Studies in material parameter sensitivity of softening solids Original Research Article

A methodology is presented for the evaluation of the material parameter sensitivity of softening solids. The algorithm is based on the differentiation of the implicit (Euler-backward) return-mapping algorithm used for integration of the constitutive equations and the system of nonlinear algebraic equations obtained from the discretization in finite elements together with an arc-length constraint. The necessity of a stable equilibrium path and the meaning of left-hand and right-hand derivatives are discussed. Examples illustrate the theoretical developments as well as the capabilities of the algorithm to predict possible localization patterns.