Stochastic modeling of functionally graded double-lap adhesive joints

Perturbation(s) in the adhesive’s properties originating from the manufacturing, glue-line application method and in-service conditions, may lead to poor performance of bonded systems. Herein, the effect of such uncertainties on the adhesive stresses is analyzed via a probabilistic mechanics framework built on a continuum-based theoretical model. Firstly, a generic 2D plane stress/strain linear-elastic model for a composite double-lap joint with a functionally graded adhesive is proposed. The developed model is validated against the results obtained from an analogous finite element model for the cases of bonded joints with metal/composite adherends subjected to mechanical and thermal loadings. Subsequently, the proposed analytical model is reformulated in probabilistic mechanics framework where the elastic modulus of the adhesive is treated as a spatially varying stochastic field for the cases of homogeneous and graded adhesives. The former case represents stochastic nature of conventional joints with a homogeneous bondline while the later case showcases the perturbation in the properties of functionally graded joints. To propagate the uncertainty in the elastic modulus to shear and peel stresses, we use a non-intrusive polynomial chaos approach. For a standard deviation in the elastic modulus, the proposed model is utilized to evaluate the spatial distribution of shear and peel stresses in the adhesive, together with probability and cumulative distribution functions of their peaks. A systematic parametric study is further carried out to evaluate the effect of varying mean value of the adhesive’s Young’s moduli, overlap lengths and adhesive thicknesses on the coefficient of variation/standard deviation in peak stresses due to the presence of a random moduli field. It was observed that the joints with stiffer adhesives and longer bondlengths show smaller coefficient of variation in peak stresses. The findings from this study underscore that the predictive capability of the proposed model would be useful for the stochastic design of adhesively bonded joints

Concurrent geometrico-topological tuning of nanoengineered auxetic lattices fabricated by material extrusion for enhancing multifunctionality: multiscale experiments, finite element modeling and data-driven prediction

This study demonstrates the multifunctional performance of innovative 2D auxetic lattices through a combination of multiscale experiments, finite element modeling and data-driven prediction. A geometric modeling approach utilizing Voronoi partitioning and a unique branch-stem-branch (BSB) structure, patterned according to 2D wallpaper symmetries, enables precise concurrent geometric and topological tuning of lattices across a continuous parameter space. Selected architectures are physically realized via material extrusion of polylactic acid (PLA) infused with carbon black (CB). Experimental characterizations, supported by Finite Element modeling, reveal the significant influence of BSB structure's design parameters on mechanical and piezoresistive performance under tensile loading, with a remarkable Poisson’s ratio of -0.74, accompanied by a 15-fold increase in elastic stiffness and a 34-fold increase in strain sensitivity. Additionally, architecturally, and topologically tailored lattice structures exhibit tunable damage sensitivity, reflecting the rate of conductive network destruction within the lattice. This offers insights into the rapidity of cell wall failure, with a steeper slope of the piezoresistance curve in the inelastic regime indicating a faster breakdown and quicker onset of mechanical failure. Integration of Gaussian Process Regression enables accurate exploration of the design space beyond realized structures, highlighting the potential of these intelligent lattice structures for applications such as sensors and in situ health monitoring, marking a significant advancement in multifunctional materials

Random matrix models and nonparametric method for uncertainty quantification

Springer ReferenceInternational audienceThis paper deals with the fundamental mathematical tools and the associated computational aspects for constructing the stochastic models of random matrices that appear in the nonparametric method of uncertainties and in the random consti-tutive equations for multiscale stochastic modeling of heterogeneous materials. The explicit construction of ensembles of random matrices, but also the presentation of numerical tools for constructing general ensembles of random matrices are presented and can be used for high stochastic dimension. The developments presented are illustrated for the nonparametric method for multiscale stochastic mod-eling of heterogeneous linear elastic materials and for the nonparametric stochas-tic models of uncertainties in computational structural dynamics