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

***CMS-9813386MasudAn内变量形式是一种新的非弹性模型族，能够表示超弹性转变和完全耦合的热-机械相变。这些模型能反映材料在拉伸和压缩条件下的不同响应，并能解释单变马氏体重取向过程。通过对变形梯度进行乘法分割，将本构模型扩展到有限变形状态。讨论了SMA中多种自然构型导致对称群变化的问题。提出了一种无条件稳定的算法来求解由SMA引起的完整的热-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.***