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Abstract
In the present dissertation, a multiscale meshless framework based on peridynamic theory is developed to study fracture behavior of cementitious composite materials. The most general form, non-ordinary state-based peridynamics (NOSBPD) is implemented as a promising computational tool in fracture analysis while using classical constitutive equations. The NOSBPD is successfully implemented for finite strain material. The dynamic relaxation method is also adopted to obtain quasi-static solution of the system of peridynamic equations. Furthermore, a higher-order approximation method is introduced to control the spurious deformation mode conventionally found in the NOSBPD formulation. This dissertation considers two major efforts in fracture modeling of heterogeneous cementitious composite materials. First, a framework is proposed to predict the response of fiber reinforced concrete (FRC) structures. This approach includes a semi-discrete method in modeling the fiber reinforcement. Second, a mesoscale modeling of concrete members is proposed in which heterogeneous concrete material is represented by four phases (cementitious matrix, coarse aggregates, interfacial transition zone and air voids) in the NOSBPD framework. A statistical study is provided to comprise the effect of random distributions of constituent materials. Finally, two approaches are considered to decrease the computational cost in NOSBPD simulations. The first approach accounts for symmetry boundary conditions in a peridynamic body. The present formulation introduces constraints which allow modeling of local symmetry conditions. Furthermore, in the second approach, the NOSBPD is coupled with the finite element method (FEM). The coupling method enables using peridynamics at discontinuities such as cracks, while using more efficient finite elements for the surrounding body. These two methods effectively reduce the solution time while maintaining accuracy. The validity of the proposed approaches is studied through various examples, and they are found successful and worthwhile for fracture analysis of brittle materials.