A macro-constitutive model for the deformation response of periodic rotating bistable auxetic surfaces is developed. Focus is placed on isotropic surfaces made of bistable hexagonal cells composed of six triangular units with two stable equilibrium states. Adopting a variational formulation, the effective stress-strain response is derived from a free energy function expressed in terms of the invariants of the logarithmic strain. A regularization of the governing equations via a gradient-enhanced first invariant of the logarithmic strain is introduced since the double-well nature of the free energy may result in mathematical ill-posedness and related numerical artifacts, such as mesh sensitivity. Despite this regularization, the numerical scheme may still suffer from divergence issues due to the highly non-linear material behavior. To enhance numerical stability, an artificial material rate-dependency is additionally introduced. Although it does not guarantee solution uniqueness or eliminate mesh sensitivity, it is conjectured to assist the numerical scheme in overcoming snap-backs caused by local non-proportional loading induced by transition fronts. The model is implemented using membrane/shell structural elements and plane stress continuum ones within the ABAQUS finite element suite. Numerical simulations demonstrate the efficacy of the proposed formulation and its implementation.

翻译：本文发展了一种用于描述周期性旋转双稳态拉胀表面变形响应的宏观本构模型。研究重点集中于由六个三角形单元构成、具有两个稳定平衡态的双稳态六边形胞元所组成的各向同性表面。采用变分公式，从以对数应变不变量表示的自由能函数推导出有效应力-应变响应。由于自由能的双阱特性可能导致数学不适定性及相关数值伪影（如网格敏感性），引入了通过对数应变梯度增强的第一不变量对控制方程进行正则化。尽管进行了正则化，数值方案仍可能因高度非线性材料行为而面临发散问题。为增强数值稳定性，额外引入了人工材料率相关性。虽然这不能保证解的唯一性或消除网格敏感性，但推测其有助于数值方案克服由相变前沿引起的局部非比例加载所导致的回弹现象。该模型在ABAQUS有限元套件中采用膜/壳结构单元与平面应力连续体单元实现。数值模拟验证了所提公式及其实现方法的有效性。