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

当由延性材料制成的部件承受高应变率时，它们通常表现出大的局部变形区，这是由材料损伤引起的软化以及由于塑性耗散引起的温度升高引起的。用严格的局部本构模型来模拟材料的行为是不够的，因为在这种情况下，偏微分方程的类型发生了变化，因此不能保证存在性、唯一性和稳定性。非局部本构模型是解决这些问题的一种合适的方法，因为它可以保留所需的性质。本构参数的确定需要满足上述准则的基本方程组。如果不满足这一要求，任何确定本构参数的优化算法都会导致错误或不收敛的结果。因此，只有本构模型在整个过程中保证解的存在唯一性和稳定性，本构参数的确定才有可能取得成功。除了应变率硬化和温度软化的本构参数外，高应变率的非局部模型还包括损伤和断裂参数。通过引入非局部方程，进一步增加了参数。这些附加参数只有在变形不均匀时才会被激活。因此，任何基于经典同质实验的识别方法都不能提供有关非局部参数的信息。因此，在手头的建议中，打算开发和分析程序，以确定非局部模型的本构参数。申请人可以从过去的研究项目中获得合金高应变率行为的实验数据。在Split-Hopkinson压力棒中对各种试样进行附加实验，并结合能够捕获现场数据的高速摄像机，以获得有关应变分布和附加高应变率行为的重要信息。整个可用数据集将用于分析和确定非局部本构参数。这种方法导致了一个以偏微分方程为约束的非线性优化问题。这些问题都要用基于导数的优化方法来解决，这种方法可以利用本构方程中已经存在的导数。该提案的结果是创建和应用一种方法来确定非局部本构模型的参数，包括对计算，理论和实验方面的贡献。因此，在高应变率下提高部件安全性的关键部分是可以预期的。

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.