Modelling and computation of microstructured materials by generalised continua

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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.