Green's Tensors and Lattice Sums for Elastostatics and Elastodynamics

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Exponentially convergent lattice sums.

For any oblique incidence and arbitrarily high order, lattice sums for one-dimensional gratings can be expressed in terms of exponentially convergent series. The scattering Green's function can be efficiently evaluated also in the grating plane. Numerical implementation of the method is 200 times faster than for the previous best result.

Dependence of Equilibrium Griffith Surface Energy on Crack Speed in Phase-Field Models for Fracture Coupled to Elastodynamics

Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is co...

Algebraic Formulation of Elastodynamics: the Cell Method

This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual sub...

A stabilized discontinuous mortar formulation for elastostatics and elastodynamics problems Part I: abstract framework

In this paper, we first recall the general assumptions and results arising in mortar methods applied to elastostatics [Woh01]. By extension to the curved interfaces case of the ideas from Gopalakrishnan and Brenner [Gop99, Bre03, Bre04], and from the introduction a generalized Scott and Zhang interpolation operator [SZ90], we prove the independence of the coercivity constant of the broken elast...