相关论文: Interfacial crack integral identities incorporatin…

After briefly recalling some computational aspects of blowing up and of representation of resolution data common to a wide range of desingularization algorithms (in the general case as well as in special cases like surfaces or binomial…

We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy…

The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling…

By employing conformal mappings, it is possible to express the solution of certain boundary value problems for the Laplace equation in terms of a single integral involving the given boundary data. We show that such explicit formulae can be…

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…

The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a…

An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…

This paper presents a computational framework for quasi-static brittle fracture in three dimensional solids. The paper set outs the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of…

Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from…

We describe creation and annihilation of particles at external sources in one spatial dimension in terms of interior-boundary conditions (IBCs). We derive explicit solutions for spectra, (generalised) eigenfunctions, as well as Green…

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…

This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights…

This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded…

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…

An integrable quantum spin ladder based on the SU(4) symmetry algebra with boundary defects is studied in the framework of boundary integrability. Five nontrivial solutions of the reflection equations lead to different boundary impurities.…

We propose inverse problems of crack propagation using the phase-field models. First, we study the crack propagation in an inhomogeneous media in which fracture toughness varies in space. Using the two phase-field models based on different…

We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The…

We use a power expansion representation of plane elasticity complex potentials due to Kolossov and Muskhelishvili, to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant…

Density functional theory calculations have been performed to study the structures and energetics of coherent and semicoherent TiC/Fe interfaces. A systematic method for determining the interfacial energy for the semicoherent interface with…