Fernandez et al 2018a - Revision history

Rimni at 12:39, 6 July 2021

2021-07-06T12:39:26Z

Rimni at 13:22, 2 July 2021

2021-07-02T13:22:50Z

Rimni: /* 3.1.1 Isotropic material */

2021-07-02T13:20:56Z

‎3.1.1 Isotropic material

Rimni at 13:19, 2 July 2021

2021-07-02T13:19:44Z

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Rimni: /* 2. The micro-macro LaTIn based Domain Decomposition Method */

2021-07-02T13:01:34Z

‎2. The micro-macro LaTIn based Domain Decomposition Method

Rimni at 09:51, 13 March 2019

2019-03-13T09:51:45Z

Rimni at 09:24, 13 March 2019

2019-03-13T09:24:35Z

Rimni at 09:23, 13 March 2019

2019-03-13T09:23:28Z

Rimni at 09:22, 13 March 2019

2019-03-13T09:22:23Z

Rimni at 09:21, 13 March 2019

2019-03-13T09:21:44Z

@@ Line 42: / Line 42: @@
 ==2. The micro-macro LaTIn based Domain Decomposition Method==
-Let us consider a laminate composite (see Figure [[#img-1|1]]) occupying the domain <math display="inline">\Omega </math> bounded by <math display="inline">\partial \Omega </math> in the current configuration, and consisting of <math display="inline">N_P</math> plies. Each ply <math display="inline">P</math> is connected to an adjacent ply <math display="inline">P' </math> through the interface <math display="inline">{\Gamma _{PP'}}</math>. The structure is subjected to an external surface traction field <math display="inline">{\underline{F}_d}</math> on the part <math display="inline">{\partial \Omega _{F_d}}</math> and to a displacement field <math display="inline">{\underline{U}_d}</math> on the complementary part <math display="inline">{\partial \Omega _{U_d}}</math>. The body force per unit of mass is written <math display="inline">{\underline{f}_d}</math>. The relevant quantities are described in reference to the undeformed configuration using the index <math display="inline">\cdot _\mathit{0}</math>. The geometrically nonlinear evolution is handled through a total Lagrangian formulation and delamination (damageable interfaces) is modeled using CZM and unilateral contact conditions. For the sake of simplicity, an extensive description of the CZM is found in <span id='citeF-24'></span>[[#cite-24|[24]]], while <span id='citeF-25'></span>[[#cite-25|[25]]] describe contact inequalities.
+Let us consider a laminate composite ([[#img-1|Figure 1]]) occupying the domain <math display="inline">\Omega </math> bounded by <math display="inline">\partial \Omega </math> in the current configuration, and consisting of <math display="inline">N_P</math> plies. Each ply <math display="inline">P</math> is connected to an adjacent ply <math display="inline">P' </math> through the interface <math display="inline">{\Gamma _{PP'}}</math>. The structure is subjected to an external surface traction field <math display="inline">{\underline{F}_d}</math> on the part <math display="inline">{\partial \Omega _{F_d}}</math> and to a displacement field <math display="inline">{\underline{U}_d}</math> on the complementary part <math display="inline">{\partial \Omega _{U_d}}</math>. The body force per unit of mass is written <math display="inline">{\underline{f}_d}</math>. The relevant quantities are described in reference to the undeformed configuration using the index <math display="inline">\cdot _\mathit{0}</math>. The geometrically nonlinear evolution is handled through a total Lagrangian formulation and delamination (damageable interfaces) is modeled using CZM and unilateral contact conditions. For the sake of simplicity, an extensive description of the CZM is found in <span id='citeF-24'></span>[[#cite-24|[24]]], while <span id='citeF-25'></span>[[#cite-25|[25]]] describe contact inequalities.
-To propose the partitioned problem, the whole domain <math display="inline">\Omega </math> is split into subdomains which are connected by interfaces with mechanical behaviors. Two possibilities are considered: “material” interfaces between plies with localized non-linearities (damage, contact) that are compatible with the mesomodeling, and “numerical” interfaces (the perfect ones) within the plies to conceive smaller problems that are suited for parallelism, as schematized in  [[#img-1|Figure 1]]. A subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> defined in the undeformed domain <math display="inline">{\Omega _{S_\mathit{0}}}</math> is connected to an adjacent undeformed subdomain <math display="inline">{{S'}_\mathit{0}}</math> through an undeformed interface <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}=\partial {\Omega _{S_\mathit{0}}}\cap \partial {\Omega _{S_\mathit{0}'}}</math>. The surface entity <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math> applies force distributions <math display="inline">{\underline{F}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{F}_{S_\mathit{0}'}}</math> and displacement distributions <math display="inline">{\underline{W}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{W}_{{S'}_\mathit{0}}}</math> to <math display="inline">{S^{\quad }_\mathit{0}}</math> and <math display="inline">{{S'}_\mathit{0}}</math> respectively (see Figure [[#img-2|2]]). Let us define <math display="inline">{\Gamma _{S_\mathit{0}}}= \cup _{{{S'}_\mathit{0}}\in {\mathbf{E}}} {\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math>. For a subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> such that <math display="inline">{\Gamma _{S_\mathit{0}}}\cap ({\partial \Omega _{F_{d_\mathit{0}}}}\cup {\partial \Omega _{U_{d_\mathit{0}}}}) \neq \emptyset </math>, the boundary condition <math display="inline">({\underline{F}_{d_\mathit{0}}},{\underline{U}_{d_\mathit{0}}})</math> is applied through a boundary interface <math display="inline">{\Gamma _{{S}_{d_\mathit{0}}}}</math>.
+To propose the partitioned problem, the whole domain <math display="inline">\Omega </math> is split into subdomains which are connected by interfaces with mechanical behaviors. Two possibilities are considered: “material” interfaces between plies with localized non-linearities (damage, contact) that are compatible with the mesomodeling, and “numerical” interfaces (the perfect ones) within the plies to conceive smaller problems that are suited for parallelism, as schematized in  [[#img-1|Figure 1]]. A subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> defined in the undeformed domain <math display="inline">{\Omega _{S_\mathit{0}}}</math> is connected to an adjacent undeformed subdomain <math display="inline">{{S'}_\mathit{0}}</math> through an undeformed interface <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}=\partial {\Omega _{S_\mathit{0}}}\cap \partial {\Omega _{S_\mathit{0}'}}</math>. The surface entity <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math> applies force distributions <math display="inline">{\underline{F}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{F}_{S_\mathit{0}'}}</math> and displacement distributions <math display="inline">{\underline{W}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{W}_{{S'}_\mathit{0}}}</math> to <math display="inline">{S^{\quad }_\mathit{0}}</math> and <math display="inline">{{S'}_\mathit{0}}</math> respectively ([[#img-2|Figure 2]]). Let us define <math display="inline">{\Gamma _{S_\mathit{0}}}= \cup _{{{S'}_\mathit{0}}\in {\mathbf{E}}} {\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math>. For a subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> such that <math display="inline">{\Gamma _{S_\mathit{0}}}\cap ({\partial \Omega _{F_{d_\mathit{0}}}}\cup {\partial \Omega _{U_{d_\mathit{0}}}}) \neq \emptyset </math>, the boundary condition <math display="inline">({\underline{F}_{d_\mathit{0}}},{\underline{U}_{d_\mathit{0}}})</math> is applied through a boundary interface <math display="inline">{\Gamma _{{S}_{d_\mathit{0}}}}</math>.

@@ Line 487: / Line 487: @@
 |}
-Results are compared to the theoretical solution <span id='citeF-29'></span>[[#cite-29|[29]]] in  [[#img-10|Figure 10]]. It is possible to observe three areas: the first is the bending mode (without delamination); the second zone appears for the crack's propagation (softening curve) and the third one is the second bending mode (when the beam has been completely delaminated). For bending, mesh (b) with three non-linear elements in the thickness is satisfactory, but it does not correctly represent delamination due to the visible zigzag. If the discretization (c) is studied, with a greater number of elements in the <math display="inline">y</math>-direction, the entire curve is correctly predicted, but the time used for the calculation is double that used for the linear discretization (a). The lack of accuracy in the response of mesh (b) could be related to the fact that the forces calculated to evaluate damage are performed at the interfaces which are discretize by constant functions <math display="inline">\mathcal{P}_0</math> (see  [[#img-3|Figure 3]]), although subdomains have finite elements of higher order. [[#img-11|Figure 11]] shows the crack's front at the beginning of the propagation.
+Results are compared to the theoretical solution <span id='citeF-29'></span>[[#cite-29|[29]]] in  [[#img-10|Figure 10]]. It is possible to observe three areas: the first is the bending mode (without delamination); the second zone appears for the crack's propagation (softening curve) and the third one is the second bending mode (when the beam has been completely delaminated). For bending, mesh (b) with three non-linear elements in the thickness is satisfactory, but it does not correctly represent delamination due to the visible zigzag. If the discretization (c) is studied, with a greater number of elements in the <math display="inline">y</math>-direction, the entire curve is correctly predicted, but the time used for the calculation is double that used for the linear discretization (a). The lack of accuracy in the response of mesh (b) could be related to the fact that the forces calculated to evaluate damage are performed at the interfaces which are discretize by constant functions <math display="inline">\mathcal{P}_0</math> ([[#img-3|Figure 3]]), although subdomains have finite elements of higher order. [[#img-11|Figure 11]] shows the crack's front at the beginning of the propagation.
 <div id='img-10'></div>

@@ Line 232: / Line 232: @@
 ====3.1.1 Isotropic material====
-It is considered an elastic modulus <math display="inline">E=210</math> [GPa] and a poisson coefficient <math display="inline">\nu=0.3</math> [-]. The geometry is partitioned into <math display="inline">64</math> identical subdomains and <math display="inline">184</math> interfaces (see  [[#img-5|Figure 5]]); each subdomain has length <math display="inline">L_{sst}=20</math> [mm], width <math display="inline">a_{sst}= 15</math> [mm] and thickness <math display="inline">h_{sst}= 4</math> [mm]. Five meshes are considered: two different initial discretization with their respective <math display="inline">h</math>-refinement while the last one is a <math display="inline">p</math>-version. Each subdomain has <math display="inline">n_x</math>(<math display="inline">n_y</math>,<math display="inline">n_z</math>) elements in the <math display="inline">x</math>(<math display="inline">y</math>,<math display="inline">z</math>)-direction, respectively, as shown in Table [[#table-1|1]] as well as the total number of elements and the total degrees of freedom used for each mesh. In order to estimate the solution's error ([[#table-1|Table 1]]), the  maximum vertical displacement is compared with the theoretical elastic curve <span id='citeF-28'></span>[[#cite-28|[28]]].
+It is considered an elastic modulus <math display="inline">E=210</math> [GPa] and a poisson coefficient <math display="inline">\nu=0.3</math> [-]. The geometry is partitioned into <math display="inline">64</math> identical subdomains and <math display="inline">184</math> interfaces ([[#img-5|Figure 5]]); each subdomain has length <math display="inline">L_{sst}=20</math> [mm], width <math display="inline">a_{sst}= 15</math> [mm] and thickness <math display="inline">h_{sst}= 4</math> [mm]. Five meshes are considered: two different initial discretization with their respective <math display="inline">h</math>-refinement while the last one is a <math display="inline">p</math>-version. Each subdomain has <math display="inline">n_x</math>(<math display="inline">n_y</math>,<math display="inline">n_z</math>) elements in the <math display="inline">x</math>(<math display="inline">y</math>,<math display="inline">z</math>)-direction, respectively, as shown in  [[#table-1|Table 1]] as well as the total number of elements and the total degrees of freedom used for each mesh. In order to estimate the solution's error ([[#table-1|Table 1]]), the  maximum vertical displacement is compared with the theoretical elastic curve <span id='citeF-28'></span>[[#cite-28|[28]]].
 <div id='img-5'></div>

@@ Line 44: / Line 44: @@
 Let us consider a laminate composite (see Figure [[#img-1|1]]) occupying the domain <math display="inline">\Omega </math> bounded by <math display="inline">\partial \Omega </math> in the current configuration, and consisting of <math display="inline">N_P</math> plies. Each ply <math display="inline">P</math> is connected to an adjacent ply <math display="inline">P' </math> through the interface <math display="inline">{\Gamma _{PP'}}</math>. The structure is subjected to an external surface traction field <math display="inline">{\underline{F}_d}</math> on the part <math display="inline">{\partial \Omega _{F_d}}</math> and to a displacement field <math display="inline">{\underline{U}_d}</math> on the complementary part <math display="inline">{\partial \Omega _{U_d}}</math>. The body force per unit of mass is written <math display="inline">{\underline{f}_d}</math>. The relevant quantities are described in reference to the undeformed configuration using the index <math display="inline">\cdot _\mathit{0}</math>. The geometrically nonlinear evolution is handled through a total Lagrangian formulation and delamination (damageable interfaces) is modeled using CZM and unilateral contact conditions. For the sake of simplicity, an extensive description of the CZM is found in <span id='citeF-24'></span>[[#cite-24|[24]]], while <span id='citeF-25'></span>[[#cite-25|[25]]] describe contact inequalities.
-To propose the partitioned problem, the whole domain <math display="inline">\Omega </math> is split into subdomains which are connected by interfaces with mechanical behaviors. Two possibilities are considered: “material” interfaces between plies with localized non-linearities (damage, contact) that are compatible with the mesomodeling, and “numerical” interfaces (the perfect ones) within the plies to conceive smaller problems that are suited for parallelism, as schematized in Figure [[#img-1|1]]. A subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> defined in the undeformed domain <math display="inline">{\Omega _{S_\mathit{0}}}</math> is connected to an adjacent undeformed subdomain <math display="inline">{{S'}_\mathit{0}}</math> through an undeformed interface <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}=\partial {\Omega _{S_\mathit{0}}}\cap \partial {\Omega _{S_\mathit{0}'}}</math>. The surface entity <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math> applies force distributions <math display="inline">{\underline{F}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{F}_{S_\mathit{0}'}}</math> and displacement distributions <math display="inline">{\underline{W}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{W}_{{S'}_\mathit{0}}}</math> to <math display="inline">{S^{\quad }_\mathit{0}}</math> and <math display="inline">{{S'}_\mathit{0}}</math> respectively (see Figure [[#img-2|2]]). Let us define <math display="inline">{\Gamma _{S_\mathit{0}}}= \cup _{{{S'}_\mathit{0}}\in {\mathbf{E}}} {\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math>. For a subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> such that <math display="inline">{\Gamma _{S_\mathit{0}}}\cap ({\partial \Omega _{F_{d_\mathit{0}}}}\cup {\partial \Omega _{U_{d_\mathit{0}}}}) \neq \emptyset </math>, the boundary condition <math display="inline">({\underline{F}_{d_\mathit{0}}},{\underline{U}_{d_\mathit{0}}})</math> is applied through a boundary interface <math display="inline">{\Gamma _{{S}_{d_\mathit{0}}}}</math>.
+To propose the partitioned problem, the whole domain <math display="inline">\Omega </math> is split into subdomains which are connected by interfaces with mechanical behaviors. Two possibilities are considered: “material” interfaces between plies with localized non-linearities (damage, contact) that are compatible with the mesomodeling, and “numerical” interfaces (the perfect ones) within the plies to conceive smaller problems that are suited for parallelism, as schematized in  [[#img-1|Figure 1]]. A subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> defined in the undeformed domain <math display="inline">{\Omega _{S_\mathit{0}}}</math> is connected to an adjacent undeformed subdomain <math display="inline">{{S'}_\mathit{0}}</math> through an undeformed interface <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}=\partial {\Omega _{S_\mathit{0}}}\cap \partial {\Omega _{S_\mathit{0}'}}</math>. The surface entity <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math> applies force distributions <math display="inline">{\underline{F}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{F}_{S_\mathit{0}'}}</math> and displacement distributions <math display="inline">{\underline{W}_{{S^{\quad }_\mathit{0}}}}</math>, <math display="inline">{\underline{W}_{{S'}_\mathit{0}}}</math> to <math display="inline">{S^{\quad }_\mathit{0}}</math> and <math display="inline">{{S'}_\mathit{0}}</math> respectively (see Figure [[#img-2|2]]). Let us define <math display="inline">{\Gamma _{S_\mathit{0}}}= \cup _{{{S'}_\mathit{0}}\in {\mathbf{E}}} {\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math>. For a subdomain <math display="inline">{S^{\quad }_\mathit{0}}</math> such that <math display="inline">{\Gamma _{S_\mathit{0}}}\cap ({\partial \Omega _{F_{d_\mathit{0}}}}\cup {\partial \Omega _{U_{d_\mathit{0}}}}) \neq \emptyset </math>, the boundary condition <math display="inline">({\underline{F}_{d_\mathit{0}}},{\underline{U}_{d_\mathit{0}}})</math> is applied through a boundary interface <math display="inline">{\Gamma _{{S}_{d_\mathit{0}}}}</math>.
@@ Line 52: / Line 52: @@
 |style="padding:10px;"|[[Image:Draft_Saavedra_368043899-reference_pb.png|700px|The reference problem, the mesomodel and its partitioning <span id='citeF-18'></span>[[#cite-18|[18]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;"| '''Figure 1:''' The reference problem, the mesomodel and its partitioning <span id='citeF-18'></span>[[#cite-18|[18]]]
+| colspan="1" style="padding-bottom:10px;"| '''Figure 1'''. The reference problem, the mesomodel and its partitioning <span id='citeF-18'></span>[[#cite-18|[18]]]
 |}
@@ Line 60: / Line 60: @@
 |style="padding:10px;"|[[Image:Draft_Saavedra_368043899-sst_v2.png|540px|Subdomains and interfaces <span id='citeF-16'></span>[[#cite-16|[16]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;"| '''Figure 2:''' Subdomains and interfaces <span id='citeF-16'></span>[[#cite-16|[16]]]
+| colspan="1" style="padding-bottom:10px;"| '''Figure 2'''. Subdomains and interfaces <span id='citeF-16'></span>[[#cite-16|[16]]]
 |}
@@ Line 196: / Line 196: @@
 ===2.2 Discretization===
-To solve both equations' sets of the multiscale algorithm, interfaces and subdomains are discretized in space using classical finite elements. At an interface <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math>, the displacements <math display="inline">{\underline{W}_{{S^{\quad }_\mathit{0}}}}</math> and forces <math display="inline">{\underline{F}_{{S^{\quad }_\mathit{0}}}}</math> belong to the approximation spaces <math display="inline">{\mathcal{W}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> and <math display="inline">{\mathcal{F}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math>. These spaces are chosen such that the bilinear form (in the sense of the interface mechanical work) is non-degenerate. Additionally, a wrong discretization for <math display="inline">{\mathcal{F}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> could generate spurious oscillating modes leading to numerical instability. These inconveniences can be evaded using a common space for the displacements and forces and including a local refinement of the mesh near the boundary (over-discretization) of the subdomains (approximation space <math display="inline">{\mathcal{U}_{S_\mathit{0}}}</math>). Two manners are possible: to increase the number of elements (<math display="inline">h</math>-version) or to use a higher degree of approximation (<math display="inline">p</math>-version) for the field <math display="inline">{\underline{u}_{{S^{\quad }_\mathit{0}}}}</math> near to the interface, as illustrated in Figure [[#img-3|3]] <span id='citeF-27'></span>[[#cite-27|[27]]]. Classically, the code MULTI has considered linear elements <math display="inline">\mathcal{P}_1</math> with local <math display="inline">h</math>-refinement along the subdomain's boundary, while the spaces <math display="inline">{\mathcal{W}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> and <math display="inline">{\mathcal{F}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> are piecewise constant functions <math display="inline">\mathcal{P}_0</math>.
+To solve both equations' sets of the multiscale algorithm, interfaces and subdomains are discretized in space using classical finite elements. At an interface <math display="inline">{\Gamma _{S_\mathit{0}{S'}_\mathit{0}}}</math>, the displacements <math display="inline">{\underline{W}_{{S^{\quad }_\mathit{0}}}}</math> and forces <math display="inline">{\underline{F}_{{S^{\quad }_\mathit{0}}}}</math> belong to the approximation spaces <math display="inline">{\mathcal{W}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> and <math display="inline">{\mathcal{F}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math>. These spaces are chosen such that the bilinear form (in the sense of the interface mechanical work) is non-degenerate. Additionally, a wrong discretization for <math display="inline">{\mathcal{F}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> could generate spurious oscillating modes leading to numerical instability. These inconveniences can be evaded using a common space for the displacements and forces and including a local refinement of the mesh near the boundary (over-discretization) of the subdomains (approximation space <math display="inline">{\mathcal{U}_{S_\mathit{0}}}</math>). Two manners are possible: to increase the number of elements (<math display="inline">h</math>-version) or to use a higher degree of approximation (<math display="inline">p</math>-version) for the field <math display="inline">{\underline{u}_{{S^{\quad }_\mathit{0}}}}</math> near to the interface, as illustrated in  [[#img-3|Figure 3]] <span id='citeF-27'></span>[[#cite-27|[27]]]. Classically, the code MULTI has considered linear elements <math display="inline">\mathcal{P}_1</math> with local <math display="inline">h</math>-refinement along the subdomain's boundary, while the spaces <math display="inline">{\mathcal{W}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> and <math display="inline">{\mathcal{F}_{{S^{\quad }_\mathit{0}}{{S'}_\mathit{0}},h}}</math> are piecewise constant functions <math display="inline">\mathcal{P}_0</math>.
 In this work, the <math display="inline">p</math>-refinement is also explored. Indeed, it is here proposed to use the second order approximation for <math display="inline">{\underline{u}_{{S^{\quad }_\mathit{0}}}}</math> not only in the boundary but in the whole subdomain.
@@ Line 205: / Line 205: @@
 |[[Image:Review_265042547183_2078_Fig3.png|600px|Modification of the classical approximations of the inter-force and local displacement along the edge of a subdomain: h-and p-versions <span id='citeF-13'></span>[[#cite-13|[13]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;"| '''Figure 3:''' Modification of the classical approximations of the inter-force and local displacement along the edge of a subdomain: <math>h</math>-and <math>p</math>-versions <span id='citeF-13'></span>[[#cite-13|[13]]]
+| colspan="1" style="padding-bottom:10px;"| '''Figure 3'''. Modification of the classical approximations of the inter-force and local displacement along the edge of a subdomain: <math>h</math>-and <math>p</math>-versions <span id='citeF-13'></span>[[#cite-13|[13]]]
 |}

@@ Line 517: / Line 517: @@
 <div id="cite-1"></div>
-[[#citeF-1|[1]]] Herakovich C.T. Mechanics of composites: A historical review. Mechanics Research Communications, 1: 1 - 20, 2012.
+[[#citeF-1|[1]]] Herakovich C.T. Mechanics of composites: A historical review. Mechanics Research Communications, 1:1-20, 2012.
 <div id="cite-2"></div>

@@ Line 498: / Line 498: @@
 |[[Image:Review_265042547183_2690_Fig11.png|650px|DCB problem: (a) subdomains and interfaces (b) crack's front after the 11<sup>th</sup> step where pre-crack is in black and d is the damage variable ranging from 0 (healthy point) to 1 (completely damaged interface point)]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;"| '''Figure 11:''' DCB problem. (a) subdomains and interfaces. (b) Crack's front after the 11<math>^{th}</math> step where pre-crack is in black and d is the damage variable ranging from 0 (healthy point) to 1 (completely damaged interface point)
+| colspan="1" style="padding-bottom:10px;"| '''Figure 11:''' DCB problem. (a) Subdomains and interfaces. (b) Crack's front after the 11<math>^{th}</math> step where pre-crack is in black and d is the damage variable ranging from 0 (healthy point) to 1 (completely damaged interface point)
 |}

@@ Line 488: / Line 488: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;max-width: 80%;"
 |-
-|[[Image:Review_265042547183_8931_Fig10.png|600px|The load-displacement curve of the DCB test]]
+|[[Image:Review_265042547183_8931_Fig10.png|700px|The load-displacement curve of the DCB test]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding-bottom:10px;"| '''Figure 10:''' The load-displacement curve of the DCB test
@@ Line 496: / Line 496: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;max-width: 80%;"
 |-
-|[[Image:Review_265042547183_2690_Fig11.png|600px|DCB problem: (a) subdomains and interfaces (b) crack's front after the 11<sup>th</sup> step where pre-crack is in black and d is the damage variable ranging from 0 (healthy point) to 1 (completely damaged interface point)]]
+|[[Image:Review_265042547183_2690_Fig11.png|650px|DCB problem: (a) subdomains and interfaces (b) crack's front after the 11<sup>th</sup> step where pre-crack is in black and d is the damage variable ranging from 0 (healthy point) to 1 (completely damaged interface point)]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding-bottom:10px;"| '''Figure 11:''' DCB problem. (a) subdomains and interfaces. (b) Crack's front after the 11<math>^{th}</math> step where pre-crack is in black and d is the damage variable ranging from 0 (healthy point) to 1 (completely damaged interface point)

@@ Line 438: / Line 438: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;max-width: 80%;"
 |-
-|[[Image:Review_265042547183_1362_Fig9.png|600px|(a) The initial configuration and the final deformation after the last time step (b) the load-displacement curve ]]
+|[[Image:Review_265042547183_1362_Fig9.png|700px|(a) The initial configuration and the final deformation after the last time step (b) the load-displacement curve ]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding-bottom:10px;"| '''Figure 9:''' (a) The initial configuration and the final deformation after the last time step. (b) The load-displacement curve

@@ Line 375: / Line 375: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;max-width: 80%;"
 |-
-| [[Image:Review_265042547183_6563_Fig7.png|600px]]
+| [[Image:Review_265042547183_6563_Fig7.png|700px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" style="padding-bottom:10px;"| '''Figure 7:''' Bending problem with orthotropic material. (a) Deflection. (b) Evolution of the iterative LaTIn error
@@ Line 386: / Line 386: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;max-width: 80%;"
 |-
-| [[Image:Review_265042547183_4572_Fig8.png|600px]]
+| [[Image:Review_265042547183_4572_Fig8.png|700px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" style="padding-bottom:10px;"| '''Figure 8:''' Results for the orthotropic material: normal stresses <math>\sigma _{xx}</math>