Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Abstract

SUMMARYInterfacial damage nucleation and evolution in reinforced elastomers subjected to finite strains is modelled using the mathematical theory of homogenization based on the asymptotic expansion of unknown variables. The microscale is characterized by a periodic unit cell, which contains particles dispersed in a blend and the particle matrix interface is characterized by a cohesive law. A novel numerical framework based on the perturbed Petrov-Galerkin method for the treatment of nearly incompressible behaviour is employed to solve the resulting boundary value problem on the microscale and the deformation path of a macroscale particle is predefined as in the micro-history recovery procedure. A fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed multiscale framework is capable of predicting the non-homogeneous microfields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.

On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver

“…Upon equilibrium, the macroscopic traction vector is evaluated using Equation (14). The solution is obtained using our multiscale parallel solver, PGFem3D [66,67], executed on up to 512 processing cores. See Appendix A for details regarding the parallel computational implementation.…”

The homogenized behavior of unidirectional fiber-reinforced composite materials in the case of debonded fibers

“…But this type of estimate simply gives a lower bound to their stiffness and one must define more precisely the effective behavior of completely or partially debonded unidirectional composites. Many works have been devoted to this task, see for instance [6,8,12,13,14,15,16,18,19,21,23,26]. In general, these studies consist in replacing the perfect bond of the interface by some "cohesive law" or simply in removing the fibers when the debonding is complete.…”

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

“…Due to the separation of scales in CH (Figure 10), the response of each RUC may be computed independently, providing high parallelism in computing the fully coupled multiscale response. The hierarchically parallel scheme uses a parallel finite element solver, PGFem3D (Matouš and Maniatty, 2004, 2009; Matouš and Geubelle, 2006;Matouš, 2015a,b, 2016), at both scales and employs a client-server coupling for passing information between the macro and micro levels. The macroscale equilibrium is computed in parallel on the "client" processors, and the contributions from the individual RUCs are computed in parallel on the "servers" (see (5) and Figure 11a).…”