SUMMARYA microstructural model for the mechanical behaviour of quasi-brittle materials is developed and veriÿed for concrete and bone specimens. The model is based on interface elements equipped with a constitutive law representing non-linear fracture, while continuum elements remain linear elastic. The interface constitutive model is implemented with a sub-stepping scheme. Non-linear geometric e ects due to large displacements are included in the model by means of an incremental Lagrangian formulation, although strains in the continuum and relative displacements in the interfaces are assumed to remain small. An arc-length procedure is used to ensure convergence during the highly non-linear behaviour in the post-peak regime. Concrete and bone specimens are idealized as two-phase particle composites and are discretized into ÿnite elements, including interface elements along the main potential crack paths. The numerical results in tension and compression are described and compared with experimental observations. The need of considering nonlinear geometric e ects in this type of calculations is also discussed.
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