相关论文: Interfacial crack integral identities incorporatin…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by…
New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are…
Driven by the growing interest in numerical simulations of dislocation-interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
Through tridimensonal numerical simulations of crack propagating in material with an elastic moduli heterogeneity it is shown that the presence of a simple inclusion can affect dramatically the propagation of the crack. Both the presence of…
Predicting crack trajectories in brittle solids remains an open challenge in fracture mechanics due to the non-local nature of crack propagation and the way cracks modify their surrounding medium. Here, we develop a framework for…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
The quantitative characterisation of crack tip loads is fundamental in fracture mechanics. Although the potential influence of higher order terms on crack growth and stability is known, classical studies solely rely on first order stress…
An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully…
A boundary integral equation (BIE) formulation for 2-D transient elastic wave propagation problems is presented. On the basis of the three-dimensional integral identity, the time-dependent kernels for the two-dimensional boundary integral…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
The relation between fracture surface morphology and the three-dimensional structure of crack fronts is investigated through direct observation of brittle cracks in gels. A key notion in this investigation is the discontinuity of the crack…
We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…
We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack.…
Discretizations of the mean curvature and extrinsic curvature components are constructed on piecewise flat simplicial manifolds, giving approximations for smooth curvature values in a mostly mesh-independent way. These constructions are…
This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…