This paper presents the development of a nonlocal damage model which describes dynamic damage accumulation processes in brittle solids. The microcrack based continuum damage model is implemented into a transient dynamic finite element computer code. The code is then applied to the study of the damage accumulation process in a concrete plate with a central hole and subjected to the action of a step tensile pulse applied at opposite edges of the plate. Several finite element discretizations are used to examine the mesh size effect. Comparisons between calculated results based on local and nonlocal formulations are made and nonlocal effects are discussed.


Continuous demands on safety and efficient design have placed increasing emphases on fracture and failure analyses of engineering materials and structures. Continuum damage mechanics have been applied to study the phenomenon of brittle fracture in solids under dynamic loads with varying degrees of success (Taylor et al. 1986; Thorne 1990, 1991; Chen 1986, 1995; Chen et al. 1986). Because of the complex geometries and loading conditions involved, numerical simulation techniques have become the tools of choice. Two common problems associated with damage analyses by classical continuum damage mechanics are softening and localization. The consequences of failing to take into account these two problems properly usually manifested in solutions which are dependent on the discretization size. A potential remedy is to cast the field equations in a nonlocal setting such that the high gradients associated with the field parameters in these problems can be captured. The nonlocality is usually represented by an internal length scale which can be introduced in formulations ranging from the Cosserat (Cosserat and Cosserat 1909) and micropolar theories (Eringen and Edelen 1972), the gradient theory (Muhlhaus and Aifantis 1991; de Borst and Muhlhaus 1992), fully nonlocal (Pijaudier-Cabot and Bazant 1987; Bazant 1986) and partially nonlocal (Bazant and Lin 1988) representations. The purpose of this research is to investigate the appropriateness of applying nonlocal damage models to analyze dynamic brittle fracture. The study is based on the comparisons between numerical results obtained from the same damage model with both a nonlocal and a local formulation. The damage model selected is the one developed by the author and his coworkers to simulate brittle rock fracturing. A non- local version is developed here by utilizing the non- local formulation suggested in (Bazant and Lin 1988) in which nonlocality is only applied to those internal state variables involved with material damage. The model has been implemented into the transient finite element code PRONTO 2D (Taylor and Flanagan 1987) for numerical analysis. An example problem has been defined and results have been obtained from both local and nonlocal calculations. To examine mesh size effect, several discretizations are used in the numerical computations. Comparisons between these results have been made. Based on these findings, it is clear that mesh size dependence can be alleviated by adopting a nonlocal damage model formulation. However, the determination of the internal length scale associate with the nonlocal formulation is certainly nontrivial.

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