Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.     

Strain rate dependent constitutive behavior investigation of AerMet 100 steel

AerMet 100 exhibits excellent mechanical properties with both high yield strength and excellent ductility. Understanding the dynamic mechanical behavior of the material should clear the road for wider application of AerMet 100 as critical mechanical parts serving in extreme mechanical conditions. In this paper, the strain rate dependency of AerMet 100 is investigated by using Split-Hopkinson pressure bar (SHPB) and also compared with its quasi-static counterpart. Based on the experiment results, a simplified Johnson–Cook model is established to describe the strain rate dependent behaviors and is proved to perform better than Cowper–Symonds model. The validation of the suggested constitutive model is embedded in the finite element analysis and can well repeat the strain wave observed from experiment results. Furthermore, the impact fracture toughness of AerMet 100 is also studied both numerically and experimentally. Finally, a thin-walled tube made of AerMet 100 is numerically simulated and the excellent crashworthiness is proven. Results may enlighten the understanding of dynamic mechanical behavior of AerMet 100 and provide fundamental experiment data for its future engineering applications.     

2024-T3铝合金动力学实验及其平板鸟撞动态响应分析

通过电子万能试验机和分离式霍普金森拉杆（SHTB）拉伸试验分别获得2024-T3铝合金材料准静态和高应变率两种应变率下的应力-应变曲线。铝合金材料的本构关系由能够反映材料硬化效应和应变率强化效应的Johnson-Cook材料模型描述,方程中的4个参数通过不同应变率下的应力-应变曲线拟合得到。基于瞬态动力学软件PAM-CRASH,结合材料动态力学性能试验所获得的2024-T3铝合金Johnson-Cook模型方程,耦合光滑粒子流体动力学（SPH）方法和有限元（FE）方法建立2024-T3铝合金平板的鸟撞数值模型,数值计算所得动态响应与鸟撞试验结果吻合较好,表明建立的鸟撞数值计算模型是合理、可靠的,整个分析流程从材料动态力学性能试验、鸟撞数值计算到最终的鸟撞试验验证为飞机结构的抗鸟撞设计与分析提供了有力的参考。     

On the characterisation of transverse tensile properties of molten unidirectional thermoplastic composite tapes for thermoforming simulations

The development of Finite Element (FE) thermoforming simulations of tailored thermoplastic blanks, i.e. blanks composed of unidirectional pre-impregnated tapes, requires the characterisation of the composite tape under the same environmental conditions as forming occurs. This paper presents a novel approach for the characterisation of transverse tensile properties of unidirectional thermoplastic tapes using a Dynamic Mechanical Analysis (DMA) system in a quasi-static manner. The relevance of the presented method is assessed by testing, under the same environmental conditions, a control material with both a universal testing machine and a DMA system. For simulation purposes, a unidirectional thermoplastic tape is characterised under environmental forming conditions using the presented test method. Experimental results, which include stress–strain behaviour and transverse viscosity, are eventually used to identify, via an inverse approach, simulation parameters of a thermo-visco-elastic composite material model (MAT 140, PAM-Form, ESI Group). Comparisons between simulated and experimental results show good agreement.     

Numerical finite element formulation of the Schapery non‐linear viscoelastic material model

This study presents a numerical integration method for the non‐linear viscoelastic behaviour of isotropic materials and structures. The Schapery's three‐dimensional (3D) non‐linear viscoelastic material model is integrated within a displacement‐based finite element (FE) environment. The deviatoric and volumetric responses are decoupled and the strain vector is decomposed into instantaneous and hereditary parts. The hereditary strains are updated at the end of each time increment using a recursive formulation. The constitutive equations are expressed in an incremental form for each time step, assuming a constant incremental strain rate. A new iterative procedure with predictor–corrector type steps is combined with the recursive integration method. A general polynomial form for the parameters of the non‐linear Schapery model is proposed. The consistent algorithmic tangent stiffness matrix is realized and used to enhance convergence and help achieve a correct convergent state. Verifications of the proposed numerical formulation are performed and compared with a previous work using experimental data for a glassy amorphous polymer PMMA. Copyright © 2003 John Wiley & Sons, Ltd.     

Assessment of different ductile damage models and experimental validation

The tough fuel economy and emissions standards facing automotive industry creates the need for lightweight construction and the use of new generation of materials. However, the use of non-conventional materials leads to difficulties in the prediction of material behaviour during sheet metal forming processes, including damage and formability limits, thus challenging the numerical simulation. This paper seeks to contribute in the prediction of fracture on sheet metal alloys. Three constitutive damage models are used, GTN, Johnson Cook and Lemaitre, to simulate, as realistically as possible, the mechanical behaviour of the sheet metal material. The corresponding parameters of damage models are identified using an inverse analysis procedure, based on experimental test data. Finally, to validate and verify the applicability of the studied damage models to predict fracture, experiments are compared with FE simulations.     

Modelling impact response of agglomerated cork

Cellular materials have been intensively used in engineering applications where a good energy absorption capability is a desired feature. Cork is a natural cellular material capable of absorbing considerable amounts of energy. When compared to synthetic cellular materials, cork also appears as a sustainable alternative, once it is fully recyclable. The purpose of this work is to simulate cork’s compressive behaviour when subjected to impact, including the material’s relaxation after dynamic compression. This study comprises experimental and numerical tests at quasi-static and dynamic strain rates under axial compressive loading. Numerical simulations are performed using Finite Element Analysis, and the material model developed is validated against experimental results. After validation, a dynamic test resorting to a drop tower is carried out successfully validating the model and representing adequately cork’s mechanical behaviour under dynamic compressions.     

Seismic performance of precast concrete frames with debonded reinforcement

This paper utilizes experimental and numerical studies to investigate the seismic behavior of precast concrete frames. The system is composed of monolithic columns and composite precast concrete beams with debonded reinforcement at the beam end, with the purpose of distributing plasticity over a larger rebar length to improve the seismic performance of traditional precast concrete frames. Two half scale precast concrete frames, with and without debonded rebar, were tested under quasi-static cyclic lateral load. The observations during the test, load–displacement curves, stiffness, energy dissipating capacity and rebar strain are discussed. The experimental findings demonstrate that rebar debonding lead to reduced strain in tensile reinforcement. The decrease in strain due to the debonded rebar was 40.2% at a drift ratio of 1%. The performance of the specimens was evaluated according to ACI 374, which demonstrates that this precast system is applicable to seismic regions. In the numerical simulation study, a macro-based finite element (FE) model was developed using fiber-section beam-column element with a modified rebar constitutive model to take into account the effect of rebar buckling. The feasibility of the FE model was verified by comparing with the experimental data.     

Axial collapse of hybrid square sandwich composite tubular components with corrugated core: numerical modelling

The present paper is dealing with the implementation of the explicit FE Code LS-DYNA to the simulation of the crash behaviour and energy absorption characteristics of thick-walled square tubular crashworthy components made of hybrid sandwich material with corrugated core subjected to axial compressive loading. The obtained numerical results are compared with actual experimental data from small-scale models in terms of deformation modes, energy absorption capability, load/deflection history and crush zone characteristics, showing very good agreement.     

Numerical implementation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers

Due to their high deformation capabilities, polymeric materials are widely used in several industries. However, polymers exhibit a complex behaviour with strain rate, temperature and pressure dependencies. Numerous constitutive models were developed in order to take into account their specific behaviour. Among these models, the ones proposed by Richeton et al Polymer 46:6035–6043 (2005a), Polymer 46:8194–8201 (2005b) seem to be particularly suitable. They proposed expressions for the Young modulus and the yield stress with strain rate and temperature dependence. Moreover, these models were also implemented in a finite elastic-viscoplastic deformation approach using a flow rule based on thermally activated process. The increase of computational capabilities allowed simulating polymer forming processes using finite element (FE) codes. The aim of the study is to implement the proposed constitutive model in a commercial FE code via a user material subroutine. The implementation of the model was verified using compressive tests over a wide range of strain rates. Next, FE simulations of an impact test and of a plane strain forging process were carried out. The FE predictions are in good agreement with the experimental results taken from the literature.     

Numerical investigation of concrete subjected to high rates of uniaxial tensile loading

The present article is concerned with the response of structural concrete prisms to high rates of uniaxial tensile loading. The numerical investigation carried out is based on a finite-element (FE) program capable of carrying out three-dimensional (3D) nonlinear static and dynamic analyses. This program is known to yield realistic predictions to the response of a wide range of plain- and reinforced-concrete structural forms subjected to arbitrary static and earthquake actions. Furthermore, its application has recently been successfully extended in predicting the response of plain-concrete prism elements under high rates of uniaxial compressive loading. The main feature of the FE program is that it incorporates a 3D material model which is characterized by both its simplicity and its attention to the actual physical behaviour of concrete in a structure. Its analytical formulation is based on the assumption that the material properties of concrete are independent of the applied loading rate (strain rate) thus attributing the effect of the applied loading rate on the prism's response to inertia. The validation of this assumption is based on a comparative study between numerical and experimental data which reveals good agreement. This constitutes a major departure from current thinking as regards material modelling of concrete under high-rate loading. In addition, the available data (numerical and experimental) show that the response of the concrete prism elements depends on a number of parameters linked to geometry and material properties of the structural forms under investigation as well as the testing method adopted. This dependence explains, to a significant extent, the scatter that characterizes the available experimental data, and it also suggests that both experimental and numerical results describe structural rather than material behaviour thus raising questions regarding the validity of the use of such data in the constitutive modelling of concrete-material behaviour under high-rate loading conditions.     

Mechanical response of a soft rubber compound compressed at various strain rates

Rate-dependent material constitutive behavior models are needed in numerical simulations of shock-mitigation structures. In this research, compressive stress–strain response of a soft rubber compound is obtained experimentally at quasi-static, intermediate and high strain rates under uniaxial-stress and uniaxial-strain loading states. Kolsky bars with modifications for characterizing soft materials and a long Kolsky bar are used to conduct the dynamic experiments, while an MTS load frame is used for conducting experiments at quasi-static rates. Compression experiments are conducted at each decade in the strain-rate scale without any gap typically seen in the intermediate range. The experimental results show significant strain-rate effects on the mechanical behavior of this soft material, which are summarized via a rate-dependent constitutive model.     

A Gurson–Tvergaard based model to simulate the fracture of aged duplex stainless steels

In order to use duplex stainless steels for components designed to withstand temperatures up to 475 °C, the knowledge of the effect of ageing on the fracture mechanisms is required. For the unaged steel, the ductile fracture takes place due to the nucleation of microvoids initiated on precipitates and inclusions present in the austenitic phase. However, the ageing of the material leads to a global loss of ductility. The ferrite phase embrittlement causes it to break by cleavage at lower levels of plastic strain. These changes, both in mechanical properties and in fracture micromechanisms, can be simulated by means of variation in the parameters that govern the constitutive equation of the material. The local approach model developed by Gurson–Tvergaard has been used to simulate, by FE analysis, the elasto‐plastic behaviour and the fracture of these materials at various stages of ageing at 400 °C. An extensive experimental program has been undertaken in order to obtain the Gurson–Tvergaard model parameters needed for numerical simulations, which considers the effect of ageing conditions (time and temperature), the ferrite content of the steel that causes the global embrittlement and the geometry of the component from the stress triaxiality by using axisymmetric notched specimens. The numerical model developed allows predictions to be made for the damage constitutive parameters for duplex steels subjected to any ageing conditions and, as a consequence, can be directly used for designing components.     

Finite element modeling of ballistic impact on multi-layer Kevlar 49 fabrics

This paper presents a material model suitable for simulating the behavior of dry fabrics subjected to ballistic impact. The developed material model is implemented in a commercial explicit finite element (FE) software LS-DYNA through a user defined material subroutine (UMAT). The constitutive model is developed using data from uniaxial quasi-static and high strain rate tension tests, picture frame tests and friction tests. Different finite element modeling schemes using shell finite elements are used to study efficiency and accuracy issues. First, single FE layer (SL) and multiple FE layers (ML) were used to simulate the ballistic tests conducted at NASA Glenn Research Center (NASA-GRC). Second, in the multiple layer configuration, a new modeling approach called Spiral Modeling Scheme (SMS) was tried and compared to the existing Concentric Modeling Scheme (CMS). Regression analyses were used to fill missing experimental data – the shear properties of the fabric, damping coefficient and the parameters used in Cowper-Symonds (CS) model which account for strain rate effect on material properties, in order to achieve close match between FE simulations and experimental data. The difference in absorbed energy by the fabric after impact, displacement of fabric near point of impact, and extent of damage were used as metrics for evaluating the material model. In addition, the ballistic limits of the multi-layer fabrics for various configurations were also determined.     

Strain rate effects for aluminum and magnesium alloys in finite element simulations of steering wheel armature impact tests

This paper addresses the strain rate effects for aluminum and magnesium steering wheel armatures when they are subjected to dynamic impact tests. Two geometrically different steering wheel armatures, a three spoke proprietary aluminum alloy armature and a four spoke magnesium alloy (AM50A) armature, underwent experimental impact testing. The testing conditions for each armature were different; testing with the aluminum alloy armature involved impacts with a deformable chestform and the magnesium armature experienced impact tests with a rigid plate. Finite element models of all testing apparatuses were developed for both testing conditions and numerical simulations were conducted based on the experimental method employed. Strain rate effects for the aluminum alloy were considered using the Cowper–Symonds constitutive relation and a Johnson–Cook material law was utilized for the magnesium alloy. Simulations were conducted with and without strain rate effects considered. The comparison between the experimental and numerical methods illustrate that there is only a minor change in the numerical testing results with the inclusion of strain rate effects, however, a better correlation between experimental and numerical methods occurs.     

A rate-dependent non-orthogonal constitutive model for describing shear behaviour of woven reinforced thermoplastic composites

A rate dependent constitutive model for woven reinforced thermoplastic matrix composites at forming temperatures is proposed in this work. The model is formulated using a stress objective derivative based on the fibre rotation. Nonlinear shear behaviour is modelled as a polynomial function and the rate dependence is described using a Cowper–Symonds overstress law formulated in terms of shear angle rate. The model parameters are determined by means of bias extension tests. The applicability of the material model is validated through a forming experiment.     

Numerical implementation of a neural network based material model in finite element analysis

Neural network (NN) based constitutive models can capture non‐linear material behaviour. These models are versatile and have the capacity to continuously learn as additional material response data becomes available. NN constitutive models are increasingly used within the finite element (FE) method for the solution of boundary value problems. NN constitutive models, unlike commonly used plasticity models, do not require special integration procedures for implementation in FE analysis. NN constitutive model formulation does not use a material stiffness matrix concept in contrast to the elasto‐plastic matrix central to conventional plasticity based models. This paper addresses numerical implementation issues related to the use of NN constitutive models in FE analysis. A consistent material stiffness matrix is derived for the NN constitutive model that leads to efficient convergence of the FE Newton iterations. The proposed stiffness matrix is general and valid regardless of the material behaviour represented by the NN constitutive model. Two examples demonstrate the performance of the proposed NN constitutive model implementation. Copyright © 2004 John Wiley & Sons, Ltd.     

A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation

The present study introduces a time‐integration algorithm for solving a non‐linear viscoelastic–viscoplastic (VE–VP) constitutive equation of isotropic polymers. The material parameters in the constitutive models are stress dependent. The algorithm is derived based on an implicit time‐integration method (Computational Inelasticity. Springer: New York, 1998) within a general displacement‐based finite element (FE) analysis and suitable for small deformation gradient problems. Schapery's integral model is used for the VE responses, while the VP component follows the Perzyna model having an overstress function. A recursive‐iterative method (Int. J. Numer. Meth. Engng 2004; 59 :25–45) is employed and modified to solve the VE–VP constitutive equation. An iterative procedure with predictor–corrector steps is added to the recursive integration method. A residual vector is defined for the incremental total strain and the magnitude of the incremental VP strain. A consistent tangent stiffness matrix, as previously discussed in Ju (J. Eng. Mech. 1990; 116 :1764–1779) and Simo and Hughes (Computational Inelasticity. Springer: New York, 1998), is also formulated to improve convergence and avoid divergence. Available experimental data on time‐dependent and inelastic responses of high‐density polyethylene are used to verify the current numerical algorithm. The time‐integration scheme is examined in terms of its computational efficiency and accuracy. Numerical FE analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented. Copyright © 2009 John Wiley & Sons, Ltd.