Parameter Identification of Nonlinear Viscoelastic Material Model Using Finite Element-Based Inverse Analysis
This study focuses on identifying the parameters of a nonlinear viscoelastic model from Berkovich nanoindentation experiment of an epoxy polymer using finite element-based inverse analysis approach. Instead of traditional approach of online optimization o
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Parameter Identification of Nonlinear Viscoelastic Material Model Using Finite Element-Based Inverse Analysis Salah U. Hamim and Raman P. Singh Abstract This study focuses on identifying the parameters of a nonlinear viscoelastic model from Berkovich nanoindentation experiment of an epoxy polymer using finite element-based inverse analysis approach. Instead of traditional approach of online optimization of model parameters, where finite element computation is placed inside of the optimization algorithm, this study utilizes a surrogate or meta-modeling approach. The surrogate model, which is based on Proper Orthogonal Decomposition (POD) and Radial Basis Function (RBF), is trained with finite element load–displacement data obtained by varying the different model parameters in a parameter space. Once trained POD–RBF based surrogate model is used to approximate the nanoindentation simulation data inside a multi-objective Genetic Algorithm. Current efforts are focused to validate identified parameter set of nonlinear viscoelastic model for different experimental conditions (e.g. maximum load, loading/unloading rate). Keywords Taguchi orthogonal array • Nonlinear viscoelastic model • Finite element analysis • Radial basis function • Proper orthogonal decomposition
19.1
Introduction
Polymer materials have found applications in a wide variety of industries in the last few decades e.g. automotive, aerospace, packaging, and microelectronics. Unlike most materials polymer exhibit time-dependent mechanical response. Due to the inherent viscoelastic or viscoplastic behavior, understanding long-term mechanical response of these materials has been a challenge. In addition to that, these materials are often used in micro- or nano-scale applications, e.g. thin films. Conventional testing methods, which can only provide the macro-scale mechanical behavior, are not suitable in characterizing nano- or microscale behavior of these materials [1, 2]. If a material system is non-homogeneous, such as ultraviolet irradiated polymer surface or nanofiller reinforced polymer, macro-scale test data fails to reflect the localized changes in a material [3]. In these situations nanoindentation or depth sensing indentation (DSI) can provide nano-scale mechanical behavior due to its high spatial resolution [4]. However, relating nanoindentation load–displacement data to mechanical properties requires suitable analytical or numerical methods [5, 6]. For materials exhibiting simple elastic or elastoplastic behavior, use of nanoindentation has been widely reported [7–10]. On the contrary, for materials exhibiting time-dependent mechanical behavior, the application of nanoindentation is still a challenge [11]. In this study, model parameters of a nonlinear viscoelastic model has been identified using finite element-based inverse analysis and a global optimization technique known as genetic algorithm (GA). Calibrating a complex mechanical constitutive relationship with the help of genetic algorithm is computationally expensive when finite element ana
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