In this work, a thermodynamically consistent constitutive formulation for the coupled thermomechanical strain gradient plasticity theory is developed in the context of the finite deformation framework. A corresponding finite element solution is presented to investigate the microstructural features of metallic volumes. The developed model is established based on an extra Helmholtz-type partial differential equation, and the nonlocal quantity is calculated in a coupled method based on the equilibrium conditions. This approach is well known for its computational strength, however, it is also commonly accepted that it cannot capture the size effect phenomenon observed in the micro-/nanoscale experiments during hardening. In order to resolve this issue, a modified strain gradient approach which can capture the size effects under the finite deformation is constructed in this work. The shear problem is then solved to carry out the feasibility study of the developed model on the size effect phenomenon. Lastly, a plane strain problem under uniaxial tensile loading with shear bands is examined to perform the mesh sensitivity tests of the model during softening.

中文翻译：

---

有限变形理论的应变梯度有限元模型：尺寸效应和剪切带

在这项工作中，在有限变形框架的背景下开发了耦合热机械应变梯度塑性理论的热力学一致本构公式。提出了相应的有限元解决方案来研究金属体积的微观结构特征。所开发的模型是基于额外的亥姆霍兹型偏微分方程建立的，非局部量是基于平衡条件以耦合方法计算的。这种方法以其计算强度而闻名，但是，人们普遍认为它无法捕捉在硬化过程中在微/纳米尺度实验中观察到的尺寸效应现象。为了解决这个问题，在这项工作中构建了一种改进的应变梯度方法，它可以捕获有限变形下的尺寸效应。然后解决剪切问题，对开发的模型进行尺寸效应现象的可行性研究。最后，检查了具有剪切带的单轴拉伸载荷下的平面应变问题，以在软化期间执行模型的网格敏感性测试。