Journal of Engineering Mechanics

This paper presents a two-way linked multiscale method that is integrated with nanomechanical tests and a cohesive zone fracture model to investigate highly heterogeneous cementitious materials such as alkali-activated geopolymer. To this end, geopolymer paste, which is known to have multiphase heterogeneous media, was fabricated and tested to identify (1) local-scale microstructures and nanomechanical properties of individual components within the paste, and (2) global-scale fracture through a three-point bending beam test. Local–global results were then integrated with the two-way linked finite-element modeling. Global and local scales were systemically represented in the model with a homogeneous bending beam structure where the elements of the potential crack zone are linked to a heterogeneous geopolymer microstructure representative volume element (RVE) in the two-way coupled multiscale modeling framework. This integrated experimental–computational multiscale approach can provide the material properties, such as micrometer-length-scale cohesive zone fracture properties, which are considered core properties but not usually feasible to identify using conventional test methods. Test-modeling results imply that the two-way linked multiscale method integrated with nanomechanical tests can be used as a method for characterization and design of various multiphase media, including materials used for critical civil infrastructure.

Modern structural analysis necessitates numerical formulations with advanced nonlinear attributes. To that end, numerous finite elements have been proposed, spanning from classical to hybrid standpoints. In addition to their individual features, all formulations originally stem from an underlying variational principle, which can be deemed as a unified energy metric of the system. The corresponding equations of structural equilibrium define a stationary point of the assumed principle. Following this logic in this work, the total potential energy is directly treated as an objective function, subject to some kinematic compatibility constraints, within the conceptions of nonlinear programming. The only approximated internal field is curvature, whereas displacements occur solely as nodal entities and Lagrange multipliers serve compatibility. Thereby, a new nonlinear programming hybrid element formulation is derived, which uses exact kinematic fields, can incorporate nonlinear assumptions of any extent, and is amenable to various applicable nonlinear programming algorithms. The suggested nonlinear program is presented in detail herein, together with its consistent second-order iterative solution procedure. The results obtained in benchmark nonlinear structural problems are validated and compared with OpenSees flexibility-based elements, showcasing notable performance in terms of accuracy, mesh density discretization, computational speed, and robustness.

In vibration-based damage identification, a common problem is that modal information is not enough and insensitive to local damage. To solve this problem, an effective method is to increase the amount of modal information and enhance the sensitivity of the experimental data to the local damage. In this paper, a damage identification method based on additional virtual masses and Bayesian theory is proposed. First, the virtual structure with optimal additional mass and high sensitivity to local damage is determined through sensitivity analysis, and then a large number of virtual structures can be obtained by adding virtual masses; thus, a lot of modal and statistical information of virtual structures can be obtained. Second, the Bayesian theory is used to obtain the posterior probability distribution of the damage factor when structural a priori information is considered. Third, by finding the extreme value of the probability density function, the damage factor is derived based on the a priori information and the statistical information of virtual structures. Finally, the effectiveness of the proposed method is verified by numerical simulations and experiments of a 3-story frame structure. Experimental and numerical results show that the proposed method can be used to identify the damage severity of each substructure and thus damaged substructures can be localized and quantified; the error in damage factor is basically within 5%, which shows the accuracy of the proposed method. The proposed method can not only provide the structural damage localization and quantification result (i.e., the damage factor), but also the probability distribution of the damage factor; moreover, it has high sensitivity to damage and high accuracy and efficiency.