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In this paper, the Discontinuous Cell Method (DCM) is formulated with theobjective of simulating cohesive fracture propagation and fragmentation inhomogeneous solids without issues relevant to excessive mesh deformationtypical of available Finite Element formulations. DCM discretizes solids byusing the Delaunay triangulation and its associated Voronoi tessellation givingrise to a system of discrete cells interacting through shared facets. For eachVoronoi cell, the displacement field is approximated on the basis of rigid bodykinematics, which is used to compute a strain vector at the centroid of theVoronoi facets. Such strain vector is demonstrated to be the projection of thestrain tensor at that location. At the same point stress tractions are computedthrough vectorial constitutive equations derived on the basis of classicalcontinuum tensorial theories. Results of analysis of a cantilever beam are usedto perform convergence studies and comparison with classical finite elementformulations in the elastic regime. Furthermore, cohesive fracture andfragmentation of homogeneous solids are studied under quasi-static and dynamicloading conditions. The mesh dependency problem, typically encountered uponadopting softening constitutive equations, is tackled through the crack bandapproach. This study demonstrates the capabilities of DCM by solving multiplebenchmark problems relevant to cohesive crack propagation. The simulations showthat DCM can handle effectively a wide range of problems from the simulation ofa single propagating fracture to crack branching and fragmentation.

Discontinuous Cell Method (DCM) for the Simulation of Cohesive Fracture and Fragmentation of Continuous Media