Abstract Constitutive models that describe anisotropic mechanical behaviour have generally focused on incompressible materials such as metals. However, many cellular materials such as foams and wood are compressible, and their mechanical response is both direction- and rate-dependent. To describe the anisotropic behaviour of these compressible cellular materials, a rate-sensitive constitutive model is proposed to capture their large deformation, dynamic response to compression, which cellular materials are often subjected to; this is based on a model proposed by the authors [1] . Anisotropy of yielding is captured via a 4th order tensor, whereby appropriate assumptions enable the 21 parameters to be determined from only six fundamental experimental tests, i.e. uniaxial compression along three principal directions and simple shear corresponding to three principal planes. Anisotropy of the post-yield response is characterized by a hardening matrix containing six hardening functions, and these are also determined by the six basic experimental tests. By inverting the hardening function matrix, the Cauchy stresses are scaled back to define a modified stress space, whereby the yield surface remains stationary; this enables anisotropic post-yield behaviour to be expressed in a simplified form. To incorporate rate-sensitivity, the six hardening functions are cast in terms of both effective plastic strain and strain rate. Assuming that rate-sensitivity of the post-yield response follows that of the yield stress, the proposed model is applied to predict the stress-strain and deformation response of a transversely isotropic crushable polyurethane foam reported in [2] . Good correlation between the predicted and experimental results demonstrates that the proposed model using the assumed form of rate-sensitivity, is able to adequately capture the large deformation mechanical behaviour and rate-dependence of anisotropic cellular materials beyond yield.

中文翻译：

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各向异性多孔材料的速率敏感本构模型——应用于横向各向同性聚氨酯泡沫

摘要 描述各向异性力学行为的本构模型通常关注不可压缩的材料，例如金属。然而，许多多孔材料（如泡沫和木材）是可压缩的，它们的机械响应与方向和速率有关。为了描述这些可压缩蜂窝材料的各向异性行为，提出了一个速率敏感的本构模型来捕捉它们的大变形、压缩的动态响应，这些蜂窝材料经常受到；这是基于作者 [1] 提出的模型。屈服的各向异性通过 4 阶张量捕获，由此适当的假设使 21 个参数能够仅从六个基本实验测试中确定，即 沿三个主要方向的单轴压缩和对应于三个主要平面的简单剪切。后屈服响应的各向异性以包含六个硬化函数的硬化基体为特征，这些也是由六个基本实验测试确定的。通过反转硬化函数矩阵，柯西应力按比例缩小以定义修改后的应力空间，从而屈服面保持静止；这使得各向异性的屈服后行为能够以简化的形式表达。为了结合速率敏感性，根据有效塑性应变和应变速率来铸造六个硬化函数。假设屈服后响应的速率敏感性遵循屈服应力的敏感性，所提出的模型用于预测 [2] 中报道的横向各向同性可压碎聚氨酯泡沫的应力应变和变形响应。预测结果和实验结果之间的良好相关性表明，所提出的模型使用假定的速率敏感性形式，能够充分捕捉超出屈服的各向异性细胞材料的大变形力学行为和速率依赖性。