Modelling and computation of microstructured materials by generalised continua

大多数材料（如复合材料、多晶、颗粒介质、软组织）的行为受到不均匀分布的微尺度性质的影响。在工程、纳米技术、生物医学应用和地球科学中可靠和有效地使用微结构材料需要并证明在其数学建模和数值处理方面付出巨大努力是合理的。在这个建议中，微观结构是由基于结构变量的广义连续统理论捕获的。在过去，新兴模型的复杂性阻碍了它们的规范和应用于工程问题。在基于变分原理的统一框架中，广义连续体的典型代表表现出迄今为止尚未认识到的相似性，从而促进了基于有限元的数值分析。因此，梯度材料和微晶材料在有限应变作用下的三维非弹性行为可以用相同的数值算法有效地处理。将展示对基准问题的适用性，其中微晶和梯度连续体的变体将被使用，例如在应变软化塑性中，而断裂力学问题将通过基于材料设置的这些类型的广义连续体的材料力方法来解决。

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.