== Descriptions == In this wiki tutorial, you will learn about how to obtain effective properties of composites possessing four microstructures, including # hexagonal packed fibers # square packed fibers with interphase layer between fiber and matrix # 0/90 laminate # two spheres included in matrix Geometric dimensions and material properties are taken from [https://cdmhub.org/resources/948 Challenge Problems for the Benchmarking of Micromechanics Analysis]. Apart from how to calculate effective material properties of these four microstructures, you will also learn about * how to extract and plot local stress values along a line after dehomogenization (in Case 2) * how to draw a sphere and assign material properties by editing command files (in Case 4) ---- == Software Used == [https://cdmhub.org/tools/scstandard/ Gmsh4SC 2.0] ---- == Case 1. Hexagonal Pack Microstructure == The hex pack microstructure describes a continuous fiber reinforced composite. Figure 1 shows the cross-section. Dark portion represents fiber. Volume fraction of fiber is 60%. Material properties are given in Figure 2. [[br]] [[Image(Fig1_hexpack.png, 226px)]] [[Image(Fig2_Materials.png, 277px)]] === Video === You may refer to the !YouTube video for hex pack micromechanics analysis. [[br]] [[Video(https://www.youtube.com/watch?v=ELFGK9FF64M&list=PLGwp8OYDfmxF2fgn3p2KZZscnVX4c8Vve&index=4)]] === Solution Procedures === * Launch [https://cdmhub.org/tools/scstandard/ Swift Comp]. * Create a new file. [[br]] [[Image(Fig3_newfile.png, 399px)]] * __Add material properties__ * Click `Material`, `Thermoelastic`, `Orthotropic`, input matrix and fiber properties given in Figure 2, click `Add` for each material. Finally click `Close`. [[br]] [[Image(Fig4_Mat1.png, 359px)]] [[Image(Fig5_Mat2.png, 350px)]] * __Define SG geometry__ * Click `Geometry`, `Common SG`, `2D SG`, `Other 2D SGs`. * Select Type of models: `Hexagonal Pack Microstructure`, input Volume fraction of fiber: `0.6`, select Fiber and Matrix materials to be `MAT2` and `MAT1`, click `Add`. The hex pack geometry is generated as shown in Figure 7. [[br]] [[Image(Fig6_Geometry.png, 615px)]] [[Image(Fig7_Geometry2.png, 270px)]] * __Mesh__ * Click `Mesh`, `Generate 2D mesh`, `Generate`. * Click `Set order 2`. [[br]] [[Image(Fig8_Mesh.png, 270px)]] [[Image(Fig9_Meshorder2.png, 538px)]] * __Homogenization__ * Click `SwiftComp`, `Homogenization`, `Solid Model` * Select `1-thermoelastic` as Type of analysis * Click `Save`, `Run`. [[br]] [[Image(Fig10_homogenization.png, 600px)]] * The effective elastic properties and CTEs of the homogenized hex pack structure is given in Figure 11. [[br]] [[Image(Fig11_results.png, 420px)]] ---- == Case 2. Square Pack Microstructure == Cross section of a square pack composite with an interphase layer is given in Figure 12. Volume fraction of fiber and interphase is 60% and 1% respectively. Material properties are given in Figure 13. [[br]] [[Image(Fig12_squarepack.png, 188px)]] [[Image(Fig13_Material.png, 266px)]] === Solution Procedures === * __Add material properties__ * Click `Material`, `Thermoelastic`, `Orthotropic`, input the 3 material properties, click `Add` for each material. Finally click `Close`. [[br]] [[Image(Fig14_Mat1.png, 475px)]] [[Image(Fig15_Mat2.png, 364px)]] [[Image(Fig16_Mat3.png, 367px)]] * __Define SG geometry__ * Click `Geometry`, `Common SG`, `2D SG`, `Other 2D SGs`. * Select Type of models: `Square Pack Microstructure`, input Volume fraction of fiber: `0.6`, Volume fraction of interphase: `0.01`, select materials, click `Add`. The square pack geometry is generated as shown in Figure 18.[[br]] [[Image(Fig17_Geometry.png, 586px)]] [[Image(Fig18_GeometryVIEW.png, 254px)]] * You may find the radii of fiber and interphase circles in `Input control`, `Edit file`. [[br]] [[Image(Fig19_radius.png, 321px)]] * __Mesh__ * As the interphase is very thin, we refine the mesh for circle arcs surrounding interphase layer. * Click `Mesh`, `Generate 2D mesh`, `Refine lines`. * Input Number of points: `50` * Click the 8 circle arcs. * Press `e`, and `q`. [[br]] [[Image(Fig20_refinemesh.png, 708px)]] * Click `Generate 2D mesh`, `Generate`. [[br]] [[Image(Fig21_mesh.png, 322px)]] * __Homogenization__ * Click `SwiftComp`, `Homogenization`, `Solid Model` * Select `1-thermoelastic` as Type of analysis * Click `Save`, `Run`. [[br]] [[Image(Fig22_homogenization.png, 590px)]] * The effective elastic properties and CTEs of the homogenized square pack structure is given in Figure 11. [[br]] [[Image(Fig23_results.png, 378px)]] * __Dehomogenization__ * Since we do not know the actual deformations, here we only show the representative local stress field, such as \sigma_{11} distribution across the cross section under \epsilon_{11} = 1 loading. * Click `Dehomogenization`, `Solid Model`. * Input `1` for e11. * Click `Save`, and `Run`. [[br]] [[Image(Fig24_s11undere11.png, 732px)]] * Axial stress \sigma_{11} shows symmetric distribution across the cross section. [[br]] [[Image(Fig25_s11.png, 318px)]] * Zoom in to check the interface layer. [[br]] [[Image(Fig26_s11interface.png, 318px)]] * __Plot \sigma_{11} along the center line__ * Click the triangular arrow beside S11, click `Plugins`. [[br]] [[Image(Fig27_Plugin.png, 268px)]] * Choose `CutGrid` for `View[10]` (S11) * Set (X0, Y0, Z0) = `(0, 0, 0)`, (X1, Y1, Z1) = `(0.5, 0, 0)`, NumPointsU = `100` (or larger). This will create a cut from (0, 0, 0) to (0.5, 0, 0) using 100 points. * (X2, Y2, Z2) is set to be the same as (X0, Y0, Z0) to avoid additional points of no interest here. * The other side, e.g., from (-0.5, 0, 0) to (0, 0, 0), is symmetric. [[br]] [[Image(Fig28_CutGrid.png, 386px)]] * Click `Run`. You'll see a new View called `S11_CutGrid`. * Save the new view as `.txt` file by clicking the triangle arrow and choose `Save As...`. [[br]] [[Image(Fig29_savecut.png, 389px)]] * File format is selected as `Generic TXT(*.txt)`, since the .txt file will only contain numbers, and is easier to be separated. [[br]] [[Image(Fig30_txt.png, 393px)]] * Download the exported CutGrid file to your local computer. Open it in Excel. If you have problems about how to download, please refer to [https://cdmhub.org/groups/yugroup/wiki/MainPage/ID:Gmsh4SCtutorials/Gmsh:analysisofacompositelaminatedbeam this tutorial] - 2.3 Check results and save files. [[br]] [[Image(Fig31_excelimport.png, 455px)]] * Find the x values (in the 5th column) and corresponding s11 values (in the 8th column). Plot S11 vs. X. [[br]] [[Image(Fig32_plot.png, 278px)]] * Since the !NumPointsV was set to be 20 by default, there will be 20 points of the same value. Feel free to remove duplicated values in Excel. * It's also good to save as other formats, such as `.pos` which is the default format. To extract (x,y,z) positions and corresponding S11 values from a .pos file, please refer to [https://cdmhub.org/groups/yugroup/wiki/MainPage/ID:Gmsh4SCtutorials/Gmsh:analysisofacompositelaminatedbeam this tutorial] - Dehomogenization part. ---- == Case 3. 0/90 Laminate == Figure 33 shows the microstructure of a 0/90 laminate. [[br]] [[Image(Fig33_laminate.png, 172px)]] [[br]] The fiber volume fraction is 60%. Diameter of the fiber is 5 microns. Fiber and matrix properties are the same as given in Figure 2 for Case 1. [[br]] We first calculate the effective properties of lamina using square pack geometry, then input lamina properties to calculate the laminate properties. === Solution Procedures === * __Calculate lamina properties__ * Click `Material`, `Thermoelastic`, `Orthotropic`, input matrix and fiber properties given in Figure 2, click `Add` for each material. Finally click `Close`. [[br]] [[Image(Fig34(1)_Mat1.png, 461px)]] [[Image(Fig34(2)_Mat2.png, 358px)]] * Click `Geometry`, `Common SG`, `2D SG`, `Other 2D SGs`. * Select Type of models: `Square Pack Microstructure`, input Volume fraction of fiber: `0.6`, select Fiber and Matrix materials to be `MAT2` and `MAT1`, click `Add`. [[br]] [[Image(Fig35_SquPack.png, 589px)]] * Click `Mesh`, `Generate 2D mesh`, `Generate`, and `Set order 2`. [[br]] [[Image(Fig36_mesh.png, 585px)]] * Click `SwiftComp`, `Homogenization`, `Solid Model`. Select `1-thermoelastic`. Click `Save`, `Run`. [[br]] [[Image(Fig37_homogenization.png, 585px)]] * Effective lamina properties are given in the .msh.k file. [[br]] [[Image(Fig38_laminaProp.png, 363px)]] * __Input lamina properties__ * Create a new .geo file for laminate. [[br]] [[Image(Fig39_new.png, 395px)]] * Click `Material`, `Thermoelastic`, `Orthotropic`, input lamina properties in Figure 39. Click `Add` and `Close`. [[br]] [[Image(Fig40_LaminaProp.png, 346px)]] * __Define SG geometry__ * Click `Geometry`, `Common SG`, `1D SG`, `Fast generate`. [[br]] [[Image(Fig41_laminateGen.png, 506px)]] * Input Layup: `[0/90]`, ply thickness: `5.7206`, click `Add`. The ply thickness is calculated by the fiber volume fraction (0.6) and fiber diameter (5).[[br]] [[Image(Fig42_thickness.png, 439px)]] [[Image(Fig43_1dSG.png, 45px)]] * __Mesh__ * Click `Mesh`, `Generate 1D mesh`, `Generate`. * __Homogenization__ * Click `SwiftComp`, `Homogenization`, `Solid Model`. Select `1-thermoelastic`. Click `Save`, `Run`. [[br]] [[Image(Fig44_homogenization.png, 586px)]] * The effective laminate properties are given in msh.k file. [[br]] [[Image(Fig45_laminateresults.png, 208px)]] ---- == Case 4. Double spherical inclusion == Reinforcing particles or voids in composites are represented by spheres inside a box. The double spherical inclusion microstructure is shown in Figure 46. The box is 2*2*2 microns. Diameter of the two spheres are 1 and 0.5 microns. The larger sphere is centered at (0.6, 0.6, 0.6) and the smaller sphere is centered at (1.5, 1.7, 1.3). Material properties are given in Figure 47. [[br]] [[Image(Fig46_2spheres.png, 165px)]] [[Image(Fig47_properties.png, 203px)]] === Solution Procedures === * __Add material properties__ * Click `Material`, `Thermoelastic`, input matrix and fiber properties given in Figure 47, click `Add` for each material. Finally click `Close`. [[br]][[Image(Fig48_Mat1.png, 466px)]] [[Image(Fig49_Mat2.png, 338px)]] * __Define SG geometry__ * !SwiftComp already coded the single spherical inclusion microstructure as one of the common SGs. Here we first create one sphere, and edit the commands to create the second sphere. * Alternatively, you may download !Gmsh 2.9.3 from http://gmsh.info//bin/, draw the two spheres, and copy the commands into the .geo file on cdmhub. * To create an arbitrary spherical inclusion microstructure, click `Geometry`, `Common SG`, `3D SG`, `Other 3D SGs`. Select `Spherical Inclusions Microstructure`, input any number as Volume fraction as we will change the radius later.[[br]][[Image(Fig50_geometry.png, 456px)]] * Click `Input control`, `Edit file`. [[br]][[Image(Fig51_onesphere.png, 437px)]] * You'll find the commands that describes the geometry starting from Point (1). * __Modify the cubic box__[[br]][[Image(Fig52_editgeo.png, 227px)]] (old commands) * Points are formatted as `Point(#) = {x,y,z, mesh size}`. * Points (1), (2), (3), (4) define a 1*1 square at x = -0.5, which is the left face of the 1*1*1 cube. * Translate of the four points by x+1 to x = 0.5, to get the other four points on the right face of the 1*1*1 cube. * The eight points represent a 1*1*1 cube from (-0.5, -0.5, -0.5) to (0.5, 0.5, 0.5)[[br]][[Image(Fig53_box.png, 218px)]] (new commands) * Now change the (x,y,z) numbers so that the cube is 2*2*2, from (0, 0, 0) to (2, 2, 2). * Change the mesh size to be 1. * Change the Translate distance to be 2. * __Modify the larger sphere__[[br]][[Image(Fig54_sphere.png, 247px)]] (old commands) * A 1/8 sphere is defined by 4 points, 3 arcs, and 1 surface. The surface is then rotated 7 times to create the entire sphere. [[br]][[Image(Fig55_newpoints.png, 218px)]] (new commands) * Change the (x,y,z) of Point (9) so that the sphere is centered at (0.6, 0.6, 0.6). * Points on the surface are (center point +/- radius). The radius of the larger sphere is 0.5. * Mesh size is changed to 1 again.[[br]][[Image(Fig56_newrotate.png, 306px)]] (new commands) * Center of rotation should be the spherical center (0.6, 0.6, 0.6). * Check the geometry in !SwiftComp by clicking `Input control`, `Reload`. Feel free to add or remove visible labels in Options.[[br]][[Image(Fig58_newview.png, 410px)]] [[Image(Fig57_viewsurface.png, 303px)]] * __Create the smaller sphere__ * Select the commands that create the larger sphere, copy and paste.[[br]][[Image(Fig59_copysphere.png, 393px)]] * Change element numbers and (x,y,z) values. * To avoid error caused by dummy element number, I did not follow a sequential order, but just changed Point(n) into Point(n+40), and changed Line(m) into Line(m+30). Surfaces are in the same sequence as Lines.[[br]][[Image(Fig60_sphere2.png, 194px)]] [[Image(Fig61_sphere2view.png, 294px)]] * For example, Point(9) is changed into Point(49), Circle(27) is changed into Circle(57). Circle means circle arc which is a line element. [[br]][[Image(Fig62_sphere2rotate.png, 307px)]] [[Image(Fig63_allview.png, 285px)]] * Rotation center should be the spherical center (1.5, 1.7, 1.3). All element numbers in Figure 62 are lines or surfaces, and are changed from m to m+30. * __Assign material properties__[[br]][[Image(Fig64_volume.png, 335px)]] * Volume(51) is the non-particle space (matrix). Volume(51) = {25, 50} means the outer surface is Surface(25) (the cubic box), while the inner hole is Surface(50) (the larger sphere). Add `80` at the end as another inner surface to exclude the small sphere from matrix. * Add a new volume for the small sphere. * Physical volume (2) is the particle. Add the small sphere. This would assign particle properties to the small sphere.[[br]][[Image(Fig65_volumeview.png, 290px)]] * __Mesh__ * Click `Mesh`, `Generate 3D mesh`, `Generate`, and `Set order 2`. [[br]][[Image(Fig66_mesh.png, 485px)]] * __Homogenization__ * Click `SwiftComp`, `Homogenization`, `Solid Model`. Select `1-thermoelastic`. Click `Save`, `Run`.[[br]][[Image(Fig67_homogenization.png, 593px)]] * The effective properties are given in .msh.k file.[[br]][[Image(Fig68_results.png, 730px)]] == References == # Andrew J Ritchey; Hamsasew Sertse; Johnathan Goodsell; Wenbin Yu; Byron Pipes (2015), "Micromechanics Simulation Challenge Level I Results," https://cdmhub.org/resources/948. # Xin Liu; Wenbin Yu (2017), "Gmsh4SC USER’S MANUAL", https://cdmhub.org/resources/1342/download/Gmsh4SCManual.pdf