by means of numerical examples.

A new computational model for Tresca plasticity at finite strains with an optimal parametrization in the principal space

Abstract A new computational model for the rate-independent elasto-plastic solids characterized by yield surfaces containing singularities and general nonlinear isotropic hardening is presented. Within the context of fully implicit return mapping algorithms, a numerical scheme for integration of the constitutive equations is formulated in the space of principal stresses. As a direct consequence of the principal stress approach, the representation of a yield surface is cast in terms of ‘optimal’ parameterization, which for the Tresca yield criterion takes a simple linear form. The associated return mapping equations then reduce to a remarkably simple format. In addition, due to assumed isotropy of the models, the associated algorithmic (incremental) constitutive functionals can be identified as particular members of a class of isotropic tensor functions of one tensor in which the function eigenvalues are expressed in terms of the eigenvalues of the argument. This observation leads to a simple closed form derivation of the consistent tangent moduli associated with the described integration algorithms. The extension of the present model to finite strains is carried out following standard multiplicative plasticity described in terms of logarithmic stretches and exponential approximation to the flow rule. The efficiency and robustness of the computational model are illustrated on a range of numerical examples.

A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces: computational issues

Abstract In order to further enhance the performance of the space-time Galerkin/least-squares method for solving incompressible Navier–Stokes problems involving free surfaces, issues related to the solution strategy and time adaptivity are addressed . Due to the a priori unknown boundary positions, a nonlinear system of equations normally arises at each space-time slab, which is solved by the Newton–Raphson approach . In addition, a linear system of equations for velocity and pressure that provides an alternative approach to the solution of the problem is also derived in this paper. This linear solution scheme can significantly reduce the computational costs in terms of computer CPU time and memory requirements without the sacrifice of the solution accuracy if the time-step size is sufficiently small. Furthermore, the possibility of adaptively adjusting time-step size is fully exploited. By choosing the volume loss rate as an error indicator, a simple adaptive time-stepping scheme is presented. Finally several numerical examples are provided to assess the performances of the proposed schemes.

Finite element simulation of the rolling and extrusion of multi-phase materials Application to the rolling of prepared sugar cane

Abstract This paper descrbes a general framework for the finite element simulation of the rolling and extrusion of multi-phase materials. Emphasis is placed on the following aspects: The characterization of the coupling between the liquid and solid phases of the material; The modelling of the (highly nonlinear) behaviour of the solid skeleton; The adaptive mesh refinement strategy, required in view of the magnitude of the strains and complex deformations involved in the processes; The use of an efficient contact algorithm and; The inverse identification of material parameters for the solid phase by means of ‘numerical experiments’. Practical application of the developed framework is made to the numerical simulation of the process by which juice is extracted from prepared sugar can by rolling.

On Computational Homogenisation of Heterogeneous Media with Debonded Inclusions

Modelling of weak interfaces is an important area of micro-mechanics, as many macroscopic phenomena are linked to the behaviour at the interfaces at different scales. In this work a computational homogenization procedure is used in constitutive description of heterogeneous media with debonded inclusions. More specifically, the objective is to determine the yield surface of an RVE that contains a fully debonded inclusion embedded within ideally plastic matrix, whereby the interface is modelled by a Coulomb type friction law. The macroscopic behaviour of the RVE is shown to coincide, in the limit cases, with the behaviour of material with voids for tensile loading conditions, whereas for compressive loading conditions, it is shown to approach the behaviour of material with fully bonded inclusions.

On Computational Procedures for Multi-Scale Finite Element Analysis of Inelastic Solids

This work is concerned with issues related to computational procedures for a family of multi-scale constitutive models, based on the volume averaging of stress and strain (or deformation gradient) tensors over a representative volume element (RVE). The computational model relies on a variational framework for multi-scale analysis of solids, which leads to a compact direct numerical procedure within fully coupled two-scale displacement based finite element environment. A particular attention is given to the techniques for efficient computational implementation of multi-scale modelling framework, and, in this context, some recently developed computational procedures are discussed. A numerical example is presented in order to illustrate the scope and benefits of the developed strategy.