Mathematical modelling of graphene-based membranes

石墨烯基膜的数学建模

• 批准号: 2481389
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2481389
• 关键词: Mathematical; modelling; graphene; based; membranes

The aims of the project are to develop a theoretical/computational model of the pressure-driven deformation of elastic membranes which comprise a graphene layer, either by itself or mounted on a thicker polymer backing. Such membranes are studied experimentally in AV's group with a view towards employing them in miniaturized pressure sensors. Multi-scale homogenization techniques will be employed to represent the graphene layer in a continuum-based model which will be amenable to a finite-element discretization. Particular attention will be paid to the formulation of boundary conditions which capture the details of how the membrane is attached the rigid support - a feature that preliminary joint work (performed via summer internships) has already identified as being particularly important, even for cases where the membrane's stiffness is dominated by the polymer backing.Specific scenarios to be studied (and carefully cross-validated against the results of existing and ongoing experimental studies) include the study of quasi-steady inflation (from small (linear) to large (nonlinear) deformations); the effect of pre-stress and the shape of the cavity the membrane is mounted on. (This is important because non-circular cavities can cause wrinkling.) Unsteady deformations in response to acoustic forcing from a compressible surrounding medium will be explored using a "small-on-large"-deformation approach in parameter regimes that are relevant for the application to an implantable microphone that is being developed in a project funded by the NIHR Manchester Biomedical Research Centre.The computational model will be implemented in oomph-lib, the object-oriented multi-physics finite-element library, developed and maintained by MH and AH (see http://www.oomph-lib.org). The incorporation of the model into this open-source library will facilitate its use in AV's group and also aid dissemination to the wider scientific community.

该项目的目的是开发弹性膜的压力驱动变形的理论/计算模型，该弹性膜包括石墨烯层，其本身或安装在较厚的聚合物背衬上。AV的小组对这种膜进行了实验研究，以期将其用于小型化压力传感器。将采用多尺度均匀化技术来表示基于连续介质的模型中的石墨烯层，该模型将服从有限元离散化。将特别注意边界条件的制定，这些边界条件捕捉了膜如何附着在刚性支撑上的细节--这是初步联合工作的一个特征。（通过暑期实习进行）已经被认为是特别重要的，即使在膜的刚度由聚合物背衬主导的情况下也是如此。（并与现有和正在进行的实验研究的结果进行了仔细的交叉验证）包括准稳定通货膨胀的研究（从小（线性）到大（非线性）变形）;预应力的影响和膜安装在其上的空腔的形状。（这一点很重要，因为非圆形空腔可能会导致波纹。）非定常变形响应声强迫从可压缩的周围介质将探索使用“小对大”的变形方法在参数制度，是相关的应用程序的植入式麦克风，正在开发的一个项目中资助的NIHR曼彻斯特生物医学研究中心。计算模型将在oomph-lib中实现，面向对象的多物理场有限元库，由MH和AH开发和维护（见http://www.oomph-lib.org）。将该模型纳入这个开源库将促进其在AV组中的使用，并有助于向更广泛的科学界传播。