Inverse Analysis in the Context of Non-local Damage and Plasticity Models at High Strain Rates for the Determination and Investigation of Non-classical Material Parameters

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When components made of ductile materials are subjected to high strain rates they typically exhibit zones of large localized deformation which are caused by softening due to material damage as well as the increase in temperature due to plastic dissipation. Modeling material behavior by strictly local constitutive models is inadequate since in this case the type of the partial differential equation changes and thus existence, uniqueness, and stability cannot be guaranteed.Non-local constitutive models are a suitable remedy for these problems in that the required properties can be preserved.The determination of constitutive parameters requires the underlying set of equations to satisfy the above criteria. If this requirement is not met, any optimization algorithm to determine the constitutive parameters will lead to erroneous or non-convergent results. Thus, the determination of constitutive parameters is only likely to lead to success if the constitutive model guarantees the existence, uniqueness and stability of the solution during the whole process.Beside constitutive parameters for strain rate hardening and temperature softening, non-local models for high strain rates also include parameters for damage and fracture. Further parameters are added through the introduction of non-local equations. These additional parameters are activated only if the deformations are inhomogeneous. Thus, any identification procedure based on classical homogeneous experiments cannot provide information concerning the non-local parameters. Therefore, in the proposal at hand, procedures are intended to be developed and analyzed that allow for the determination of constitutive parameters of non-local models.Experimental data on the high strain rate behavior of an alloy is available to the applicant from past research projects. Additional experiments with various specimens in a Split-Hopkinson pressure bar combined with high speed cameras capable of capturing field data are planned to obtain important information concerning the strain distribution and additional higher strain rate behavior. The whole available dataset is to be used for analysis and determination of non-local constitutive parameters.This approach leads to a non-linear optimization problem with partial differential equations as constraints. These are to be tackled with derivative based optimization methods which can draw on derivatives already present in the constitutive equations.The outcome of the proposal is the creation and the application of a method to determine the parameters of a non-local constitutive model including contributions to computational, theoretical as well as experimental aspects. In consequence, a crucial part in improving component safety at high strain rates is to be expected.