Computational homogenisation of thermo-viscoplastic composites: Large strain formulation and weak micro-periodicity

An electro-mechanically coupled computational multiscale formulation for electrical conductors

“…The particular form (32) has been chosen in accordance with thermo-mechanical multiscale formulations as discussed in [2,6]. However, in contrast to the temperature, the electric potential is assumed to enter the constitutive equations only in terms of its gradient, i.e., the electric field vector, such that alternative definitions that do not account for φ M are possible.…”

“…Homogenization methods for generalized continua, in particular, second-order homogenization methods that account for the macroscopic deformation tensor and for its gradient, are elaborated in [12,17,18,23]. Moreover, extensions to thermomechanical coupling are presented in [2,6,24,28,29] and electro-mechanically coupled multiscale formulations for piezo-and ferroelectric materials are discussed in [13,14,26].…”

A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

“…[17,25,26,32]. Moreover, computational homogenisation schemes for thermo-mechanically coupled problems are addressed in [2,3,33,37,39], formulations for magneto-mechanically coupled problems are discussed in [18,38], and formulations that focus on the simulation of piezo-and ferroelectric materials are elaborated in [20,21,35]. Compared to the present formulation, the latter developments on electro-active solids are based on the fundamentals of electrostatics, whereas the present formulation relies (amongst others) on the continuity equation for the electric current.…”

Non-linear FE2 multiscale simulation of damage, micro and macroscopic strains in polyamide 66-woven composite structures: Analysis and experimental validation

“…(2019); Berthelsen and Menzel (2019). Besides the kinematic fields, the combination will allow capturing the local thermomechanical responses as well as the coupling of the damage with the local dissipations and its influence on the temperature variations during a thermomechanical loading.…”

“…Xu et al (2020) have proposed a novel data-driven multiscale finite element method for composite materials and structures. Applications of multiphysics FE 2 schemes, based on the homogenization theory, concerning the same reinforcement have been developed in Sengupta et al (2012); Javili et al (2013); Schröder et al (2016); Berthelsen et al (2017); Berthelsen and Menzel (2019); Tikarrouchine et al (2019), and for the textile composite in Rique et al (2020). Furthermore, a new FE 2 strategy has been proposed recently for concurrent modelling.…”