Level Set-Based Extended Finite Element Modeling of the Response of Fibrous Networks Under Hygroscopic Swelling

Materials like paper, consisting of a network of natural fibers, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behavior is particularly important for understanding the hygro-mechanical response of sheets of paper in applications like digital printing. A two-dimensional microstructural model of a fibrous network is therefore developed to upscale the hygro-expansion of individual fibers, through their interaction, to the resulting overall expansion of the network. The fibers are modeled with rectangular shapes and are assumed to be perfectly bonded where they overlap. For realistic networks, the number of bonds is large, and the network is geometrically so complex that discretizing it by conventional, geometry-conforming, finite elements is cumbersome. The combination of a level-set and XFEM formalism enables the use of regular, structured grids in order to model the complex microstructural geometry. In this approach, the fibers are described implicitly by a level-set function. In order to represent the fiber boundaries in the fibrous network, an XFEM discretization is used together with a Heaviside enrichment function. Numerical results demonstrate that the proposed approach successfully captures the hygro-expansive properties of the network with fewer degrees-of-freedom compared to classical FEM, preserving desired accuracy.

Modeling and Simulation of 3-D Interfacial Cracks by XFEM

The structural integrity of multi-layered material depends on the mechanical properties and the fracture behaviour at the interface. The sudden jump in mechanical properties across the interface is the major source of failure in layered materials. An accurate evaluation of mixed-mode SIFs becomes essential for safe design of layered structure components. In this work, extended finite element method (XFEM) has been used to analyze interfacial cracked three-dimensional structures under mechanical loading. In XFEM, partition of unity enrichment concept is used to model a crack e.g. a crack surface is modeled by Heaviside enrichment function whereas a crack front is modeled by branch enrichment functions. Discontinuity due the presence of bi-material interface is modeled by the signed distance function. Modified domain based interaction integral approach has been used to evaluate the individual stress intensity factors. Three-dimensional cylindrical domain having an interfacial crack is taken for the simulations. A comparative analysis has been performed with and without an interface for an embedded penny shape crack. The effect of material interface on the SIFs has been analyzed in detail. Finally, a three-dimensional interfacial crack growth simulation has been performed for arbitrary shape crack.

CRACK ANALYSIS IN ORTHOTROPIC MEDIA USING COMBINATION OF ISOGEOMETRIC ANALYSIS AND EXTENDED FINITE ELEMENT

The main contribution of this paper is to propose an IGA formulation to model stationary cracks within orthotropic media by combination of XFEM enrichment functions and level set functions. For modeling cracks in solution field crack face and crack tips are considered separately and the control points that are related to each part are enriched with different approaches. The control points related with the crack face are enriched using the Heaviside enrichment functions. Level set functions are used to distinguish the control points correspond to crack tips and crack face. Stress intensity factors are employed to compare the results of XIGA with other methods. Several numerical examples considering crack inclination angle and material orientation axis are solved to verify the XIGA formulation. The results fairly conform to available methods, however less DOFs are used in XIGA.

Modeling Abrasion Resistant Materials by Modeling Large Sliding Frictional Contact

— In this paper, our goal is to simulate abrasion resistance material. We therefore need a robust algorithm to model this phenomenon which is a kind of large frictional contact problem. In order to reach to our aim, we have proposed a new method to impose contact constraints in eXtended Finite Element Method (XFEM) framework. In this algorithm, we have modeled large sliding contact problems by using the Node To Segment (NTS) concept. Furthermore, friction between two sliding interface has been modeled based on the Coulomb friction law. In addition, the penalty method which is the most convenient way of imposing non-penetration constraints has been employed. In our algorithm, new Lagrangian shape functions have been used to solve the problems of the conventional Heaviside enrichment function. Finally, a numerical simulation has been delivered to prove the accuracy and capability of our new algorithm.