Elastic Theory Has Zero Radius of Convergence.

In nonlinear elastic theory, the inverse bulk modulus K , for example, depends on the compression P: 1yKsPd ­ c0 1 c1P 1 c2P 1 · · · 1 cnP 1 · · · . Elastic materials that allow cracks are unstable at finite temperature with respect to fracture under a stretching load. As a result, the above power series has zero radius of convergence: it is an asymptotic series. For a two-dimensional isotropic elastic medium allowing cracks we compute the asymptotic form cn11ycn ! Cn1y2 as n ! `. We present an explicit formula for C as a function of temperature and material properties. [S0031-9007(96)00920-9]