Elsevier stands against racism and discrimination and fully supports the joint commitment for action in inclusion and diversity in publishing. List of the recent articles made freely available as part of this journal’s. Proposed second order tensorial framework is shown to be exact in the case of two orthogonal arrays of cracks, open and/or closed, it is approximate in the general case of many arrays of cracks, open and/or closed. An important feature of the proposed method is that it does not rely on the classical assumption of separation of scales, which permits its application to a broad range of architectured composites including phononic crystals and acoustic metamaterials. By representing the target metric of the mesh as a sum of a coarse-grained component and a component quadratic in surface gradients, an improved surface mesh may be obtained. The notion of plane or space curves is one of the elementary ones in the theory of differential geometry, because the concept of a manifold comes from the generalization of a curve or a surface in R3. Numerical examples of this smoothing methodology, demonstrating the efficiency of the proposed approach, are presented. Special issues published in Differential Geometry and its Applications. The properties of a differential manifold M are independent of a chosen coordinate system. Using this q-difference equation, some multilinear generating functions for Hn are discussed. The entire field of Geometric Deep Learning hinges on it. The accuracy and computational efficiency of the approach are demonstrated for both phononic crystals and acoustic metamaterials. By continuing you agree to the use of cookies. The weak form of the grid equations is solved using the finite element approximation, which reduces the grid equations to a nonlinear, algebraic set. The finite element method is applied to grid smoothing for two-dimensional planar geometry. 262-277, Nonlinear Analysis: Real World Applications, Volume 21, 2015, pp. A similar approach is used by Pacoste [5] for beam elements in instability problems. A geometrically exact beam finite strain formulation is defined. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). The question of both indicial and constitutive symmetries of different crack density tensors is addressed: for instance the standard fourth order crack density tensor Dc is rari-constant (totally symmetric) and the fourth order closed cracks density tensor by which closed cracks are acting is found to have the square symmetry. Copyright © 2020 Elsevier B.V. or its licensors or contributors. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Once production of your article has started, you can track the status of your article via Track Your Accepted Article. We present a Bayesian technique to estimate the fine-scale properties of a binary medium from multiscale observations. It is equivalent to say, that there exists smooth or Cr differentiable atlases which are compatible. An abstract infinite dimensional manifold of mappings, a configuration space, is constructed which permits an exact linearization of algorithms, locally. Smoothing is achieved by computing the metric tensor on the dual mesh elements, which incorporates the influence of neighbor elements. Please click here for more information on our author services. Moreover, we extend the previous result to the case of multi-dimensional filtrations, requiring that our filtration is also complete. In partnership with the communities we serve; we redouble our deep commitment to inclusion and diversity within our editorial, author and reviewer networks. This paper develops a set of adaptive surface mesh equations by using a harmonic morphism, which is a special case of a harmonic map. The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate. Choice. Common examples are employed to test the accuracy of the information provided by the method. The procedure is based on determining two Muskhelishvili complex potentials in terms of complex Fourier series, and applying the Schwartz alternating method repeatedly until the boundary conditions on the contour of every hole are satisfied. Developments in the fields of computational science—the finite element method—and mathematical foundations of continuum mechanics result in many new algorithms which give solutions to very complicated, complex, large scaled engineering problems. This journal has an Open Archive. The tensorial nature of crack density of an initially isotropic 2D medium with open and closed cracks is studied by means of polar decomposition rewriting of standard micro-mechanics results. The observations consist of coarse-scale (of the order of the domain size) measurements of the effective permeability of the medium (i.e., static data) and tracer breakthrough times (i.e., dynamic data), which interrogate the fine scale, at a sparsely distributed set of locations.