A Mico-Mechanics Based Thermo-Mechanica Constitutive Model for Finite Deformation Analysis of Shape Memory Materials

*CMS-9813386 Masud提出了一种新的非弹性模型族的内变量形式，该模型族能够表示形状记忆合金的超弹性相变以及完全耦合的热-机械相变。这些模型能反映材料在拉伸和压缩时的不同响应，并能解释单变量马氏体再取向过程。本构模型扩展到有限变形制度，采用乘法分裂的变形梯度。由于SMA的多个自然配置的对称群的变化的问题得到解决。本文提出了一种无条件稳定的算法来求解形状记忆合金引起的完全热力耦合系统。详细讨论了通过返回映射方案对本构方程进行数值积分的技术问题，以及实现高阶收敛所需的算法一致切线的形式。*

***CMS-9813386MasudAn internal-variable formalism is developed for a new family of inelastic models that are capable of representing the super-elastic transformations as well as the fully coupled thermo-mechanical phase transformarion is Shape Memory Alloys. These models can show different material response in tension and compression, and can account fof th single-variant-martensite reorientation prcess. The constitutive models are extended to the finite deformation regime by employing a multiplicative split of the deformation gradient. The issue of change in symmetry group because of the multiple natural configurations in SMA's is addressed. An unconditionally stable algorithm is develloped to solve the completed coupled thermo-mechanical system arising is SMA's. Technical issues related to numerical integration of the constitutive equations via the return mapping schemes, and the form of algorithmically consistent tangents needed to achieve higher order convergence are addressed in detail.***