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Abstract We present a stabilized finite element method that generalizes Nitsche's method for enforcing stiff anisotropic cohesive laws with different normal and tangential stiffness. For smaller values of cohesive stiffness, the stabilized method resembles the standard method, wherein the traction on the crack surface is enforced as a Neumann boundary condition. Conversely, for larger values of cohesive stiffness, the stabilized method resembles Nitsche's method, wherein the cohesive law is enforced as a kinematic constraint. We present several numerical examples, in two-dimensions, to compare the performance of the stabilized and standard methods. Our results illustrate that the stabilized method enables accurate recovery of crack-face tractions for stiff isotropic and anisotropic cohesive laws; whereas, the standard method is less accurate due to spurious traction oscillations. Also, the stabilized method could mitigate spurious sensitivity of load–displacement results to displacement increment in mixed-mode fracture simulation, owing to its stability and accuracy. [ABSTRACT FROM AUTHOR]

[Display omitted] • Strain-sensing ability of a nanoengineered self-sensing cementitious composite is assessed by integrating multiscale finite element analysis simulations and machine learning. • Hyperparameter-optimized feed-forward multilayer perceptron-based neural network showed excellent efficacy for the prediction of strain-sensing ability. • Shapley Additive Explanations algorithm reveals that coating thickness shows higher influence on the sensing ability than fraction of coated sand. • Comprehensive approach presented here can be used as starting point toward development of reliable performance standards for self-sensing cementitious composites. Prediction of in-situ strain sensing efficiency of self-sensing cementitious composites using machine learning (ML) requires a large, representative, consistent, and accurate dataset. However, such large experimental dataset is not readily available. Moreover, the success of the ML approach depends on its ability to abide by the fundamental laws of physics. To address these challenges this paper synergistically integrates a validated finite element analysis (FEA)-based multiscale simulation framework with ML to predict the strain-sensing ability of self-sensing cementitious composites enabled by incorporating nano-engineered interfaces. The multiscale simulation framework is leveraged to develop a balanced, representative, complete, and consistent dataset containing 3000 combinations of strain-dependent electromechanical responses. This large dataset is used to predict the strain-sensing ability of the nanoengineered cementitious composites using a feed-forward multilayer perceptron-based neural network (NN) approach which shows excellent prediction efficacy. This paper also applies a Shapley Additive Explanations (SHAP) algorithm to interpret the NN predictions in light of the relative importance of different design parameters on the strain-sensing ability of the composite. Overall, the synergistic and comprehensive approach presented here can be used as a starting point toward the development of reliable performance standards to accelerate the acceptance of these self-sensing cementitious composites for large-scale applications. [ABSTRACT FROM AUTHOR]

An immersed enriched finite element method is proposed for the analysis of phononic crystals (PnCs) with finite element (FE) meshes that are completely decoupled from geometry. Particularly, a technique is proposed to prescribe Bloch–Floquet periodic boundary conditions strongly on non-matching edges of the periodic unit cell (PUC). The enriched finite element formulation effectively transforms a periodic non-confirming discretization into an enriched node-to-node periodic discretizations where periodicity is enforced by any standard procedure. The enriched formulation is also used to describe the interior material interface. This completely eliminates the tedious process of generating matching or fitted meshes during the design process, as it allows changing the inclusion's geometry as well as the PnC's lattice type without changing the FE mesh. The proposed approach, which is used to analyze phononic crystals in 1-D, 2-D, and 3-D using structured meshes, exhibits the same performance as the standard finite element analysis on fitted meshes. • Full decoupling of phononic crystal geometry and mesh without loss of accuracy. • The unit cell boundaries and inclusion geometries can be varied without remeshing. • Bloch–Floquet BCs are prescribed strongly on edges that do not match the mesh. • Transforms non-conforming periodicity into an enriched node-to-node periodicity. • Also suitable for standard and Bloch–Floquet periodic BCs on non-periodic meshes. [ABSTRACT FROM AUTHOR]

We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. Using a stabilized method combining Galerkin least squares stabilization and a penalty on the gradient jumps we obtain stability of the discrete formulation under the condition h k < C , where h denotes the mesh size, k the wave number and C a constant depending mainly on the surface curvature κ , but not on the surface/mesh intersection. Optimal error estimates in the H 1 and L 2 -norms follow. • Implementation and analysis of a TraceFEM for the Helmholtz equation on surfaces. • Stablizing terms make the semi-discretized method absolutely stable. • The fully discrete method is stable under a mild mesh condition h k < C. • Optimal error bounds in the H 1 - and L 2 -norms. • The numerical performance compared to the standard Galerkin method is excellent in situations close to resonance. [ABSTRACT FROM AUTHOR]