A neural network is inserted into a theoretical framework for modeling the inelastic behavior of materials. The neural network replaces functional expressions for such phenomena as isotropic and directional hardening and viscoplasticity. The theoretical framework, into which the neural network is inserted, is Eulerian in the sense that all state variables are defined in the current state of the material, and the framework is independent of history variables, such as plastic strain, accumulated equivalent plastic strain, etc. The neural network-based model is compared to and trained to reproduce the uniaxial tension response of theoretical reference solutions as well as experimental results. The neural network-based model is able to reproduce the reference results with excellent precision. Also, the neural network-based model was implemented as a VUMAT in Abaqus together with one of the theoretical reference models. Deformation of a plate with a hole in it was simulated, and the outcome from the reference model and the trained neural network-based model was compared. The solutions, in terms of von Mises stress and accumulated equivalent plastic strain, were very similar. Hence, it seems like training the neural network model by use of uniaxial stress data is sufficient for being able to make accurate 3D predictions.

The mechanical behaviour of thermoplastics is strongly rate-dependent. One thermoplastic that is commonly used in industrial applications is polyoxymethylene (POM). In a previous paper (Mechanics of Time-dependent Materials, 2024, vol 28, p 43-63), the uniaxial tensile properties of POM were tested, and in the present study, those tests are complemented by compression tests, bending tests, and punch tests. The test data in this study can be divided into calibration data and verification data. The calibration experiments consist of both tensile and compression tests carried out in monotonic loading, stress relaxation, and zero-stress creep. Three-point bending and quasi-static punch tests are used as verification tests. Overall, the experiments showed good repeatability, and there was a low dispersion in the experimental results. The paper compares the performance of three constitutive models that have been developed for modelling these materials. Two hyperelastic models and one hypoelastic model are compared. The models are calibrated using the uniaxial data and then applied to the results from the more advanced tests. The material models are calibrated by utilizing commercially available optimization software. All models have the ability to model visco-elasticity. Two of the models are network models with three visco-elastic branches/legs/phases. These two models are built in a similar way with two main novelties. The first novelty is that the stiffness can vary with the elastic deformation (in contrast to a standard neo-Hookean and Hookean model). The second novelty is that the exponent of viscous relaxation can vary with viscous deformation. The third model is an Eulerian model, meaning that all state variables are defined in the current state of the material. Taken together, the models were able to describe the experimental results relatively well. It was concluded that they have different strengths and weaknesses. The hypoelastic model was able to describe the uniaxial calibration data best. On the other hand, this model became unstable at large deformations when simulating the punch tests. The two hyperelastic models could not model the zero-stress creep in the uniaxial tests but were able to predict the outcome from the punch tests quite well. It was clear from the simulations that further model development is needed in order to capture all aspects of the experimental results.

The mechanical behavior of thermoplastics is strongly rate-dependent, and oftentimes it is difficult to find constitutive models that can accurately describe their behavior in the small to moderate strain regime. In this paper, a hyperelastic network model (modified neo-Hookean) and a set of experiments are presented. The testing consists of monotonic tensile loading as well as stress relaxation and zero stress creep. Two materials were tested, polyoxymethylene (POM) and recycled polypropylene (rPP), representing one more rigid and brittle and one softer and more ductile semi-crystalline polymer. The model contains two main novelties. The first novelty is that the stiffness is allowed to vary with the elastic deformation (in contrast to a standard neo-Hookean model). The second novelty is that the exponent governing viscous relaxation is allowed to vary with the viscous deformation. The basic features of the new model are illustrated, and the model was fitted to the experimental data. The model proved to be able to describe the experimental results well.

In the present work, neural networks are used to enhance and generalise an Eulerian formulation of inelasticity. The framework as such has been developed in previous works, and in the present work, neural networks are used to model the rate-dependence and hardening of the material. Functional forms for these material properties are then replaced by neural networks. The neural network-based model is applied to both theoretical reference data as well as actual experimental data in the form of stress-strain data. Simulated annealing is used to optimise/train the neural networks. The model was able to reproduce both the theoretical reference solutions as well as the experimental data very well. An implicit FE formulation was also provided in the form of a subroutine (UMAT) in Abaqus. The implementation was applied to two 3D examples, and the implementation seems to be robust and shows nice convergence properties. Overall, the present neural network-enhanced framework seems to be promising and there is potential for further development, such as inclusion of directional hardening and a more general neural network-based treatment of rate-dependence and material hardening.

Stress relaxation of high-density polyethylene is addressed both experimentally and theoretically. Two types of stress relaxation testing are carried out: uniaxial tensile testing at constant test specimen length and compression testing of a 3D structure producing inhomogeneous deformation fields and relaxation. A constitutive model for isotropic, semi-crystalline polymers is also proposed. The model has the ability to model stress relaxation at different time scales. The developed model was implemented as a user subroutine in Abaqus (UMAT). The implicit integration scheme including an algorithmic tangent modulus is described in detail. The material model is calibrated by use of the uniaxial tensile tests, and the model is then validated by simulating the compression tests of the 3D structure. The model is able to describe the uniaxial tension tests well, and the comparison between the simulations and experimental testing of the 3D structure shows very good agreement.

High strain -rate testing of high -density polyethylene is the focus of the present work. This testing is accomplished by two types of experimental testing: uniaxial tensile testing using standard testing technique, and impact testing of a 3D structure with non -trivial geometry. Both the uniaxial tests and the impact tests were evaluated using a material model suited for rate -dependent inelasticity of polymers that has been developed. In the uniaxial tensile tests, a maximum strain -rate of about 28/s was attained. In the impact tests, strain -rates of the order of 100/s and beyond were predicted in the analyses. The impact tests were simulated and analysed by use of finite element simulations. Coupled Eulerian-Lagrangian (CEL) analyses were employed for some of the tests where there was an interaction between the compressed structure and air trapped inside it. Overall, the simulations were able to reproduce the outcome from the experiments well. In particular, the deformation scenarios in the impact tests for different loading situations could be reproduced.

Semi-crystalline polymers is an important group of materials that is used in a vast array of products. In this study, the rate-dependent properties of high-density polyethylene (HDPE) are investigated, both experimentally and theoretically. Experimental compression testing of a three-dimensional HDPE structure is performed and analysed numerically by use of the finite element method. In addition, an Eulerian constitutive material model for isotropic, semi-crystalline polymers is proposed. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, pressure-dependence of inelastic deformations, and damage. The proposed material model was implemented in Abaqus as a VUMAT, which is an explicit implementation. The material model was calibrated by use of uniaxial tensile tests performed on HDPE dog-bone shaped samples, and the model was further explored by applying the VUMAT implementation to the compression tests of the HDPE structure. The simulation model was able to reproduce the experimental results well, both the uniaxial tests and the compression tests. In particular, the friction present in the compression tests seems to play an important role in determining the buckling mode of the structure.

A constitutive model for isotropic, semi-crystalline polymers is proposed. The model is Eulerian in the sense that it is independent of measures of total deformation and plastic/inelastic deformations. It is able to account for such essential phenomena as strain-rate dependence, work hardening, stress relaxation, volumetric inelastic deformations, and damage. The model was applied to uniaxial tension tests performed on polyoxymethylene (POM), which is a semi-crystalline polymer widely used in the industry. Three types of tests were conducted: monotonic tests at different strain rates, stress relaxation tests, and loading-unloading tests. The model was able to reproduce the experimental results well. The proposed model was also implemented as a VUMAT in Abaqus, and the deformation of a 3D geometry was simulated.

A constitutive model for isotropic, semi-crystalline polymers is proposed. The model is Eulerian in the sense that it is independent of measures of total deformation, plastic/inelastic deformations, and all state variables are defined in the current state of the material. The deformation state of the material is represented by a unimodular tensor, characterizing elastic distortional deformation, and an elastic dilatation. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, stress relaxation, volumetric inelastic deformations, and damage. Uniaxial tension tests were performed on polyoxymethylene (POM), which is a semi-crystalline polymer widely used in the industry. Three types of tests were conducted: monotonic loading tests at different strain rates, stress relaxation tests, and loading-unloading tests. These tests produced large elastic and inelastic deformations which were reproduced well by the model. The model was also implemented as a VUMAT in Abaqus, and the deformation of a 3D geometry was simulated. Specifically, a simple structure of the POM material was deformed and then unloaded. Thenresulting elastic spring-back and residual stress state was investigated.