Cement is one of the most widely used construction materials. It has relatively high compressive strength but poor resistance to deformation and tensile stress, e.g., cement-based structural members are vulnerable to seismic loading and impact. Hence, fiber-reinforced cementitious composites (FRCCs) are produced by mixing reinforcing fibers with cement paste to achieve improved ductility and post-cracking strength. More recently, a new class of cementitious composites called engineered cementitious composite (ECC) or strain-hardening cementitious composite (SHCC) was developed through rigorous micromechanics design, which exhibits a strain-hardening tensile behavior through the multiple cracking process. The enhanced mechanical properties brought by fibers are highly dependent on the matrix strength, fiber types, fiber geometries, and fiber-matrix interface properties.

The present study aimed to establish a reliable quantitative link between the mechanical properties of fiber-reinforced cementitious composites and the constituent parameters and identify the fundamental strengthening and toughening mechanisms using a newly developed multiphase framework. The key idea is to idealize the composites as the mixture of a finite number of fiber phases characterized by various orientations and the matrix phase with independent kinematic descriptors, which interact through nonlinear interfaces to account for the realistic fiber-matrix load transfers explicitly. Through the variational formulation of the macro and micro- balance equations, the resulting weak form of the system determines how the contribution of each underlying mechanism can be captured transparently at the macro scale, enabling a detailed study of the competitive interactions between different mechanisms.

First, an XFEM cohesive fracture-based multiphase framework was proposed to investigate the pre-failure mechanical performance of fiber-reinforced cementitious composites subjected to localized cracking. The quasi-brittle fracture of the cement matrix was characterized by the XFEM-cohesive crack framework. For exploring the fiber-bridging mechanism, the horizontal fiber phases corresponding to different embedding lengths were superimposed over the near-crack region of the matrix phase, while an effective homogeneous Cauchy medium was assumed outside the multiphase region. The sliding interface for each fiber phase was described by a slip field, leading to a new nonlocal slip model being proposed, which can be used to treat arbitrary fiber distributions. The weak formulation of the balance equations verified that the toughening effect is induced by the interfacial shear stress rather than fiber tensile stress. Prior to evaluating new problems, the capability of the proposed model was validated to reproduce consistent fracture behaviors with the experimentations. A parametric analysis was then conducted to explore the effect of fiber Young's Modulus, fiber diameter, fiber volume fraction, interfacial strength, and interfacial stiffness on the composite bending strength and toughness.

Subsequently, to overcome the limitations of the above approach, a more advanced plastic-damage multiphase model was developed. This approach can capture a major set of essential failure modes for fiber-reinforced cementitious composites subjected to single cracking, including the damage and plasticity in the matrix crack, fiber plasticity and rupture, fiber-matrix interface bond breaking, slip hardening/weakening, fiber pullout, and instantaneous structural failure. This is achieved by the following novelties: (i) adopting a damage-plastic interface model to characterize stiffness degradation and permanent deformation of the matrix crack; (ii) proposing a new unified damage-plastic interface framework for the fiber-matrix interface, capable of characterizing the slip-dependent behavior, fiber pullout, and fiber rupture simultaneously; (iii) a modified nonlocal slip model was proposed to depict the micro-slippage of arbitrarily distributed fibers with a minimum number of auxiliary kinematic descriptors; (iv) last but not least, the usage of a quadtree-based mesh refinement technique enabled the modeling framework to study various composites fracture problems efficiently. It was demonstrated that the composite toughening effect originated not only from interfacial friction but also from elastoplastic stretching of fibers and pulley force actions, among which the interfacial friction is the dominating energy absorbing mechanism. The model was validated against experimental data from the single-fiber level and the structural level.

Finally, a cyclic plastic-damage multiphase model, aimed to evaluate the multiple cracking of strain-hardening cementitious composites subjected to tensile loading, was developed. The key to predicting the multi-crack growth and ultimately tune the composites' tensile property lies primarily in the realization regarding the competitive propagation of closely spaced microcracks strung by fibers through the novel multiphase configuration, i.e., the stacked fiber bundles model, in which fiber phases with different projection lengths on the tensile direction representing various fiber inclination angles are stacked layer by layer on the matrix phase with multiple closely spaced potential cracks. The modeling framework has the following novelties: (i) regarding the matrix cracking, a new damage-plastic interface model was proposed to characterize the stiffness degradation and the gradual recovery of contact stiffness for cementitious composites during cyclic loadings; (ii) targeting the crack resistance effect, a unified nonlinear bond-friction model was formulated which can capture the elastic bond breaking, friction hardening, fiber rupture, fiber pullout, and the cyclic loading behavior of the fiber-matrix interface simultaneously; (iii) considering the snubbing effect intrinsic to cracks, a two-stage evolution algorithm for the fiber bridging force was implemented to distinguish the bridging efficiency in intact and cracked medium.


Energetic formulation of the balance configuration delivers the three balance states at different scales. At the macroscale, the bulk composites stress is constant throughout the specimen under tensile loading. Besides, the summation of the fiber bridging stress and the matrix cohesive traction at the crack surfaces should be equal to the bulk composite stress. At the microscale, the fiber tensile stress accumulates with the surface friction stress at the fiber-matrix interface. Three tensile tests of representative strain-hardening cementitious composites demonstrate the good predictive ability of the model in different aspects, including the global stress-strain responses, the crack pattern, the crack widths, and the crack spacing. Through microstress analysis, the development of residual compressive tractions in matrix cracks was identified for the first time. Parametric studies were also conducted to explore the role of fiber orientation distribution, fiber length, fiber diameter, and interfacial strength in the composite tensile properties.