Abstract

One type of singularity that may appear in a three-dimensional fracture problem under elastic behavior is the free corner singularity, which occurs at the intersection of the crack with a free boundary and whose effect is usually ignored. The extended finite element method (XFEM) is a technique that allows the efficient numerical modeling of fracture problems, by using enrichment functions within a finite element model that incorporate the geometry and effect of the crack. However, when applied to the study of a problem with corner singularity, the singular behavior is not properly captured. The reason is that the usual enrichment in the XFEM only describes the typical crack front singularity. Hence, in order to include the effect of the free border singularity, the enrichment has to be modified. In this work, we present a new set of functions which relies on spherical harmonics and is able to capture the behavior of the free border singularity.

Abstract

The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations. First of all, a spatial enrichment is employed to improve the approximation properties of the Eulerian mesh. This is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface. Then, the Lagrangian Particle Level Set (PLS) method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method. While the local enrichment can be understood in the general context of the XFEM, we employ an element-local variant, which allows preserving the matrix graph, and hence highly improving the computational efficiency.

Abstract

Abstract

Research on Soft Active Materials (SAMs) has flourished in recent years driven mainly by potential applications to actuation systems, tissue engineering, and soft robotics. These applications benefit from the unique properties of SAMs such as large deformations, a wide range of stimulants, and high motion complexities. Hydrogels are among the dominant members of SAMs. Their highly nonlinear chemo-mechanical transient behavior is described by equations that include rates of internal state variables representing the local swelling state of the gel. Hence, the simulation of hydrogels requires intricate numerical approaches with stabilization schemes. This paper presents an immersed boundary analysis technique to simulate models with internal state variables. A hydrogel model is used as an example to describe the components of the proposed technique. Level sets define the material layout on a fixed background mesh and a generalized version of the extended finite element method predicts the response. The influence of the internal state variables on the stability of the physical analysis is examined. While focusing on an XFEM approach for hydrogels, the presented theory can be extrapolated to similar applications using models with internal state variables (e.g., shape memory polymers) and other immersed boundary analysis technique (e.g., CutFEM).

Abstract

This work investigates the behavior of unidirectional composite materials through a microscale modeling approach, with a particular focus on crack initiation and propagation under transverse and shear loading. Representative Volume Elements (RVEs) are used to model unidirectional plies with varying geometrical configurations, altering both the relative angles between fibers and the distances between them. Simulations are carried out in ABAQUS/Standard, applying periodic boundary conditions (PBCs) to accurately represent the microstructure and integrating cohesive surfaces at the fiber–matrix interfaces to model interactions and failure at these junctions. Additionally, the Extended Finite Element Method (XFEM) is employed to analyze in detail the initiation and propagation of cracks associated with matrix fracture.

This study advances the understanding of the relationship between microstructure and failure mechanisms, offering tools for the design and optimization of composite materials with improved fracture resistance under multiaxial loading conditions. The results show that the relative angle between fiber centers plays a critical role in determining failure mechanisms at the ply level.

Abstract

The present work focuses on the mechanical characterization of polymer matrix composites reinforced with graphene oxide (GO) nanostructures. Firstly, the selection of the polymer matrix, the parameters for performing a proper curing and the fabrication of the composite material are carried out. The proposed procedure results in an adequate dispersion of the GO, without the need for solvents, which positively influences the mechanical properties of the resulting material. The epoxy resin selected as matrix is ​​reinforced with different percentages of GO in order to study the influence of the reinforcement on the apparent mechanical properties. The composites obtained using such nanostructures are characterized by compression and three-point bending testing. Through the use of the Digital Image Correlation (DIC) technique is possible to evaluate the strain state of the material during the tests. This behaviour is combined with the analytical estimations developed to take into account in the results of the bending testing the difference of the tensile and compressive elastic properties of the material. In addition, numerical simulations are developed by applying both the Finite Element Method (FEM) and the eXtended Finite Element Method (XFEM) whose results are used to validate the experimental data and the analytical model.