MICROMECHANICAL MODELING OF STRAIN-HARDENING AND TENSION SOFTENING INCEMENTITIOUS COMPOSITES

This paper will describe a procedure for modelling the complete macros copic response (including strain hardening and tension softening) of t wo short fibre reinforced cementitious composites and show how their m icrostructural parameters influence this response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the opening of multiple cracks in elastic solids u nder unidirectional tensile loading. The strain hardening is essential ly due to elastic bridging forces which are proportional to crack open ing displacements. After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and thereafter provide a residual bridging force by frictional pull-ou t, while others continue to provide full bridging. This results in a k ind of elastoplastic bridging law which governs the initial tension so ftening response of the composite. Besides the usual square-root singu larity at crack tips, the elasto-plastic bridging law introduces a log arithmic singularity at the point of discontinuity in the bridging for ce. These singularities have been analytically isolated, so that only regular functions are subjected to numerical integration. Unbridged mu ltiple crack problems have in the past been solved using double infini te series which have been found to be divergent. In this paper a super position procedure will be described that eliminates the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple cracks. The paper will end by s howing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain hardening and the initial tension soft ening response of two cementitious composites.