In hypoelastic constitutive models, an objective stress rate is related to the rate of deformation through an elasticity tensor. The Truesdell, Jaumann, and Green–Naghdi rates of the Cauchy and Kirchhoff stress tensors are examples of the objective stress rates. The finite element analysis software ABAQUS uses a co-rotational frame which is based on the Jaumann rate for solid elements and on the Green–Naghdi rate for shell and membrane elements. The user subroutine UMAT is the platform to implement a general constitutive model into ABAQUS, but, in order to update the Jacobian matrix DDSDDE in UMAT, the model must be expressed in terms of the Jaumann rate of the Kirchhoff stress tensor. This study aims to formulate and implement various hypoelastic constitutive models into the ABAQUS UMAT subroutine. The developed UMAT subroutine codes are validated using available solutions, and the consequence of using wrong Jacobian matrices is elucidated. The UMAT subroutine codes are provided in the “Electronic Supplementary Material” repository for the user’s consideration.

在低弹性本构模型中，客观应力率与通过弹性张量的变形率有关。Cauchy和Kirchhoff应力张量的Truesdell，Jaumann和Green-Naghdi比率是客观应力比率的示例。有限元分析软件ABAQUS使用同向旋转框架，该框架基于固体元素的Jaumann速率和基于壳和膜元素的Green-Naghdi速率。用户子例程UMAT是将通用本构模型实现到ABAQUS中的平台，但是，为了更新雅可比矩阵DDSDDE在UMAT中，必须以Kirchhoff应力张量的Jaumann速率表示模型。这项研究的目的是在ABAQUS UMAT子例程中制定和实现各种次弹性本构模型。使用可用的解决方案验证了开发的UMAT子例程代码，并阐明了使用错误的Jacobian矩阵的后果。用户可以考虑在“电子补充材料”存储库中提供UMAT子例程代码。