Dynamic analysis of failure paths of truss structures: Benchmark examples including material degradation

Abstract We propose novel benchmark examples of dynamic failure paths of truss structures. Novelty arises from use of a logarithmic strain measure, within a total Lagrangian formulation, combined with a continuum material damage model. Previous benchmarks have considered the usual engineering strain measure, which is not always useful, as it can lead to material degeneration under finite levels of stress. Ductile material behavior has been considered in the literature, addressing plasticity and some material softening, but neglecting material degradation. Herein, damage accumulation is associated to the hydrostatic component of plastic strains, leading to a stable and explicit representation of material degradation. The original static formulation, presented elsewhere by the authors, is extended herein to the dynamic analysis of failure paths of truss structures. Several numerical examples from the literature are studied, and the differences in dynamic behavior are pointed out. In our implementation, as individual bars are damaged, elastic unloading and load redistribution are observed. When the critical damage hypothesized by Lemaitre is reached by individual bars, these are fully unloaded, with no material degeneration or numerical instability. Numerical results highlight the significant effects of material degradation in the dynamic behavior of truss structures under exceptional loads. We propose the set of examples addressed herein as the new benchmarks to which future developments in geometrical and material non-linear truss modelling will be compared.

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