A rate-dependent peridynamic model for ductile material via multi-time-step integral

Strain rate dependent constitutive model for predicting the material behaviour of polyurea under high strain rate tensile loading

In this work, five solder materials of Sn-3.0Ag-0.5Cu (SAC305), Sn-2.0Ag-0.5Cu (SAC205), Sn-1.0Ag-0.5Cu (SAC105), Sn-1.0Ag-0.5Cu-0.05Ni (SAC105Ni0.05) and Sn-1.0Ag-0.5Cu-0.02Ni (SAC105M0.02) were tested using tensile loading at room temperature to investigate the Ag content and Ni dopant effect on solder mechanical properties, respectively. In addition, different testing temperature conditions including -35 deg.C, 25 deg.C, 75 deg.C and 125 deg.C were used for SAC105M0.02 solder to investigate the temperature effect on mechanical properties. Tensile test under different strain rates from 0.000011/s to 0.11/s was conducted to study the strain rate effect on material properties. Test results show that the material properties of modulus, UTS and yield stress increase with strain rate and Ag content, but decrease with temperature. The 500 ppm Ni dopant has the significant effect on material properties of Sn-Ag-based solder than 200 ppm Ni dopant. Lower modulus, yield stress and UTS, higher elongation can be achieved for SAC105M0.05 solder compared to SAC105M0.02 solder. The rate dependent and Ag content dependent material models were developed for Sn-Ag-Cu lead free solders. In addition, the temperature and rate dependent models were developed for SAC105M0.02 solder. The microstructures of different solder alloys were analyzed based on SEM images. It was found that Ag content affects the Ag <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn intermetallic compound dispersion and Sn grain size. The microstructure of solder alloy has finely dispersed IMC and fine Sn grain size for the high Ag content solder, which make the solder exhibit high strength.

Carbon fiber reinforced thermoplastic polymer (CFRTP) laminates can be used in packaging electronics components to reduce weight and shield external disturbance. The CFRTP structures in operation are inevitably to suffer dynamic loading conditions such as falling rocks, tools and impacts. In this study, a strain rate dependent material model for accurately evaluating the dynamic response of CFRTP laminates with different stacking sequence was proposed. The model was composed of three components: a strain rate dependent constitute model, a strain rate related damage initiation model and an energy-based damage evolution model. The strain rate effect of modulus and strength was described by a stacking sequence related matrix, and the damage initiation model could describe the matrix, fiber and delamination damage of CFRTP laminates without introducing cohesive elements. The material model was implemented into finite element software ABAQUS by user defines subroutine VUMAT. The low velocity impact tests of CFRTP laminates with quasi-isotropic and angle-ply stacking sequence were used to provide validation data. The dynamic response of CFRTP laminates from numerical results were highly consistent with the experimental results. The mechanical response of CFRTP laminates were affected by stacking sequence and impact energy, and the numerical error of proposed material model significantly decreased with the increasing impact energy especially for the laminae with damage occur.

Non-linear strain rate dependent micro-mechanical composite material model for finite element impact and crashworthiness simulation

A strain rate dependent nonlinear elastic orthotropic model for SFRC structures

A generalized visco-plasticity model and its algorithmic implementation

It is not conservative to directly use the strength tested under the laboratory loading rates to evaluate the long-term creep strength of polymers. A suitable strain rate-dependent constitutive model is crucial for accurately predicting the long-term strength and mechanical behavior of polymer pressure pipes. In this study, the Kondner hyperbolic constitutive model is considered the base model in deriving the rate-dependent constitutive model for PE100 pipe material, and the yield stress and initial tangent modulus are the two rate-dependent parameters of the model. Uniaxial tension tests are carried out under five specified strain rates ranging from 10−5 s−1 to 5 × 10−2 s−1 to obtain these two parameters. It is demonstrated that the strain rate dependence of the yield stress and the initial tangent modulus can be described by either a power or a logarithm law. The predictions from the two models are in good agreement with the experiments. In contrast, the power-law rate-dependent Kondner model is more suitable for describing the rate-dependent tensile behavior of PE100 pipe material than the logarithm-law rate-dependent Kondner model, especially for the cases of very low strain rates which relate to the polymer pressure pipe applications.

This study presents an elastoplastic material model with a pressure and rate dependent yield criterion for freshwater polycrystalline ice, implemented to simulate the structural damage in a full-scale AA5083-H116 aluminium panel subject to ice impact load in a drop test. The proposed ice material model is validated against physical ice-crushing tests with a good correlation between the experimental and numerical results. The material model is based on the Tsai-Wu yield surface, which is defined to evolve differently in the ductile and brittle regimes of ice to account for the ‘ductile-to-brittle transition’. The relationships between ice strength and strain rate in the constitutive laws are obtained from the literature. The constitutive laws are written in Fortran as vectorised user material (VUMAT) for the Abaqus Explicit solver. The mechanical behaviour of AA5083-H116 alloy is simulated using the Johnson-Cook plasticity model. The numerical simulation of the ice drop test on the stiffened aluminium panel produced excellent agreements with the experimental data using the proposed material model for ice and the Johnson-Cook model for AA5083-H116 alloy.

Elastomer foam materials are shock absorbers that have been extensively used in applications of electronic packaging. Finite element modeling simulation plays an important role in helping the designers determine the best elastomer foam material and the best structure of a shock absorber. Elastomer foam materials have very complicated material behaviors. The prediction of the rate responsive behavior is one of the most interesting topics in elastomer material modeling. The focus of this article is to present a unique method for deriving the rate dependent constitutive model of an elastomer foam based on the extension of the Cowper and Symond law and the curve fitting on experimental test data. The research on rate dependent material models and the material models available in commercially available finite element analysis software have been reviewed. Test data collection at various strain rates has been discussed. Two steps of curve fitting on experimental test data are used to retrieve analytical expression of the constitutive model. The performance of the constitutive model for a foam material has been illustrated and shown to be quite good. This method is easy to understand and the simple formulation of the constitutive model is very suitable for applications in numerical simulation. The constitutive model could be used to predict the stress-strain curves of a foam material at any strain rate, especially at the intermediate strain rates, which are the most difficult to collect so far. In addition, this model could be readily integrated with the hyperelastic material models to more efficiently evaluate the mechanical behavior of an elastomer foam material. The model could potentially be implemented in commercially available software such as ABAQUS and LS-DYNA. The method presented is also useful in deriving constitutive models of rubberlike elastomer materials.

Development of a strain rate dependent material model of human cortical bone for computer-aided reconstruction of injury mechanisms

Stability and well-posedness of a rate-dependent damage model for brittle materials based on crack mechanics

Mechanical characterization and finite element implementation of the soft materials used in a novel anthropometric test device for simulating underbody blast loading

A modified rate-dependent peridynamic model with rotation effect for dynamic mechanical behavior of ceramic materials

Rate-dependent damage model for polymeric composites under in-plane shear dynamic loading

An implicit numerical algorithm has been developed for a rate-dependent model for damage and failure of ductile materials under high-rate dynamic loading [F. L. Addessio and J. N. Johnson, J. Appl. Phys. 74, 1640 (1993)]. Over each time step, the algorithm first implicitly determines the equilibrium state on a Gurson surface, and then calculates the final state by solving viscous relaxation equations, also implicitly. Numerical examples are given to demonstrate the key features of the algorithm. Compared to the explicit algorithm used previously, the current algorithm allows significantly larger time steps that can be used in the analysis. As the viscosity of the material vanishes, the results of the rate-dependent model are shown here to converge to that of the corresponding rate-independent model, a result not achieved with the explicit algorithm.