Scalable Linear Solvers for Computational Material Design of Filled Rubbers

Material design of enhanced tire using nano-fillers requires multi-objective design optimization and data mining, where the Multi-Objective Design Exploration (MODE) method [Koishi et al. 2014] is introduced to enrich the design knowledge for decision making throughout the product design process. One very important procedure of MODE is to predict the mechanical properties of rubbers using nonlinear implicit analysis which involves multiple numerical issues including large model size (tens of millions d.o.f.), periodic constraints, large material deformation and material nonlinearity. To overcome these challenges, we utilize a convex generalized meshfree approximation (GMF) [Wu et al. 2009] for large material deformation analysis. This ensures the positive approximation in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. Moreover, we use a nearly-incompressible hyperelastic material model with linear viscoelasticity for the rubber matrix and interfacial bound material in nonlinear analysis. Thus, the GMF method is coupled with the pressure smoothing scheme [Hu et al. 2010] to relieve numerical volumetric locking at the incompressible limit of the rubber material. The large-scale discrete system is solved in implicit analysis with a cyclic loading path, where the numerical solution of the resulting very ill-conditioned linear systems of equations needs most of the computational time in the whole simulation. Classical direct solvers are in general too expensive for the required model size due to their nonlinear memory demands and operation counts. Thus, we apply an iterative SAMG solver [SAMG] to overcome these limitations. SAMG is a highly robust and efficient solver that typically shows optimal linear scaling with respect to memory and operations. We present numerical results to demonstrate the effectiveness of the computational framework proposed in this work. They clearly show that with the help of SAMG the numerical treatment of this extremely challenging application becomes feasible.