Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Many applications are based on the use of materials with heterogeneous microstructure. Prominent examples are fiber-reinforced composites, multi-phase steels or soft tissue to name only a few. The modeling of structures composed of such materials is suitably carried out at different scales. At the micro scale, the detailed microstructure is taken into account, whereas the modeling at the macro scale serves to include sophisticated structural geometries with complex boundary conditions. The procedure is crucially based on an intelligent bridging beten the scales. One of the methods derived for this purpose is the meanwhile ll established FE\(^2\) method which, hover, leads to a very high computational effort. Unfortunately, this impedes the use of the FE\(^2\) method and similar methodologies for practically relevant problems as they occur e.g. in production or medical technology. The goal of the present paper is to significantly improve computational efficiency by using model reduction. The suggested procedure is very generally applicable. It holds for large deformations as ll as for all relevant types of inelasticity. An important merit of the work is the computation of the consistent tangent operator based on the reduced stiffness matrix of the microstructure. In this way a very fast (in most cases quadratic) convergence within the Newton iteration at macro level is achieved.
['Annika Radermacher', 'Brett Bednarcyk', 'Bertram Stier', 'Jaan-Willem Simon', 'Lei Zhou', 'Stefanie Reese']
I am writing a research paper on a idea Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition
[{"from": "human", "value": "I am writing a research paper on a idea Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Many applications are based on the use of materials with heterogeneous microstructure. Prominent examples are fiber-reinforced composites, multi-phase steels or soft tissue to name only a few. The modeling of structures composed of such materials is suitably carried out at different scales. At the micro scale, the detailed microstructure is taken into account, whereas the modeling at the macro scale serves to include sophisticated structural geometries with complex boundary conditions. The procedure is crucially based on an intelligent bridging beten the scales. One of the methods derived for this purpose is the meanwhile ll established FE\\(^2\\) method which, hover, leads to a very high computational effort. Unfortunately, this impedes the use of the FE\\(^2\\) method and similar methodologies for practically relevant problems as they occur e.g. in production or medical technology. The goal of the present paper is to significantly improve computational efficiency by using model reduction. The suggested procedure is very generally applicable. It holds for large deformations as ll as for all relevant types of inelasticity. An important merit of the work is the computation of the consistent tangent operator based on the reduced stiffness matrix of the microstructure. In this way a very fast (in most cases quadratic) convergence within the Newton iteration at macro level is achieved."}]