Author(s)

C.Y. Chan and L. Ke

Abstract

An efficient numerical method using radial basis functions is developed to simulate the evolution of a damage process in elastic materials caused by compression and tension. An estimate of the critical parameters for the total damage is discussed. 1 Introduction Let us consider a one-dimensional rod of length a. It is fixed at its left end while a traction acts on its right end. Let v(x,i) be the displacement and u(x,i] be the damage. When u = 1, the material is undamaged; when u — 0, it is completely damaged, that is, the rod is broken. When 0 < u < 1, the material has some open cracks, but it retains its elastic behavior (with modified (softer) elastic moduli). Let Ey be the Young's modulus of the material, /<, be the density (per unit length) of the applied forces, c (> 0) be the

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