Abstract Materials exhibiting a heterogeneous and non-uniform composition in terms of elastic and anisotropic properties such as biological tissues require special efforts to accurately describe their constitutive behavior. In contrast to classical models, micromorphic formulations can predict the macroscopically observable material response as originated from distinct scale-dependent micro-structural deformation mechanisms. This is facilitated by additional independent degrees of freedom and associated additional strain and stress quantities. Here, a generalized continuum is mathematically constructed from a macro-continuum and a micro-continuum which are both adequately coupled on kinematics and constitutive levels as well as by micro-boundary conditions. In view of biomechanical modeling, the potential of the formulation is studied for a number of academic examples characterized by an anisotropic material composition to elucidate the micromorphic material response as compared with the one obtained using a classical continuum mechanics approach. The results demonstrate the ability of the generalized continuum approach to address non-affine elastic reorientation of the preferred material direction in the macro-space and its dispersion in the micro-space as affecting deformation, strain and stress on the macroscopic level. In particular, if the anisotropy in the micromorphic formulation is solely linked to the extra degrees of freedom and associated strain and stress measures, the deformation for small and large strains is shown to be distinctly different to the classical response. Together with the ability to implicitly account for scale-dependent higher-order deformation effects in the constitutive law the proposed generalized micromorphic formulation provides an advanced description, especially for fibrous biological materials.

中文翻译：

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考虑首选材料方向的变化和分散的广义微晶方法

摘要 在弹性和各向异性特性方面表现出异质和非均匀成分的材料，例如生物组织，需要特别努力来准确描述其本构行为。与经典模型相比，微形态公式可以预测宏观可观察的材料响应，因为它源于不同的尺度相关的微观结构变形机制。这通过额外的独立自由度和相关的额外应变和应力量来促进。在这里，广义连续体是由宏观连续体和微观连续体在数学上构建的，它们在运动学和本构水平以及微观边界条件上都充分耦合。从生物力学建模来看，研究了许多以各向异性材料成分为特征的学术实例的配方的潜力，以阐明与使用经典连续介质力学方法获得的材料响应相比的微晶材料响应。结果表明，广义连续介质方法能够解决宏观空间中首选材料方向的非仿射弹性重新定向及其在微观空间中的分散，从而在宏观层面上影响变形、应变和应力。特别是，如果微晶公式中的各向异性仅与额外的自由度以及相关的应变和应力测量相关，则小应变和大应变的变形与经典响应明显不同。