In this work we analyze the possibilities of applying model reduction in the advanced simulation of materials and processes. The use of such strategies allows impressive computing time savings in the numerical simulations of complex models without degrading the solution accuracy. For this purpose we apply proper generalized decompositions of multidimensional models that can be associated to usual models in computational mechanics. The proposed approach is based in introducing all the parameters of interest as new extra-coordinates in the model and then solving it allowing computing the solution in the space and time for any value of the selected parameters. This approach increases the dimensionality of the model, but by applying a separated representation of the unknown field the redoubtable curse of dimensionality can be circumvented.