Recent Advances in Computational Methods in Engineering Mechanics

Almasi et al. (2019) present the particle difference method (PDM) as a reliable computational method for the prediction of grain growth and stress analysis of polycrystalline materials. The PDM is a meshfree collocation method that directly discretizes the strong form of the equations. Mahdavi et al. (2020) introduce a harmonic-enriched reproducing kernel (HRK) approximation together with the collocation method for highly oscillatory partial differential equations (PDEs). The performance of this method is compared with standard meshless and finite-element methods. Shu and Stanciulescu (2019) study monolithic and staggered schemes using a locking-free solid-shell element to analyze the behavior of thin-walled structural components subjected to combined thermal and mechanical loads. They discuss the difficulties in solving such coupled field problems and propose remedies to preserve numerical stability and appropriate convergence properties. Wei et al. (2020) develop a stabilized meshfree formulation for modeling nonlinear, multiphase porous media with application to landslides of geomaterials. They employ the naturally stabilized nodal integration (NSNI) technique to achieve a stable and efficient reproducing kernel mixed formulation. Abdellatef and Alnaggar (2020) present a formulation for calibration-free coarse graining approach within the framework of the lattice-discrete particle model (LDPM). They validate their approach against various test cases, showing success in replicating similar fine-scale response and failure patterns at a fraction of the fine-scale computational cost. Helgedagsrud et al. (2019) employ isogeometric analysis (IGA) within a finite-element framework to simulate turbulent flows over moving bridge sections and compare their results with wind tunnel experiments. Zhu et al. (2019) present a stabilized interface-capturing approach, based on the level-set method, for two-phase flows with large-amplitude free-surface motion. The derivation is facilitated by the variational multiscale (VMS) framework, which yields interfacial terms that stabilize the moving interface.

Bahmani and Abedi (2019) propose a new damage formulation for failure analysis of brittle materials under dynamic loading. The approach is shown to overcome mesh sensitivity with less computational effort than some other existing approaches. They employ the asynchronous spacetime discontinuous Galerkin (aSDG) method and show various advantages of this approach. Bogdanor et al. (2019) provide a combined computational-experimental investigation of the interaction of damage mechanisms in carbon fiber–reinforced polymer (CFRP) laminated composites subjected to fatigue loading. A computational homogenization-based multiscale life prediction model, which relies on a model order reduction methodology, is employed. Nikoukalam and Sideris (2019) introduce a novel nonlocal hardening-damage model for beams within a flexibility-based frame element formulation. The proposed formulation eliminates strain singularities and achieves convergence with mesh refinement. Londono et al. (2020) propose a viscoelastic constitutive model for an asphalt-concrete material that accounts for temperature and material degradation effects. The model is implemented within a finite-element framework and consists of a new nonlocal damage regularization approach. Liao and Mao (2019) propose to compute accurate stress intensity factors (SIFs) of face-loaded cracks by a simple stress substitution approach that replaces the unknown stress field by analytical solutions. The approach is implemented using the subregion generalized variational principle and quadrature element method (QEM).

Goh and Kallivokas (2019) propose a dispersion-constrained optimization problem to control wave propagation in an elastic medium by engineering its dispersive properties. The inverse problem leading to optimal material properties of the medium is solved by a gradient-based algorithm. San et al. (2020) extend a classical analytical solution concerning the shape optimization of a hanging bar to include varying density and elastic modulus. The well-known solution determines the optimal cross section of a bar that minimizes elongation under various loads and constraints. They also develop a gradient-based numerical optimization algorithm to validate the analytical results and extend the approach to multidimensional hyperelastic bars.

Karakoç et al. (2020) introduce a data-driven computational homogenization method that bridges representative volume elements (RVEs) and in situ material-scale properties using image processing methods. Their minimization scheme enables the bridging of scale-based features of both virtually generated and image-reconstructed domains.

Hatami-Marbini and Rohanifar (2020) provide a numerical study on the tensile response of cellular solids considering various lattice shapes composed of both elastic and elastoplastic struts. They conclude that the spatial distribution of struts with different material properties can be considered a novel approach in the design of cellular solids with desired properties.