A General Purpose Constitutive Model Fitting Approach Using Inverse Methods

Abstract

Computer simulation techniques such as finite element (FE) methods are used extensively to ensure functionality, reliability, and safety. The accuracy of these simulations is reliant on how accurately one can describe material behavior through the use of mathematical formulations known as constitutive material models. However, traditional methods of fitting constitutive material models are slow, tedious, and require a skilled researcher to perform correctly. In this thesis, an alternative fitting technique is investigated. Known as inverse material modeling (IMM), this technique couples experimental testing, FE modeling, and numerical optimization algorithms. Unlike traditional fitting techniques, IMM displays a high degree of automation, reducing the time and effort needed to fit constitutive material models without sacrificing accuracy. Moreover, as the FE model replicates the experiment being conducted, non-linearities such as irregular states of stress and specimen fixturing are accounted for; something which cannot be done with traditional fitting techniques.

This thesis is devoted to the development and use a custom-built IMM framework known as COMPCAM. To investigate the effectiveness of IMM and COMPCAM, two separate investigations were undertaken. In the first, five wrought alloys of varying composition and mechanical behavior are fit to four separate constitutive models. The goal of this study was to fit the stress-strain behavior of each material. In the second, twelve ferrous sintered powder metallurgy (PM) alloys consisting of four elemental compositions and three sintered densities are each fit to four constitutive models each. In addition to stress-strain behavior, the second investigation aimed to uncover how well said constitutive models and COMPCAM fit each alloy's densification behavior.

The results of these investigations show that COMPCAM is effective for the fitting of constitutive material models across a range of material behaviors and constitutive models for metals. However, there are limitations to COMPCAM's effectiveness. In particular, COMPCAM and IMM are unable to produce realistic fits for constitutive models which are not appropriate to describe the material behavior. However, this limitation can be overcome though appropriate selection of constitutive models by the user.