Predictions of the mechanical properties of unidirectional fibre composites by supervised machine learning

We present an application of data analytics and supervised machine learning to allow accurate predictions of the macroscopic stiffness and yield strength of a unidirectional composite loaded in the transverse plane. Predictions are obtained from the analysis of an image of the material microstructure, as well as knowledge of the constitutive models for fibres and matrix, without performing physically-based calculations. The computational framework is based on evaluating the 2-point correlation function of the images of 1800 microstructures, followed by dimensionality reduction via principal component analysis. Finite element (FE) simulations are performed on 1800 corresponding statistical volume elements (SVEs) representing cylindrical fibres in a continuous matrix, loaded in the transverse plane. A supervised machine learning (ML) exercise is performed, employing a gradient-boosted tree regression model with 10-fold cross-validation strategy. The model obtained is able to accurately predict the homogenized properties of arbitrary microstructures

The response of an elastic-plastic clamped beam to transverse pressure loading

This study presents a new analytical model to predict the response of elastic-plastic, fully clamped beams to transverse pressure loading. The model accounts for travelling elastic flexural waves, stationary and travelling plastic hinges, elastic-plastic stretching and plastic shear deformation. The predictions of the model are validated by detailed Finite Element simulations. The model is used to construct deformation mechanism maps and design charts

A data-driven rate and temperature dependent constitutive model of the compression response of a syntactic foam

Polymeric syntactic foams are used in aerospace and marine applications requiring low density and low moisture absorption together with high specific strength and stiffness. Their mechanical response is highly sensitive to temperature and strain rate and such sensitivity must be modelled accurately. In this study, the uniaxial compressive response of a polymeric syntactic foam is measured at strain rates in the range [10−3, 2.5·103] /s and temperatures varying between −25°C and 100°C. The resulting dataset is used to train a neural network to predict the compressive response of the foam at arbitrary strain rates and temperatures. It is found that the surrogate model is highly effective in predicting the material response at temperature and rates not included in its training set. Finally, a stochastic version of the data-driven model to allow predictions of the variability in the stress versus strain response is proposed

A new stiffness-sensing test to measure damage evolution in solids

We propose and assess a procedure to measure the damage evolution in solids as a function of the applied strain, by conducting stiffness-sensing mechanical tests. These tests consist in superimposing to a monotonically increasing applied strain numerous, low-amplitude unloading/reloading cycles, and extracting the current stiffness of the specimens from the slope of the stress–strain curve in each of the unloading/reloading cycles. The technique is applied to a set of polymeric and metallic solids with a wide range of stiffness, including CFRP laminates loaded through the thickness, epoxy resins, injection-moulded and 3D printed PLA and sintered Ti powders. The tests reveal that, for all the materials tested, damage starts developing at the very early stages of deformation, during what is commonly considered an elastic response. We show that the test method is effective and allows enriching the data extracted from conventional mechanical tests, for potential use in data-driven constitutive models. We also show that the measurements are consistent with the results of acoustic and resistive measurements, and that the method can be used to quantify the viscous response of the materials tested

Numerical predictions of the anisotropic viscoelastic response of uni-directional fibre composites

Finite Element (FE) simulations are conducted to predict the viscoelastic properties of uni-directional (UD) fibre composites. The response of both periodic unit cells and random stochastic volume elements (SVEs) is analysed; the fibres are assumed to behave as linear elastic isotropic solids while the matrix is taken as a linear viscoelastic solid. Monte Carlo analyses are conducted to determine the probability distributions of all viscoelastic properties. Simulations are conducted on SVEs of increasing size in order to determine the suitable size of a representative volume element (RVE). The predictions of the FE simulations are compared to those of existing theories and it is found that the Mori-Tanaka (1973) and Lielens (1999) models are the most effective in predicting the anisotropic viscoelastic response of the RVE

A strategy to formulate data-driven constitutive models from random multiaxial experiments

We present a test technique and an accompanying computational framework to obtain data-driven, surrogate constitutive models that capture the response of isotropic, elastic-plastic materials loaded in-plane stress by combined normal and shear stresses. The surrogate models are based on feed-forward neural networks (NNs) predicting the evolution of state variables over arbitrary increments of strain. The feasibility of the approach is assessed by conducting virtual experiments, i.e. Finite Element (FE) simulations of the response of a hollow, cylindrical, thin-walled test specimen to random histories of imposed axial displacement and rotation. In these simulations, the specimen's material is modelled as an isotropic, rate-independent elastic-plastic solid obeying J2 plasticity with isotropic hardening. The virtual experiments allow assembling a training dataset for the surrogate models. The accuracy of two different surrogate models is evaluated by performing predictions of the response of the material to the application of random multiaxial strain histories. Both models are found to be effective and to have comparable accuracy

A machine learning approach to modelling temperature-dependent cyclic behaviour

This study presents a methodology for developing a temperature-dependent cyclic plasticity surrogate model as an efficient alternative to phenomenological temperature-dependent constitutive models. The titanium alloy Ti-6Al-4V, known for its widespread use in various engineering applications, was selected for this investigation. The surrogate model, based on a feedforward neural network, was trained using random amplitude stress-strain histories at various temperatures. To generate the training dataset, constitutive models were calibrated at specific temperatures using both experimental and available literature data, enabling the simulation of virtual temperature-dependent experiments. Cyclic loading simulations were performed at random axial strains within the range [-4 %, 4 %] and temperatures of 20℃, 400℃, 500℃, and 600℃. The predictive accuracy of the surrogate model was evaluated using unseen random stress-strain histories and temperature conditions, demonstrating high accuracy and computational efficiency