{"product_id":"micro-to-macro-composites-via-homogenization-von-smith","title":"Micro to Macro: Composites via Homogenization","description":"A composite material is generally taken to be a material consisting of two or more constituents\nor phases [96]. These heterogeneities can include voids, fibers and stiff or soft inclusions and\ncan vary in size. Any material, human-made or natural, can thus be considered heterogeneous\nat a particular scale. The ongoing improvement of technology over the past century has led to\nthe rapid development of heterogeneous materials, and the need to understand the interactions\nbetween these heterogeneities. In the past, experimental test methods would be conducted on\na series of material samples to determine its \"effective properties\" [41]. This approach has\nbecome less appealing in recent times though due to the number of resources required, such as\ntime and money.\nConversely, to accurately model the microstructure at the macroscopic level, each constituent\nin the heterogeneous structure would need to be modeled explicitly. While a hypothesis on the\nmicrostructural behavior at the macro scale is not required in this case, the method is often\nimpractical due to the enormous difference in length scales between the heterogeneities and\nthe macroscopic sample. Moulinec and Suquet [69] used Fast Fourier Transforms, with images\nof the microstructure, to reduce the size of the meshing, but still required computers with high\nmemory capabilities. The application of micro modeling is thus limited to localized\nphenomena cases, where analysis of the microstructure is required. These include contact\nproblems [27, 112], microstructural damage [73] and micro-cracking [40]. A parameter fitting\ntechnique was implemented by Geers [20] and Meuwissen [62] to obtain the effective property\nof a material’s microstructure. By fitting material parameters to experimental data, one can\nobtain the macroscopic strain-energy function of the material. Though successful, this\napproach is tedious and, despite being optimized by Gendy and Saleeb [22] and Ogden et al.\n[72], requires large volumes of experimental data.\nAn alternative method to obtain the effective properties is homogenization. This technique\nreplaces the complex microstructure with one that is statistically homogeneous at the\nmacroscopic level. The replacement of the complex microstructure with one that is\nhomogeneous overcomes the need for complex meshing. Also, depending on the chosen\nhomogenization theory, the mechanical response can be investigated with no prior knowledge\nof the material, giving a first approximation on the stress distribution at the micro level. These\ncharacteristics surpass the limitations posed by the other methods, making it the preferred\nchoice when modeling composites. There are several different homogenization approaches, of\nwhich the most common are briefly discussed below. For a more comprehensive review, we\nrefer the reader to Nemat-Nasser and Hori [71].\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783384225443\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783384225443","offer_id":48646255640901,"sku":"9783384225443","price":26.19,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/68ab5051-3235-41c6-8a98-46272c5b5c71.jpg?v=1776489554","url":"https:\/\/shop.autorenwelt.de\/products\/micro-to-macro-composites-via-homogenization-von-smith","provider":"Autorenwelt Shop","version":"1.0","type":"link"}