A micromechanics framework for modelling the longitudinal failure of unidirectional fibre composites, in both tension and compression, is presented. Appropriate constitutive models are used for the different constituents (i.e., fibre and matrix) and interfaces. An algorithm for the generation of the fibre misalignment is reported. It combines a stochastic process with an optimization procedure in order to match the numerical and experimental misalignment angle distributions. Two alternative strategies could be used for the optimization procedure, based on the minimization of the standard error of the likelihood or probability, respectively, whose pros and cons are discussed. Finally, micromechanical modelling in tension and compression are reported, and the influence of the fibre misalignment angle distribution is assessed.

Designing future-proof materials goes beyond a quest for the best. The next generation of materials needs to be adaptive, multipurpose, and tunable. This is not possible by following the traditional experimentally guided trial-and-error process, as this limits the search for untapped regions of the solution space. Here, a computational data-driven approach is followed for exploring a new metamaterial concept and adapting it to different target properties, choice of base materials, length scales, and manufacturing processes. Guided by Bayesian machine learning, two designs are fabricated at different length scales that transform brittle polymers into lightweight, recoverable, and supercompressible metamaterials. The macroscale design is tuned for maximum compressibility, achieving strains beyond 94% and recoverable strengths around 0.1 kPa, while the microscale design reaches recoverable strengths beyond 100 kPa and strains around 80%. The data-driven code is available to facilitate future design and analysis of metamaterials and structures (https://github.com/mabessa/F3DAS).

To simplify the analysis and characterisation of composite laminates, an invariant-based approach to stiffness that takes the trace of the plane stress stiffness matrix as a material property was recently proposed. In the present work, a study based on micro-mechanical models brings new insight to this invariant-based approach. The Rule of Mixtures and the Halpin-Tsai models are used to establish the relations between the fibre volume fraction, the fibre/matrix stiffness ratios, and the trace-normalised engineering constants of unidirectional laminae and multidirectional laminates. For sufficiently high longitudinal fibre/matrix stiffness ratios and for fibre volume fractions between 50% and 70%, typical of advanced CFRPs, the variation of the trace-normalised longitudinal Young's modulus is within 6% for unidirectional laminae and within 1% for multidirectional laminates, supporting the definition of an invariant-based approach to stiffness based on a Master Ply concept and laminate factors derived thereof, defining clearly a domain of applicability of the invariant theory and confirming the empirical observations of the past.

Carbon fiber reinforced plastics (CFRPs) are attracting growing attention in industry because of their enhanced properties. Preforming of thermoset carbon fiber prepregs is one of the most common production techniques of CFRPs. To simulate preforming, several computational methods have been developed. Most of these methods, however, obtain the material properties directly from experiments such as uniaxial tension and bias-extension where the coupling effect between tension and shear is not considered. Neglecting this coupling effect deteriorates the prediction accuracy of simulations. To address this issue, we develop a Bayesian model calibration and material characterization approach in a multiscale finite element preforming simulation framework that utilizes mesoscopic representative volume element (RVE) to account for the tension-shear coupling. A new geometric modeling technique is first proposed to generate the RVE corresponding to the close-packed uncured prepreg. This RVE model is then calibrated with a modular Bayesian approach to estimate the yarn properties, test its potential biases against the experiments, and fit a stress emulator. The predictive capability of this multiscale approach is further demonstrated by employing the stress emulator in the macroscale preforming simulation which shows that this approach can provide accurate predictions.

Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress-strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.

A data-driven computational framework combining Bayesian regression for imperfection-sensitive quantities of interest, uncertainty quantification and multi-objective optimization is developed for the design of complex structures. The framework is used to design ultra-thin carbon fiber deployable shells subjected to two bending conditions. Significant increases in the ultimate buckling loads are shown to be possible, with potential gains on the order of 100% as compared to a previously proposed design. The key to this result is the existence of a large load reserve capability after the initial bifurcation point and well into the post-buckling range that can be effectively explored by the data-driven approach. The computational strategy here presented is general and can be applied to different problems in structural and materials design, with the potential of finding relevant designs within high-dimensional spaces.