Modelling and computation of microstructured materials by generalised continua

大多数材料（如复合材料、多晶体、颗粒介质、软组织）的行为都受到非均匀分布的微尺度性质的影响。微结构材料在工程、纳米技术、生物医学应用和地球科学中的可靠和有效使用需要并证明在数学建模和数值处理方面付出的巨大努力是合理的。在这一建议中，微观结构被捕获的广义连续理论的基础上结构变量。新兴模型的复杂性在过去阻碍了他们的规格和工程问题的应用。在一个统一的框架的基础上变分原理，典型代表的广义连续体表现出迄今未被认识的相似性，从而促进其有限元为基础的数值分析。因此，梯度材料和微形态材料在有限应变下的三维非弹性行为可以用相同的数值算法有效地处理。适用性将被证明为基准的问题，从而变体的微形态和梯度连续将被使用，例如在应变软化塑性，而断裂力学问题将通过采用材料力的方法，这些类型的广义连续的基础上的材料设置来解决。

The behavior of most materials (e.g. composites, polycrystals, granular media, soft tissues) is influenced by inhomogeneously distributed microscale properties. A reliable and efficient use of microstructured materials in engineering, nanotechnology, biomedical application and earth sciences requires and justifies high efforts in their mathematical modeling and numerical treatment. In this proposal, microstructure is captured by generalised continuum theories based on structural variables. The complexity of the emerging models has in the past hindered their specification and application to engineering problems. In a unifying framework based on variational principles, typical representatives of generalised continua exhibit so-far unrecognized similarities, facilitating thus their finite-element-based numerical analysis. Consequently, threedimensional inelastic behavior of gradient and micromorphic materials subject to finite strains can be treated efficiently by the same numerical algorithms. Applicability will be demonstrated for benchmark problems, whereby variants of micromorphic and gradient continua will be used e.g. in strain softening plasticity, while fracture mechanics problems will be tackled by employing a material force method for these types of generalised continua based on the material setting.