E.A. de Souza Neto

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 phenomenological three-dimensional rate-idependent continuum damage model for highly filled polymers: Formulation and computational aspects

Abstract A three-dimensional rate-independent model for damage in highly filled polymers is presented. The model generalizes the one-dimensional theory proposed by Gurtin and Francis [(1981) Simple rate-independent model for damage. J. Spacecraft 18 (3), 285–286] to describe the behaviour of highly filled solid propellants. The objective is to simulate the Mullins effect observed when these materials are subjected to alternate loading. A simple algorithm for integration of the proposed constitutive equations is presented, which is formulated in terms of principal directions. A closed form of the spatial tangent modulus for two-dimensional applications is derived. This provides the basis for the Newton-Raphson iterative scheme for solution of the associated incremental boundary value problem. The suitability of the proposed model to large scale computations is demonstrated by means of finite element simulations.

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.

An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization

This paper is concerned with characterizing the quasistatic mechanical behaviour of arterial tissue undergoing finite deformation through hyperelastic constitutive functions. Commonly the parameters of constitutive functions are established by a process of optimization based on experimental data. Instead we construct a finite element model of a representative volume element of the material and compute its homogenized response to a range of deformations. These data are then used to provide objective functions for optimizing the parameters of two analytical models from the literature.

Remarks on symmetry conditions in computational homogenisation problems

Purpose – The purpose of this paper is to use symmetry conditions for the reduction of computing times in problems involving finite element‐based multi‐scale constitutive models of nonlinear heterogeneous media.Design/methodology/approach – Two types of representative volume element (RVE) symmetry often found in practice are considered: staggered‐translational and point symmetry. These are analyzed under three types RVE of kinematical constraints: periodic boundary fluctuations (typical of periodic media), linear boundary displacements (which gives an upper bound for the macroscopic stiffness) and the minimum kinematical constraint (corresponding to uniform boundary tractions and providing a lower bound for the macroscopic stiffness).Findings – Numerical examples show that substantial savings in computing times are achieved by taking advantage of such symmetries. These are particularly pronounced in fully coupled two‐scale analyses, where the macroscopic equilibrium problem is solved simultaneously with a...

The exact derivative of the exponential of an unsymmetric tensor

An exact series representation for the derivative of the exponential of a generic unsymmetric tensor is derived. The computer implementation of the derived formula is straightforward and allows the computation of the derivative of the tensor exponential to any desired degree of accuracy. In practice, the accuracy of the computed derivatives will be limited by machine precision. The application of the proposed formula to the numerical treatment of anisotropic rate-dependent and rate-independent finite single crystal plasticity is outlined.

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.

A phenomenological model for frictional contact accounting for wear effects

A simple phenomenological model for frictional contact accounting for wear effects is proposed. The objective is the numerical simulation of the frictional behaviour of contacting bodies subjected to large sliding distances and variable normal pressures. Within the context of thermodynamics with internal variables, the friction coefficient is assumed to be a function of the density of frictional work resulting in a theory analogous to classical work hardening elastoplasticity. The technique for experimental identification of the proposed model, applied to sheet materials, is described and the material parameters for some steel sheets commonly used in industry are determined. The framework for the computer simulation of the model in large scale problems is based on a fully implicit finite-element scheme and the Newton-Raphson method. A robust algorithm based on an operator split method (elastic predictor-frictional sliding corrector) is used for numerical integration of the friction constitutive equations. The simulation of a series of sliding tests is carried out and the results are compared with experiments.

A phenomenological model for frictional contact of coated steel sheets

A simple phenomenological model for frictional contact with hardening is proposed. The objective is to simulate the frictional behaviour of coated steel sheets subjected to large sliding distances. Within the context of thermodynamics with internal variables, the friction coefficient is assumed to be a function of the frictional work resulting in a theory analogous to classical work-hardening elastoplasticity. The technique for experimental identification of the proposed model is described briefly and the material parameters obtained for Electrogalvanised steel sheet and BAF Al-killed steel sheet are presented. Within the computational scheme, a robust algorithm based on an operator split method (elastic predictor-frictional sliding corrector) is used for numerical integration of the friction constitutive equations. The finite-element simulation of a series of sliding tests is carried out and the results are compared with experiments.