In this paper, we provide a retrospective examination of the developments and applications
of the extended finite element method (X-FEM) in computational fracture mechanics. Our …

We review different techniques to enforce essential boundary conditions, such as the
(nonhomogeneous) Dirichlet boundary condition, within a discrete variational framework …

We present a novel physics-informed neural networks (PINNs) framework for modeling
interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks …

We explore the use of the non-symmetric Nitsche method for the weak imposition of
boundary and coupling conditions along interfaces that intersect through a finite element …

We introduce a phase‐field method for continuous modeling of cracks with frictional
contacts. Compared with standard discrete methods for frictional contacts, the phase‐field …

An adaptive phase-field method is developed and applied to model fracture propagation in
orthotropic composites. The proposed approach extends the work of Muixí et al.(2020) to …

The non-symmetric variant of Nitsche's method was recently applied successfully for
variationally enforcing boundary and interface conditions in non-boundary-fitted …

In design optimization of structures, design domains are often described by multiple non-
uniform rational B-spline (NURBS) patches. To perform multi-material topological design in …

In this paper, an Uzawa-type augmented Lagrangian contact formulation is presented for
modeling frictional discontinuities in the framework of the X-FEM technique. The …

We present a barrier method for treating frictional contact on interfaces embedded in finite
elements. The barrier treatment has several attractive features, including:(i) it does not …