This thesis presents a study of defects in materials through a multiscale approach. The multiscale approach we have used is based on the systematic coarsening of the domain by applying judicious kinematic constraints. In this fashion, a seamless bridging of the subatomic/atomistic and the continuum fields is performed using the Quasicontinuum (QC) methodology. During the first part of this thesis, we have studied the problem of ductile failure in single crystals at finite temperature using the HotQC method, which is an extension of the QC to nonequilibrium thermodynamic systems. It uses the \textit{max-ent} principle to estimate the probability density function which best fits the problem. Then, based on the variational mean field approximation, a local free energy is computed by phase averages using Gaussian Quadratures.

To prove the feasibility of the HotQC method, we have studied the early onset of void growth by dislocation emission at finite temperature, which is the crucial stage in ductile failure mechanism. Our work is focused on FCC crystals, in particular Cu and Al. For each material, a detailed study of dislocations emission and temperature evolution under different loading states is performed using quasi-static and dynamic approaches. This work shows that birth and growth of the dislocations push away from the void surface a flux of material along with a heat flux through the crystal. In order to understand how different interatomic potentials might influence the dislocation emission process, we have used several interatomic potentials throughout the course of our simulations. As a result, we have discovered that even for similar potentials, the void growth and dislocations emission process, temperature evolution and stress strain curves might change very significantly. Furthermore, due to the semi-empirical nature of the interatomic potentials, they introduce a source of error that should not be neglected.

In order to solve this problem, we have used a second method which uses Density Functional Theory (DFT) as the only input to study the mechanics of materials. The methodology applied in this work is based on the Linear Scaling Spectral Gauss Quadrature (LSSGQ) method, which propose a reformulation of the DFT introducing the spectral theorem and the use of Gaussian Quadratures. Both, nodes and weights of this quadrature rule are obtained using the Lanczos algorithm which presents a linear scaling with the number of atoms for metals as well as for insulators. Then, the method has been validated through simple tests such as surface relaxation process and single vacancy in BCC crystals. Throughout these simulations, we have demonstrated the linear scaling of the procedure for 3D problems. Finally, we have introduced a coarse graining approximation based on the QC framework. Within this technique, a systematically coarsening of the domain is performed, reducing the total number of degrees of freedom of the system. Therefore, the combination of the LSSGQ method and the coarse graining approximation allows us to simulate problems on crystals having a $\sqrt{n}$ scaling, where n is the number of atoms in the crystal.