Implicit scheme of RVE calculation for FCC polycrystals

Considering the coupling effect between the nodal force equilibrium and internal variables evolution, an implicit scheme of solving the non-linear FEM problem is presented to modelling the texture evolution and the anisotropic behaviour of polycrystals for large deformation. This algorithm is based on the isomorphism theory that the current elastic law can be achieved through transferring the reference elastic law by a plastic transformation. Different time steps have been adopted with respect to the global and local iteration systems and the consistent tangent module is also calculated to construct a high speed integration algorithm.     

Viscoelastic analysis of a polyurethane thermosetting resin under relaxation and at constant compression strain rate

The evolution of the viscoelastic behaviour of a polyurethane resin was investigated on the basis of uniaxial compression tests in stress relaxation and at constant strain rate. Both methods were applied to PUR specimens whose curing cycle was interrupted at different steps. The experimental data were precisely modelled in terms of a three-parameter constitutive equation whose general form was derived from the Kohlrausch relaxation law. The viscoelastic behaviour was followed during the cross-linking process and during the final cooling ramp. A close correlation was found between the degree for cross-linking and the elastic modulus increase during the curing period. Furthermore, it was stated that the evolution of the viscoelastic parameters during the cooling phase describes in a quantitative way the construction of the glassy behaviour and that it controls the development of internal stresses in PUR mouldings.     

A model for process-based crash simulation

Manufacturing of a bumper system from aluminium extrusions often involves series of forming operations performed in the soft W-temper condition, and then artificially age-hardening of the components to the material's peak hardness T6 condition. It is probable that proper finite element (FE) modelling of the crash performance of the resulting systems must rely upon a geometry obtained from an FE model following the process route, i.e., including simulation of all major forming operations. The forming operations also result in an inhomogeneous evolution of some internal variables (among others the effective plastic strain) within the shaped components. Results from tensile tests reveal that plastic straining in W-temper leads to a significant change of the T6 work-hardening curves. In addition, the tests show that the plastic pre-deformation causes a reduction of the elongation of the T6 specimens. In the present work, these process effects have been included in a user-defined elastoplastic constitutive model in LS-DYNA incorporating a state-of-the-art anisotropic yield criterion, the associated flow rule and a non-linear isotropic work hardening rule as well as some ductile fracture criteria. A first demonstration and assessment of the modelling methodology is shown by ‘through-process analysis’ of two uniaxial tensile test series. The industrial use and relevance of the modelling technique is subsequently demonstrated by a case study on an industrial bumper beam system.     

A model for anisotropic viscoelastic damage in composites

A model for continuous damage combined with viscoelasticity is proposed. The starting point is the formulation connecting the elastic properties to the tensor of damage variables. A hardening law associated with the damage process is identified from available experimental information and the rate-type constitutive equations are derived. This elastic damage formulation is used to formulate an internal variable approximation to viscoelastic damage in the form of a non-linear Kelvin chain. Elastic and viscoelastic equations are implemented into a finite element procedure. The code is verified by comparison with closed-form solutions in simplified configurations, and validated by fitting results of experimental creep tests.     

Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

Technological forming processes of thermo-elastoviscoplastic solids are numerically simulated via finite elements based on an appropriate theoretical framework. Departing from the local balance laws of linear momentum and internal energy, the constitutive behaviour is introduced via the concept of ‘generalized standard materials (gsm)’, where a thermodynamic potential and a dissipation potential are the only two scalar quantities needed. They are expressed in invariants of symmetric mixed-variant tensors, respectively. Then the dissipation term evolves from the thermodynamic potential in a very natural way as well as the evolution equations for the internal variables emanate from the dissipation potential. An Eulerian setting is used. The numerical solution (of the non-linear coupled thermomechanical problem) is carried out via ‘displacement and assumed enhanced displacement-gradient’-based finite ring-elements in an ‘isentropic’ mechanical phase and via ‘temperature’-based finite ring-elements in an isogeometrical thermal phase and a global Newton–Raphson iterative method in both phases, respectively. The coupled consistent tangent moduli are carefully derived. Numerical results of the thermally triggered necking of a circular bar and of the impact of a copper rod on a rigid wall are given. © 1998 John Wiley & Sons, Ltd.     

Generalized midpoint finite element dynamic analysis of elastoplastic systems

The application of a four-parameter generalized midpoint integration method to small-displacement elastoplastic dynamic problems is considered. The integration of the governing relations over a time step is formulated as a non-linear algebraic problem (finite-step problem) by making use of generalized variables finite element modelling. Uniqueness and an extremum characterization of the solution of the finite-step problem are discussed. Sufficient conditions for convergence of various iterative algorithms, including Newton-Raphson, are given. The B-stability of the proposed procedure is assessed.     

Finite element modelling of hardening concrete: application to the prediction of early age cracking for massive reinforced structures

This article presents finite element modelling to predict the early age cracking risk of concrete structures. It is a tool to help practitioners choose materials and construction techniques to reduce the risk of cracking. The proposed model uses original hydration modelling (allowing composed binder to be modelled and hydric consumption to be controlled) followed by a non-linear mechanical model of concrete at early ages involving creep and damage coupling. The article considers hydration effects on this mechanical model, which is based on a non-linear viscoelastic formulation combined with an anisotropic, regularized damage model. Details of the numerical implementation are given in the article and the model is applied successively to a laboratory structure and to a massive structure in situ (experimental wall of a nuclear power plant studied in the framework of the French national research project CEOS.fr).     

Some exactly solvable models for the statistical evolution of internal variables during plastic deformation

A class of exactly solvable statistical models for the evolution of internal (microstructural) variables in the course of plastic deformation is discussed. The common feature of these models is that the microstructural evolution is described in terms of stochastic differential equations (Langevin equations) which by a non-linear transformation can be mapped onto a Wiener or Ornstein–Uhlenbeck process. Examples include the textural evolution of planar polycrystals, the evolution of dislocation density distribution in unidirectional plastic deformation, and the combined dynamics of mobile dislocations and dislocation obstacles leading to slip-channel formation.     

Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach

This paper presents the development of a constitutive model able to accurately represent the full non-linear mechanical response of polymer-matrix fibre-reinforced composites with unidirectional (UD) plies under quasi-static loading. This is achieved by utilising an elasto-plastic modelling framework. The model captures key features that are often neglected in constitutive modelling of UD composites, such as the effect of hydrostatic pressure on both the elastic and non-elastic material response, the effect of multiaxial loading and dependence of the yield stress on the applied pressure.The constitutive model includes a novel yield function which accurately represents the yielding of the matrix within a unidirectional fibre-reinforced composite by removing the dependence on the stress in the fibre direction. A non-associative flow rule is used to capture the pressure sensitivity of the material. The experimentally observed translation of subsequent yield surfaces is modelled using a non-linear kinematic hardening rule. Furthermore, evolution laws are proposed for the non-linear hardening that relate to the applied hydrostatic pressure.Multiaxial test data is used to show that the model is able to predict the non-linear response under complex loading combinations, given only the experimental response from two uniaxial tests.     

Determination of shear modulus and Poisson's ratio of polymers and foams by the anticlastic plate-bending method

In this paper, results of research towards development of a test method for the determination of shear modulus and Poisson's ratio of polymers and structural foams are presented. Through this work, a test apparatus was developed which employed anticlastic plate bending behaviour; this device was used for calibration tests on steel and aluminium samples and for tests on a number of polymers, including high density Polyethylene (PE-HD), unplasticized Polyvinylchloride (PVC-U), Polymethylmethacrylate (PMMA) and rigid Polyurethane (PUR) foam. Long-term tests and temperature-dependent tests on PVC-U, PE-HD and PMMA samples were also performed. In some cases, results of the tests with the anticlastic bending method were compared with those obtained from tests carried out with the torsion pendulum method. For theoretical simulation, an analytical formula and a number of finite element analyses were performed. Through these simulations, values for the short-term, long-term and temperature-dependent shear modulus and Poisson's ratio of PE-HD, PMMA, PVC-U and PUR foam were obtained.     

Numerical analysis and experimental correlation of composite shell buckling and post-buckling

This paper deals with the buckling and post-buckling behaviour of carbon fibre reinforced plastic cylindrical shells under axial compression. The finite element analysis is used to investigate this problem and three different types of analysis are compared: eigenvalue analysis, non-linear Riks method and dynamic analysis. The effect of geometric imperfection shape and amplitude on critical loads is discussed. A numerical–experimental correlation is performed, using the results of experimental buckling tests. The geometric imperfections measured on the real specimens are accounted for in the finite element model. The results show the reliability of the method to follow the evolution of the cylinder shape from the buckling to the post-buckling field and good accuracy in reproducing the experimental post-buckling behaviour.     

Computational implementation of a novel constitutive model for multidirectional composites

This paper details the numerical implementation of a constitutive model for unidirectional (UD) polymer-matrix fibre-reinforced composites, which is able to accurately represent the full non-linear mechanical response. Features such as hydrostatic pressure sensitivity, the effect of multiaxial loading and the dependence of the yield stress on the applied pressure are often neglected in constitutive modelling, but are included in this model.The constitutive model includes a novel yield function, non-associative flow rule and a non-linear kinematic hardening rule. It is combined with suitable failure criteria and associated damage model. The complete model is implemented in an explicit finite element code.Experimental test data is used to show that the model is able to predict the non-linear response of both unidirectional and multidirectional composite laminates. The model is shown to accurately predict the constitutive response under complex multiaxial loading and unloading, including significant hydrostatic pressure. Predictions are also shown to compare favourably for the evolution of matrix cracking after initial matrix cracking is detected by the failure criteria.     

Governing equations for the steady state creep in orthotropic materials

Summary A general constitutive equation for creep deformation is presented based upon the concept of tensorial internal variables. The consequences of the theory of tensor functions representation are discussed with respect to the evolution equations. In a particular case of steady evolution of internal variables the governing equation for the secondary creep rate is derived in terms of a scalar inelastic potential. The material parameters required to characterize the stationary creep behaviour of the orthotropic composite are obtained from the unidirectional tension creep tests performed on a glass woven fabric xylok composite. Further check on the theory is made for the bidirectionally loaded specimens.With 4 Figures     

Concrete beams with externally bonded flexural FRP-reinforcement: analytical investigation of debonding failure

This paper studies the problem of early concrete cover delamination and plate-end failure of reinforced concrete beams strengthened with externally bonded FRP-reinforcement. The accuracy of analytical models and finite element (FE) methods for predicting this type of failure is assessed against published experimental data. Two design approaches based on the maximum concrete tensile strength and the shear capacity of concrete beams were examined first and it was found that linear elastic analysis cannot accurately predict the brittle plate-end concrete failure. It was also found that the extent of strengthening that can be achieved is limited by the shear capacity of concrete beams. The FE analysis is used to examine the effects of internal tensile reinforcement on the magnitude of principal tensile stresses in the critical region. The non-linear behaviour of FRP-strengthened beams is also examined in the FE analysis using the smeared crack model for concrete which is shown to adequately display the inelastic deformation of the beam. Finally, the mixed mode of failure due to the combined shear and concrete cover delamination is addressed through modelling plate-end and shear crack discontinuities using the discrete crack approach.     

Formulation and solution of the non-linear,damped eigenvalue problem for skeletal systems

This paper presents and discusses an Arnoldi-based eigensolution technique for evaluating the complex natural frequencies and mode shapes from frequency dependent quadratic eigenproblems associated with vibration analysis of damped structures. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices. This modelling provides the ability to represent a frequency dependent damping matrix in vibration analysis of skeletal systems. The eigensolution methodology presented here is based upon the ability to evaluate a specific set of parametrized curves for the non-linear eigenvalue problem at given values of the parameter. Numerical examples illustrate that this method, used in conjunction with a secant interpolation, accurately evaluates the complex natural frequencies and modes of the quadratic non-linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models.     

Cyclic stress-strain response during isothermal and thermomechanical fatigue

Isothermal high-temperature low-cycle fatigue and in-phase and out-of-phase thermomechanical fatigue tests were carried out on 316L austenitic stainless steel specimens controlled by computer. A non-linear kinematic hardening model with internal variables was used to simulate the cyclic stress-strain behaviour of isothermal fatigue. This model was modified by considering thermal cyclic effects in order to describe the cyclic stress-strain behaviour of thermomechanical fatigue (TMF) using only isothermal fatigue data and the material performance data. A very good approximation of the hysteresis loops was obtained by comparing with experiments of both in-phase and out-of-phase cases. The thermomechanical fatigue behaviour described by isothermal fatigue data gives the possibility of developing the TMF lifetime prediction technique.     

Motorcyclist helmet composite outer shell characterisation and modelling

In this study a new finite element model of composite outer shell of motorcyclist helmet is proposed, by modelling each layer of the composite material that builds the laminated structure of the outer shell of the helmet. Elastic and rupture properties of the laminate are taken into account for developing the finite element (FE) model and are extracted experimentally. A coupled experimental–numerical method combined with experimental modal analysis on beam samples is used to obtain the elastic characteristics of each layer of the outer shell. The rupture properties for each layer are extracted by experimental impact tests. The FE model of the outer shell is then validated with experimental data for elastic and rupture behaviour.     

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.     

Modelling of debonding between old concrete and overlay: fatigue loading and delayed effects

The paper focuses on the propagation of debonding along an interface between a substrate simulating old concrete and a cement-based thin bonded overlay. The aim of the study was to obtain the data necessary for relevant and efficient debonding modelling. The work combined experiment and simulation. Two types of overlay materials were investigated, fibre reinforced mortar (FRM) and plain mortar. Tensile tests were performed to obtain the residual normal stress–crack opening relationship. The shrinkage of the overlay material was characterized by tests on prismatic specimens that showed the evolution of both drying shrinkage and autogenous shrinkage versus time. The substrate—overlay interface was investigated by static tensile tests to provide the relationship between debonding opening and residual normal tensile stress. Its evolution under fatigue loading was assumed to follow a cyclic bridging law for plain concrete. Three-point flexural fatigue tests were then performed on repaired substrate to obtain information on the structural behaviour of the interface. The debonding propagation was monitored by a video-microscope with a magnification of 175× . Relying on the identified and quantified parameters, the above mentioned fatigue tests were modelled by the finite element method using the CAST3M code developed in France by Atomic Energy Commission (CEA). A comparison between model and experimental results shows good agreement and proves the important role of interlocking in the debonding mechanism.     

Numerical models of steady rolling for non-linear viscoelastic structures in finite deformations

A Lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented. These laws are expressed by a non-linear differential equation governing the evolution of an internal variable. Then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics. A finite element approximation and a solution technique of the algebraic system is proposed. The eiimination of the internal variable allows one to keep an elastic-like algorithm with an independent solution of the viscoelastic equation. Numerical tests show the feasibility and the efficiency of the proposed methods in large three-dimensional situations.