Truncated integration for simultaneous simulation of sintering using a separated representation

Abstract : Recent developments of multidimensional solvers using separated representation make it possible to account for the multidimensionality of mechanical models in materials science when doing numerical simulations. This paper aims to extend the separated representation to inseparable equations using an efficient integration scheme. It focuses on the dependence of constitutive equations on material coefficients. Although these coefficients can be optimized using few experimental results, they are not very well known because of the natural variability of material properties. Therefore, the mechanical state can be viewed as a function depending not only on time and space variables but also on material coefficients. This is illustrated in this paper by a sensitivity analysis of the response of a sintering model with respect to variations of material coefficients. The considered variations are defined around an optimized value of coefficients adjusted by experimental results. The proposed method is an incremental method using an extension of the integration scheme developed for the Hyper Reduction method. During the incremental solution, before the adaptation of the representation, an assumed separation representation is used as a reduced-order model. We claim that a truncated integration scheme enables to forecast the reduced-state variables related to the assumed separated representation. The fact that the integrals involved in the formulation can not be written as a sum of products of one-dimensional integrals, this approach reduces the extent of the integration domain.