A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials

Horacio D. Espinosa*, Pablo D. Zavattieri, Sunil K. Dwivedi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

148 Scopus citations


A dynamic finite element analysis of large displacements, high strain rate deformation behavior of brittle materials is presented in total Lagrangian coordinates. A continuum/discrete damage model capable of capturing fragmentation at two size scales is derived by combining a continuum damage model and a discrete damage model for brittle failure. It is assumed that size and distribution of potential fragments are known a priori, through either experimental findings or materials properties, and that macrocracks can nucleate and propagate along the boundaries of these potential fragments. The finite deformation continuum multiple-plane microcracking damage model accounts for microcracks within fragments. Interface elements, with cohesive strength and reversible unloading before debonding, between potential fragments describe the initiation of macrocracks, their propagation, and coalescence leading to the formation of discrete fragments. A surface-defined multibody contact algorithm with velocity dependent friction is used to describe the interaction between fragments and large relative sliding between them. The finite element equations of motion are integrated explicitly using a variable time step. Outputs are taken at discrete time intervals to study material failure in detail. The continuum/discrete damage model and the discrete fragmentation model, employing interface elements alone, are used to simulate a ceramic rod on rod impact. Stress wave attenuation, fragmentation pattern, and overall failure behavior, obtained from the analyses using the two models, are compared with the experimental results and photographs of the failing rod. The results show that the continuum/discrete model captures the stress attenuation and rod pulverization in agreement with the experimental observations while the pure discrete model underpredicts stress attenuation when the same potential fragment size is utilized. Further analyses are carried out to study the effect of potential fragment size and friction between sliding fragments. It is found that compared with the continuum/discrete damage model, the discrete fragmentation model is more sensitive to the multi-body discretization.

Original languageEnglish (US)
Pages (from-to)1909-1942
Number of pages34
JournalJournal of the Mechanics and Physics of Solids
Issue number10
StatePublished - Oct 1 1998


  • A. dynamic fracture
  • A. grain boundaries
  • A. microcracking
  • B. crack mechanics
  • C. finite elements

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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