The representative directions method is a continuum mechanical based practical approach to transfer 1D material models to 3D. The selection of the directional energy and the corresponding directional stress is generally based on the standard uniaxial tension (UT) solution of hyperelastic models. However, this approach results in a somewhat different model than hyperelastic models in the context of elasticity and inelasticity. For instance, enrichment of the UT based directional stress with the non-affine stretch does not provide close results unless huge p-root values are considered. Hence, the main objective of this contribution is to determine the directional stresses, which can provide equivalent or close results to first and second invariant based hyperelastic models. Accordingly, the directionalisation concept in the framework of affine representative directions method is introduced. Directional stresses are obtained with a top-down approach from the first and second invariant based hyperelastic models. The standard Mooney-Rivlin model is directionalised to obtain the corresponding 1D energies and stresses using the micro-stretch and the macro-area-stretch. The approach is then utilised to directionalise several hyperelastic-like models as alternatives for statistical-thermomechanics based chain models. Moreover, a new optimisation strategy is proposed to improve the material asymmetry resulting from numerical integration schemes. Optimisation results demonstrate that the material symmetry of the standard Bažant points can be improved. Finally, two nonhomogenous finite-element (FE) simulations demonstrate that the directionalisation approach presented here contributes a good step towards numerically robust inelastic extensions.

代表性方向方法是一种基于连续机械的实用方法，可将1D材料模型转换为3D。方向能量和相应方向应力的选择通常基于超弹性模型的标准单轴张力（UT）解决方案。但是，在弹性和非弹性的情况下，这种方法导致的模型与超弹性模型有所不同。例如，除非考虑巨大的p根值，否则基于非仿射拉伸的基于UT的方向应力的富集不会提供接近的结果。因此，这一贡献的主要目的是确定方向应力，该方向应力可以提供与基于第一和第二不变性的超弹性模型同等或接近的结果。因此，介绍了仿射代表方向方法框架下的定向概念。通过自上而下的方法从基于第一和第二不变性的超弹性模型中获得方向应力。使用微拉伸和大面积拉伸对标准的Mooney-Rivlin模型进行定向，以获得相应的一维能量和应力。然后，该方法用于定向多个类似超弹性的模型，以替代基于统计热力学的链模型。此外，提出了一种新的优化策略，以改善数值积分方案引起的材料不对称性。优化结果表明，可以改善标准Bažant点的材料对称性。最后，