Available online at www.sciencedirect.com ScienceDirect Comput. Methods Appl. Mech. Engrg. 351 (2019) 694–717 www.elsevier.com/locate/cma A novel computational multiscale approach to model thermochemical coupled problems in heterogeneous solids: Application to the determination of the “state of cure” in filled elastomers Gustavo Roberto Ramos a , Rodrigo Rossi b,∗ a Universidade Federal de Santa Maria, Campus Cachoeira do Sul, Rua Ernesto Barros, 1345, Cachoeira do Sul, RS, 96506-322, Brazil b Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite, 425, Porto Alegre, RS, 90046-902, Brazil Received 11 January 2018; received in revised form 26 March 2019; accepted 28 March 2019 Available online 9 April 2019 Abstract In this paper, we present a computational homogenization framework to model coupled transient heat conduction with heat generation and chemical kinetics in solids. The proposed method considers that both macro and microscales are under transient heat conduction, being the chemical kinetics (which gives rise to internal heat generation source in the heat conduction problem) defined either in some of the constituents of the microscale or even in the whole microscale. The numerical solution is based on a nested solution strategy, in which the finite element method is used for solving both the macro and the microscale problems, configuring a FE 2 scheme. By solving the coupled problem of transient heat conduction with internal heat generation and chemical kinetics defined in a finite representative volume element, we extract the effective thermal properties and chemical kinetics contribution of the composite and employ them to solve the transient macroscale heat conduction problem (also with internal heat generation). This novel numerical framework is employed in the prediction of the State Of Cure (SOC) in filled elastomers. Numerical solutions of some in-plane heat conduction problems are presented in order to assess the proposed numerical strategy, showing that the multiscale model developed is capable of numerically determining transient non-homogeneous maps of the SOC at the microscale. c ⃝ 2019 Elsevier B.V. All rights reserved. Keywords: Computational homogenization; Heterogeneous solids; Transient heat conduction; Multiscale; Chemical kinetics 1. Introduction One of the main challenges in modeling materials, and especially in polymers, is to understand the fundamental phenomena in different length (spatial) and time scales. Computational multiscale homogenization methods have emerged in the last decades promising an “integrated” view along different scales of matter. In hierarchical multiscale methods the “correctness of information” passed between scales as well the establishment of “rational” bridging between them plays a central role. ∗ Corresponding author. E-mail addresses: gustavo.ramos@ufsm.br (G.R. Ramos), rrossi@ufrgs.br (R. Rossi). https://doi.org/10.1016/j.cma.2019.03.055 0045-7825/ c ⃝ 2019 Elsevier B.V. All rights reserved.