Rational Mechanics of Material Strength in Brittle Solids
Material strength is a classical concept that has recently found renewed applications in fracture mechanics, especially in models for crack nucleation in brittle solids. In this paper, we formulate material strength in the setting of finite elasticity and examine its geometric, constitutive, and symmetry-theoretic foundations. We show that spatial covariance requires a strength function to depend on both stress and the corresponding strain measure, so that strength is not controlled by stress alone, but by the pair (stress,strain).