In a number of applications, large size structures subjected to loads that cause highly non-linear behavior need to be analyzed. With the peridynamic theory, proposed by Stewart Silling in 2000 and 2007, elasticity and damage in quasibrittle structures such as plain and reinforced concrete structures can be modeled with the peridynamic theory. To model these structures, lattice models with brittle beam elements are used to model concrete. A shortcoming of lattice and particle models is that they are highly demanding of computational power. Molecular dynamics may be, in some cases an appropriate tool for analyzing microcracks in quasibrittle materials in compression, but molecular dynamics becomes infeasible at scales larger than a few million atoms. For example, in masonry structures, cracks form in the brick mortar joints, and concrete blocks can be assumed to have a uniform displacement field. This allows us to use the peridynamic finite element model, which is an improvement over discrete lattice models. This model assumes a continuous displacement field within each finite element, with displacement discontinuities allowed to develop between finite elements. The objective of this work is to model cracks in quasibrittle structures, with the peridynamic model. The peridynamic finite element model is shown to be much more computer time-and memoryefficient than the similar discrete particle-based models. Results show that this implementation appears to be more computationally efficient than particle or lattice models.

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There exists a great potential for application in soil mechanics with the use of mechanistic models such as the finite element model, and other non-local models, such as the peridynamic model, since the soil mass can be modelled as a group of particles that interact with each other. In this work, we determine the bearing capacity of deep foundations where stresses are transmitted to deep deposits, which generally present better characteristics in terms of compressibility and shear strength. One of the main elements are driven piles, which must be previously designed, made and tested before their final use. In this work, a comparison with different methods is presented. The finite element method and the peridynamic model are used. Because the effect of consolidation was not taken into account, in these examples, the assumption is made that the structures are cemented in inert soil. Likewise, it is assumed that the water table has no influence on the simulations. Failure envelopes were observed where bonds between particles present high gradients of deformation and fracture. Bearing capacities were estimated and compared with those obtained from the Terzaghi and Meyerhof methods.