The mechanical behavior of polylactic acid (PLA) films: fabrication, experiments and modelling

Polylactic acid (PLA) is one of the highly applicable bio-polymers in a wide variety of applications including medical fields and packaging. In order to quantitatively model the mechanical behaviour of PLA and PLA based bio-composite materials, and also tailor new bio-composites, it is required to characterize the mechanical behaviour of PLA. In this study, thin films of PLA are fabricated via hot-pressing and tensile experiments are performed under different strain rates. To model the mechanical behaviour, an elasto-viscoplastic constitutive model, developed in a finite strain setting, is adopted and calibrated. Using the physically based constitutive model, all regimes of deformation under uniaxial stress state, including post-yield softening, were adequately captured in the simulations. Also, the rate dependency of the stress-strain behaviour was properly modelled

Macroscale modelling of 3D-woven composites: Elasto-plasticity and progressive damage

There is a growing need across multiple industries for lightweight materials with improved material performance and reduced manufacturing costs. Composites with 3D-woven reinforcement could help fill this need. Their use however, requires the development of computationally efficient and industrially applicable material models to predict their non-linear behaviour. This work proposes a macroscale elasto-plasticity and damage model to capture the experimentally observed inelastic strains and stiffness reductions. The model is general, thermodynamically consistent and allows for various non-linear phenomena to be added and calibrated in a modular fashion depending on loading direction. Further it allows for a simplified parameter identification routine in which the damage and hardening laws are identified directly from experimental curves without the need for complex calibration routines. In order to demonstrate the applicability of the proposed macroscale model, focus is given to predicting the material response of a 3D glass fibre reinforced epoxy material system. The damage and hardening parameters are identified based on uniaxial tensile and in-plane shear experimental curves with unloading cycles. The model performance is validated against an off-axis tensile test with unloading cycles and shows good agreement to the experimental result

An adaptive shell element for explicit dynamic analysis of failure in laminated composites Part 2: Progressive failure and model validation

To enable modelling of the progressive failure of large, laminated composite components under crash or impact loading, it is key to have a numerical methodology that is both efficient and numerically robust. A potential way is to adopt an adaptive method where the structure is initially represented by an equivalent single-layer shell model, which during the analysis is adaptively transformed to a high-resolution layer-wise model in areas where higher accuracy is required. Such a method was recently developed and implemented in the commercial finite element solver LS-DYNA, aiming at explicit crash analysis (Fr\ue4mby, Fagerstr\uf6m and Karlsson: An adaptive shell element for explicit dynamic analysis of failure in laminated composites - Part 1: Adaptive kinematics and numerical implementation, 2020). In the current work, the method is extended to the case of interacting inter- and intralaminar damage evolution. As a key part, we demonstrate the importance of properly regularising the intralaminar failure described by a smeared-crack model, and show that neglecting to account for the crack-versus-mesh orientation may lead to significant errors in the predicted energy dissipation. We also validate the adaptive approach against a four-point beam bending test with matrix-induced delamination growth, and simultaneously show the capability of the proposed method to – at lower computational expense – replicate the results from a refined, non-adaptive model

An adaptive shell element for explicit dynamic analysis of failure in laminated composites Part 1: Adaptive kinematics and numerical implementation

To introduce more fibre-reinforced polymers in cars, the automotive industry is strongly dependent on efficient modelling tools to predict the correct energy absorption in crash simulations. In this context, an adaptive modelling technique shows great potential. However, as the critical energy absorption in a crash occurs over a very short period of time, and since the deformation behaviour is very complex, car crash simulations are usually performed using explicit dynamic finite element solvers. Therefore, any practical adaptive technique must be adapted to an explicit setting in a software available to the automotive companies. In this paper, we propose an adaptive method for explicit finite element analysis and describe its implementation in the commercial finite element solver LS-DYNA. The method allows for both so-called weak discontinuities (discontinuities in strain), which are crucial for accurate stress and intralaminar damage predictions, and strong discontinuities (discontinuities in displacements), needed for a proper representation of growing delamination cracks. In particular, we detail the implementation of the proposed method into LS-DYNA and also how we propose to remedy the non-physical oscillations arising from the implementation of the adaptive scheme in a explicit dynamic setting. The paper is concluded with numerical examples where we demonstrate the potential for the adaptive approach and also perform a detailed study on its accuracy and stability

Development and validation of a finite deformation fibre kinking model for crushing of composites

A mesoscale model for fibre kinking onset and growth in a three-dimensional framework is developed and validated against experimental results obtained in-house as well as from the literature. The model formulation is based on fibre kinking theory i.e. the initially misaligned fibres rotate due to compressive loading and nonlinear shear behaviour. Furthermore, the physically-based response is computed in a novel and efficient way using finite deformation theory. The model validation starts by correlating the numerical results against compression tests of specimens with a known misalignment. The results show good agreement of stiffness and strength for two specimens with low and high misalignment. Fibre kinking growth is validated by simulating the crushing of a flat coupon with the fibres oriented to the load direction. The numerical results show very good agreement with experiments in terms of crash morphology and load response

Efficient modelling of delamination growth using adaptive isogeometric continuum shell elements

The computational efficiency of CAE tools for analysing failure progression in large layered composites is key. In particular, efficient approximation and solution methods for delamination modelling are crucial to meet today’s requirements on virtual development lead times. For that purpose, we present here an adaptive continuum shell element based on the isogeometric analysis framework, suitable for the modelling of arbitrary delamination growth. To achieve an efficient procedure, we utilise that, in isogeometric analysis, the continuity of the approximation field easily can be adapted via so-called knot insertion. As a result, the current continuum shell provides a basis for an accurate but also computationally efficient prediction of delamination growth in laminated composites. Results show that the adaptive modelling framework works well and that, in comparison to a fully resolved model, the adaptive approach gives significant time savings even for simple analyses where major parts of the domain exhibit delamination growth

An adaptive isogeometric shell element for the prediction of initiation and growth of multiple delaminations in curved composite structures

In order to model prominent failure modes experienced by multi-layered composites, a fine through-thickness discretisation is needed. If the structure also has large in-plane dimensions, the computational cost of the model becomes large. In light of this, we propose an adaptive isogeometric continuum shell element for the analysis of multi-layered structures. The key is a flexible and efficient method for controlling the continuity of the out-of-plane approximation, such that fine detail is only applied in areas of the structure where it is required. We demonstrate how so-called knot insertion can be utilised to automatise an adaptive refinement of the shell model at arbitrary interfaces, thereby making it possible to model multiple initiation and growth of delaminations. Furthermore, we also demonstrate that the higher-order continuity of the spline-based approximations allows for an accurate recovery of transverse stresses on the element level, even for doubly-curved laminates under general load. With this stress recovery method, critical areas of the simulated structures can be identified, and new refinements (cracks) can be introduced accordingly. In a concluding numerical example of a cantilever beam with two initial cracks, we demonstrate that the results obtained with the adaptive isogeometric shell element show good correlation with experimental data

A generalised path-following solver for robust analysis of material failure

When analysing complex structures with advanced damage or material models, it is important to use a robust solution method in order to trace the full equilibrium path. In light of this, we propose a new path-following solver based on the integral of the rate of dissipation in each material point, for solving problems exhibiting large energy dissipating mechanisms. The method is a generalisation and unification of previously proposed dissipation based path-following solvers, and makes it possible to describe a wider range of dissipation mechanisms, such as large strain plasticity. Furthermore, the proposed method makes it possible to, in a straightforward way, combine the effects from multiple dissipation mechanisms in a simulation. The capabilities of the solver are demonstrated on four numerical examples, from which it can be concluded that the proposed method is both versatile and robust, and can be used in different research domains within computational structural mechanics and material science

A multiscale deep learning model for elastic properties of woven composites

Time-consuming and costly computational analysis expresses the need for new methods for generalizing multiscale analysis of composite materials. Combining neural networks and multiscale modeling is favorable for bypassing expensive lower-scale material modeling, and accelerating coupled multi-scale analyses (FE2). In this work, neural networks are used to replace the time-consuming micromechanical finite element analysis of unidirectional composites, representing the local material properties of yarns in woven fabric composites in a multiscale framework. Leveraging the fast multiscale data generation procedure, we presented a second neural networks model to estimate the elastic engineering coefficients of a particular weave architecture based on a broad range of dry resin and fiber properties and yarn fiber volume fraction. As an outcome, this paper provides the user with a generalized, neural network-based approach to tackle the balance of computational efficiency and accuracy in the multiscale analysis of elastic woven composites

A framework for macroscale modelling of inelastic deformations in 3D-woven composites

The use of 3D-woven composite materials has shown promising results. Along with weight-efficient stiffness and strength, they have demonstrated encouraging out of plane properties, damage tolerance and energy absorption capabilities. The widespread adoption of 3D-woven composites in industry however, requires the development of efficient computational models that can capture the material behaviour. The following work proposes a framework for modelling the mechanical response of 3D-woven composites on the macroscale. This flexible and thermodynamically consistent framework, decomposes the stress and strain tensors into two main parts motivated by the material architecture. The first is governed by the material behaviour along the reinforcement directions while the second is driven by shear behaviours. This division allows for the straightforward addition and modification of various inelastic phenomena observed in 3D-woven composites. In order to demonstrate the applicability of the framework, focus is given to predicting the material response of a 3D glass fibre reinforced epoxy composite. Prominent non-linearities are noted under shear loading and loading along the horizontal weft yarns. The behaviour under tensile loading along the weft yarns is captured using a Norton style viscoelasticity model. The non-linear shear response is introduced using a crystal plasticity inspired approach. Specifically, viscoelasticity is driven on localised slip planes defined by the material architecture. The viscous parameters are calibrated against experimental results and off axis tensile tests are used to validate the model