A new scheme for hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. Then, Piola–Kirchhoff stress is coupled with internal balance equation. Strain energy function is expressed in terms of principal invariants of the deformation gradient decomposed counterparts. Recent work introduces a strain energy function in terms of principal stretches of the deformation gradient multiplicatively decomposed counterparts directly. Hence, a new reformulation of Piola–Kirchhoff stress and internal balance equation are provided. This work focuses on developing the mathematical framework to calculate the elasticity tensor for material model formulated in terms of decomposed principal stretches. This paves the way for future implementation of these classes of material model in FE formulation.

基于将微积分变分论证应用于变形梯度的二因子乘法分解，开发了一种新的超弹性材料方案。然后，将 Piola-Kirchhoff 应力与内部平衡方程耦合。应变能函数用变形梯度分解对应项的主不变量来表示。最近的工作直接根据变形梯度的主拉伸引入了应变能函数乘法分解对应部分。因此，提供了 Piola-Kirchhoff 应力和内部平衡方程的新重新表述。这项工作的重点是开发数学框架来计算根据分解主拉伸制定的材料模型的弹性张量。这为未来在有限元公式中实施此类材料模型铺平了道路。