![\"welsim_release_2026r2\"](\"\\assets\\blog\\20260401\\welsim_release_2026r2.png\")
\n<\/p>\n\nWELSIM, a general-purpose engineering simulation and analysis software, has released its latest 2026R2 version (internal version 3.3). Compared to the previous release, version 2026R2 introduces a majorly upgraded underlying framework alongside a new dark theme, improving the graphical user interface.<\/p>\n
\n \n<\/p>\n\n
The newly added dark theme reflects current desktop application designs and is gentler on the eyes. Users can set the appearance theme in Preferences and have three options available: Classic, Dark, and Light.<\/p>\n
\n ![\"welsim_thermal_ss_dark\"](\"\\assets\\blog\\20260401\\welsim_thermal_ss_dark.png\")
\n<\/p>\n\n
The Classic theme is similar to the Light theme, whereas the Dark theme features a dark background with light\u2011colored text and icons in the foreground. Starting with this version 2026R2, WELSIM\u2019s default style will be the Dark theme.<\/p>\n\n
The new version upgrades the key foundational framework, including updating the GUI framework Qt from 5.15 to 6.10 and the 3D rendering engine VTK from 8.2 to 9.2.<\/p>\n
\n ![\"welsim_about\"](\"\\assets\\blog\\20260401\\welsim_about.png\")
\n<\/p>\n\n
Upgrading both core frameworks across major versions has improved WELSIM\u2019s stability and performance.<\/p>\n\n
The new release optimizes and advances existing features and adds more automated test cases, delivering a better user experience in WELSIM.<\/p>\n\n
Disclaimer: WelSim and its developers are not affiliated with Qt or VTK, nor are they associated with the above\u2011mentioned development teams or organizations. References to Qt and VTK are made solely for reference in technical blog posts and software documentation.<\/em><\/p>\n\n","pubDate":"Wed, 01 Apr 2026 00:00:00 +0000","link":"https:\/\/welsim.com\/2026\/04\/01\/welsim-2026r2-releases-with-all-new-dark-theme-gui.html","guid":"https:\/\/welsim.com\/2026\/04\/01\/welsim-2026r2-releases-with-all-new-dark-theme-gui.html"},{"title":"Multi-style interface for Qt-based desktop\u00a0software","description":" Qt is one of the most popular cross-platform C++ Graphical User Interface (GUI) application frameworks in the world. Its most powerful feature is its cross-platform capability: developers write code once and, after recompilation, are able to run it on desktop (Windows, macOS, Linux), mobile (iOS, Android), and embedded systems (QNX, VxWorks, various RTOS). Software products, particularly large-scale industrial software, are frequently built on the Qt framework. From a developer perspective, this article discusses how to optimally implement multi-theme interfaces in Qt software, focusing on Dark theme.<\/p>\n \n In regards to the development of large-scale Qt desktop applications, such as IDEs, industrial control software, or productivity tools, the UI is more than just aesthetics; it concerns operational comfort during long usage sessions, the clarity of information hierarchy, and brand professionalism. As a result, modern large-scale visualization software support multiple interface styles, commonly categorized into Light and Dark themes. Because Light mode is typically the default, Dark mode requires dedicated functional implementation by developers. From a practical standpoint, just these two styles are generally sufficient for most needs.<\/p>\n\n There are several established solutions for implementing and dynamically switching between themes in Qt. This article focuses on the two most common methods: Source Code<\/strong> and QSS files<\/strong>.<\/p>\n \n This is the classic approach. Developers define different themes directly in the source code, with customized colors for each theme, and apply the themes to the QApplication via the setStyle and setPalette functions. The advantage of this method is its simplicity, speed, and ease of maintenance\u200aas developers manage styles alongside other Qt code. However, because user-defined styles require access to the source code, this technique has limited scalability. For large commercial software, especially engineering software, users rarely customize interface styles anyways, making direct QStyle configuration in source code an efficient solution. The general-purpose engineering simulation software WELSIM also adopts this approach.<\/p>\n\n This is a more flexible and adaptable method, implemented by loading different\u00a0.qss files combined with variable substitution (using regular expressions or setProperty). One advantage is the seperation of the style from the application functionality as\u200astyle modifications do not require recompiling the source code, and end-users can modify or add QSS files to achieve custom styles. The drawbacks include slightly reduced rendering performance for complex interfaces and a relatively cumbersome development and maintenance process that requires a proficiency in QSS syntax.<\/p>\n\n Light and dark are the two primary color schemes for multi-style development. The light style is similar to the operating system\u2019s native display, so the main task in developing a multi-theme interface is implementing the dark theme. These two themes can be switched on demand, much like the map system in a car\u2019s central display where it\u2019s a\u200alight background during the day and dark background at night. Dark-themed desktop software is becoming increasingly popular because it is eye-friendly, For users of large-scale engineering software who spend extended periods viewing screens, dark interfaces effectively reduce eye strain.<\/p>\n \n Many developers mistakenly believe dark mode is a simple color inversion. In reality, directly flipping white background\/black text to black background\/white text causes visual fatigue due to extreme contrast and a halo effect. Below are the recommended color schemes for light and dark themes:<\/p>\n\n Background<\/strong>: Avoid pure black (#000000); use dark gray (e.g., #121212 or #1E1E1E) for depth through shadows.\nLayout<\/strong>: Follow the \u201clighter is closer\u201d principle for persepective. The base background is darkest, while pop-ups or floating dialogs should be slightly lighter.\nText<\/strong>: Avoid pure white (#FFFFFF); use off-white or light gray (e.g., #E0E0E0) to reduce glare.<\/p>\n\n Background<\/strong>: Choose a very light gray (e.g., #F5F5F5) as the primary background, reserving pure white for editing or core content areas.\nContrast<\/strong>: Use subtle borders rather than large shadows to distinguish modules.\nColor Balance<\/strong>: Ensure accent colors (status bars, icons) have enough saturation to remain visible under bright light.<\/p>\n\n Notably, Qt\u2019s built-in Fusion style is an excellent base theme with built-in light and dark variants; developers can directly use Fusion as a development template.<\/p>\n\n Background color changes may render existing icons incompatible (e.g., icons designed for light themes become lose contrast on dark backgrounds). Qt provides solutions for multi-style icons, with three common methods:<\/p>\n \n When using two sets of icon themes, determine whether the application\u2019s current theme is dark. If it is, apply the dark icons; otherwise, use the light icons. There are several ways to detect a dark theme; for Qt 6.5 and above, you can use the following method:<\/p>\n\n Dynamically load icons in updateIcon() function.<\/p>\n\n Place updateIcon() in the changeEvent(QEvent *e) slot function. Capture system theme changes via e->type() == QEvent::PaletteChange or e->type() == QEvent::StyleChange.<\/p>\n\n Many large applications include OpenGL-based rendering widgets where Qt\u2019s default QWidget theme settings do not automatically apply. Manual synchronization is required:<\/p>\n \n Taking a VTK-implemented chart as an example, synchronizing the 2D plotting area requires setting the renderer background, chart background, and axis colors, then updating the renderer.<\/p>\n\n The source code for theme synchronization is shown below.<\/p>\n\n In addition to the 2D drawing window, OpenGL-driven 3D windows can also be configured with corresponding color themes. However, in actual product design, this is often unnecessary because 3D windows provide their own color schemes. As shown in the figure, WELSIM\u2019s 3D rendering window supports three background options: blue-white gradient, black, and white. Users can customize the style and color of the 3D OpenGL rendering window to fit their needs.<\/p>\n\n \n \n Nowadays, for any well-established large-scale engineering software, supporting multiple themes has become an essential feature. At the very least, the software should include both Light and Dark modes. The core challenge lies in the implementation of the Dark theme because although the technical difficulty is not necessarily high, it involves a vast amount of meticulous development and testing. This takes significant development time as well as long-term optimization and maintenance. If the existing codebase contains local style modifications, such as setStyle or setStyleSheet functions, they must be updated accordingly. From a maintenance perspective, it is best to remove those local styling snippets and instead allow a global style manager to govern the entire software interface.<\/p>\n\n WELSIM and its author are not affiliated with Qt or the Qt development team\/organization. All open-source software names and images referenced herein are for technical blog and software usage reference only.<\/em><\/p>\n\n","pubDate":"Fri, 20 Mar 2026 00:00:00 +0000","link":"https:\/\/welsim.com\/2026\/03\/20\/multi-style-interface-for-qt-based-desktop-software.html","guid":"https:\/\/welsim.com\/2026\/03\/20\/multi-style-interface-for-qt-based-desktop-software.html"},{"title":"Parameters in hyperelastic model curve\u00a0fitting","description":" Many tasks in finite element analysis require curve fitting. Especially in materials engineering, when only experimental test data is available, engineers must perform curve fitting to determine the parameters in a given numerical model. Common types of material curve fitting include hyperelastic, plastic, viscous, core loss materials, and more.<\/p>\n \n Unlike other types of curve fitting, curve fitting for finite element material models requires both a small error and physically valid fitted parameters; furthermore, these parameters must be conducive to convergence in subsequent nonlinear finite element computation. As a result, there are high standards placed on the algorithms and details of parameter fitting.<\/p>\n\n Rarely do articles discuss the parameters, initial values, and reasonable bounds for hyperelastic model parameters despite their importance when implementing hyperelastic model curve fitting and verifying the rationality of fitted parameters. From a development perspective, this article discusses how to better perform curve fitting for hyperelastic material models, with a particular focus on setting parameter bounds and initial values, as well as identifying the characteristics of reasonable parameters.<\/p>\n\n Due to the large number of hyperelastic models and order-dependent variation, this article describes the computational details of each hyperelastic model in separate sections to avoid confusion.<\/p>\n\n The neo-Hookean model is first because it is one of the most simple and classic hyperelastic models. Many other models can be simplified to the neo-Hookean model under specific parameter conditions. Its strain energy density function W is expressed as:<\/p>\n \n where \u03bc is the shear modulus. During curve fitting computation, the shear modulus must be greater than zero, i.e., \u03bc>0. The initial value is set to \u03bc0\u200b=E\/3, where Young\u2019s modulus E can be obtained from the slope of the stress-strain curve near the origin (strain < 5%).<\/p>\n \n To check for physical validity after parameter fitting, you can refer below for the approximate correspondence between common hyperelastic materials and \u03bc:<\/p>\n\n A fitted parameter \u03bc that differs significantly from the uniaxial tension data indicates that the material may exhibit a strong second strain invariant effect, in which the Mooney-Rivlin or other suitable models should be used instead.<\/p>\n\n The Mooney-Rivlin model is another one of the most commonly used hyperelastic models in engineering analysis. It is a direct extension of the neo-Hookean model and is characterized by its simple and flexible form. If the neo-Hookean is considered the entry-level model in hyperelasticity, then the Mooney-Rivlin would be the standard model for handling small-to-moderate deformations (100%-200% strain). Its simple mathematical form and linear dependence on material constants allows it to converge easily in Finite Element Analysis (FEA) calculations.<\/p>\n\n Depending on the order, the Mooney-Rivlin model has several different forms with varying amounts of parameters, the most complex being the 9-parameter model. This section uses the 9-parameter Mooney-Rivlin model as an example to discuss parameter ranges and initial value settings. Its strain energy density function W includes all combinations from linear to cubic terms:<\/p>\n \n Physically, the shear modulus \u03bc>0. Therefore, \u03bc=2(C10\u200b+C01\u200b)>0. The most robust constraint for practical calculations is C10\u200b>0 and C01\u200b\u22650. In many rubber materials, C10\u200b is the dominant term, and C01\u200b is relatively small; C11\u200b is also usually positive. The third-order parameter C30\u200b\u22650. C03\u200b, C21\u200b, C12\u200b can capture the sharp stiffening at extremely large deformations (strain > 400%) and are generally 3\u20134 orders of magnitude smaller than the first-order parameters.<\/p>\n \n Regarding initial conditions, C10\u200b=0.9\u00d7(\u03bc0\u200b\/2), C01\u200b=0.1\u00d7(\u03bc0\u200b\/2), with the initial shear modulus \u03bc0\u200b=E\/3. The initial values for C11\u200b, C20\u200b, C02\u200b, C30\u200b, C21\u200b are often chosen to be small, typically 0.1% of C10\u200b. The initial values for C12\u200b and C03\u200b can be set to zero. For most synthetic rubbers (e.g., NBR, EPDM, Neoprene), the parameters generally follow the order-of-magnitude rules below:<\/p>\n\n The Mooney-Rivlin model has its limitations. When rubber is stretched to its limit (molecular chains fully extended), the stress rises sharply (the \u201cupturn\u201d phenomenon). The Mooney-Rivlin model cannot account for this stiffening at high strains; the Ogden or Gent model is recommended when simulating extremely large deformations (strain > 300%). If the experimental data is not comprehensive, a more robust model with fewer parameters is advised, such as the Yeoh model or the 5-parameter Mooney-Rivlin model.<\/p>\n\n The Yeoh hyperelastic model is known for its simplicity and stability. It discards the second invariant I2\u200b (terms like C01\u200b), which is highly susceptible to experimental error, retaining only the first invariant I1\u200b. Therefore, it is more robust than the Mooney-Rivlin model when fitting large-deformation data. The strain energy density function W is as follows:<\/p>\n \n Common Yeoh models are 1st to 3rd-order, with 1 to 3 parameters respectively. During fitting, C10\u200b>0 is required since the material loses shear resistance and crashes the simulation immediately if C10\u200b\u22640. C20\u200b is usually negative; its magnitude is not too large and can be constrained to be greater than 1% of C10\u200b. C30\u200b is positive and is used to capture the stiffening at large strain.<\/p>\n \n The initial value settings are relatively simple: the initial value of C10\u200b is E\/6, where Young\u2019s modulus E is the slope of the test data at small deformations. C20\u200b=\u22120.1\u00d7C10\u200b, C30\u200b=0.01\u00d7C10\u200b.<\/p>\n\n The parameters of the Yeoh model for common materials are as follows:<\/p>\n\n The Polynomial hyperelastic model is also based on the power series expansion of the strain energy density function W with respect to the invariants I1\u200b and I2\u200b. It is one of the most widely used frameworks in hyperelasticity theory, and many models (Mooney-Rivlin, Yeoh, Neo-Hookean) are essentially its special cases. The general strain energy density function W is expressed as:<\/p>\n \n where N is the order of the model. Common polynomial models are 1st to 3rd-order, corresponding to 2, 5, and 9 parameters. Like the Mooney-Rivlin model, during fitting, it is necessary for C10\u200b>0 and C10\u200b>\u2223C01\u200b\u2223. C30\u200b is also usually required to be positive. Generally, the higher the order, the smaller the magnitude of the values. The reasonable parameter ranges for hyperelastic materials are shown below.<\/p>\n\n For initial value settings, set C10\u200b=E\/6. C20\u200b=\u22120.1\u00d7C10\u200b, C30\u200b=0.01\u00d7C10\u200b or smaller. Although the value of C30\u200b is small, its high power amplifies its impact on the end of the curve.<\/p>\n\n The Arruda-Boyce model is unique in hyperelastic material simulation, and it is constructed based on statistical mechanics (molecular chain network theory). The strain energy density function W is expressed as:<\/p>\n \n A key feature of this model is its low requirement for test data, and uniaxial data alone is sufficient to start. Unlike polynomial models that require multi-axial data to determine parameters, the Arruda-Boyce model\u2019s parameters have clear physical definitions, in which relatively accurate \u03bc and \u03bbm\u200b can usually be obtained from the high-quality uniaxial tension data.<\/p>\n\n The value range for the initial shear modulus \u03bc is straightforward; it must be greater than 0 and lie between 0.1~5 MPa, with common values for rubber materials ranging from 0.5~1.5 MPa. \u03bbm\u200b must be greater than and typically limited to [1.1, 20]. The model becomes extremely stiff when \u03bbm\u200b is too close to 1, leading to highly unstable numerical calculations. For most industrial rubbers, setting \u03bbm\u200b between 3.0 and 7.0 usually covers most working conditions.<\/p>\n \n Initial value determination is also straightforward: set \u03bc=E\/3. \u03bbm\u200b=5 is a robust starting point.<\/p>\n\n Typically, the Arruda-Boyce parameters correspond to rubber materials as follows:<\/p>\n\n The Blatz-Ko model is a simple model used to simulate foams and porous materials. The most commonly used form contains only one parameter, the shear modulus \u03bc.<\/p>\n \n Like other hyperelastic models, the shear modulus must be greater than zero. Poisson\u2019s ratio \u03bd is fixed as a theoretical property of this model is that its effective Poisson\u2019s ratio is locked at approximately 0.25. This means the material is assumed to shrink significantly in volume when compressed, rather than expanding sideways like ordinary rubber. Do not use the Blatz-Ko model for solid rubber (Poisson\u2019s ratio near 0.5, incompressible).<\/p>\n\n As long as the Blatz-Ko model ensures that the shear modulus \u03bc is positive (\u03bc>0) and the material is indeed a compressible foam, fitting is usually straightforward.<\/p>\n\n Since Poisson\u2019s ratio \u03bd is often fixed at 0.25, according to the linear elastic conversion relationship: \u03bc = E\/[2(1+\u03bd)] = E\/2.5 = 0.4E. The initial value can be set to 0.4E.<\/p>\n\n Typically, the shear modulus corresponds to the materials as follows:<\/p>\n\n The Gent model is a physically based hyperelastic model, similar in behavior to the Arruda-Boyce model. Its greatest advantage is its simple form, which can effectively capture the nonlinear behavior of polymer chains reaching their limiting extension length using only two constants. The mathematical form of the Gent model is a logarithmic function, and the computational cost for curve fitting is lower than that of the Arruda-Boyce model.<\/p>\n\n The Gent model has only two core parameters: \u03bc (initial shear modulus) and Jm\u200b (limiting invariant). Its strain energy density function is defined as:<\/p>\n \n The parameter \u03bc must be greater than 0; Jm\u200b must be greater than the maximum measured value of I1\u200b\u22123. If Jm\u200b is too small, causing (I1\u200b\u22123)\/Jm \u200b\u2265 1, the logarithm becomes undefined, so the calculation will fail.<\/p>\n\n The initial value of the shear modulus \u03bc is simply determined by \u03bc=E\/3. Mathematically, Jm\u200b defines the upper limit for I1\u200b\u22123, so its initial value must be slightly larger than the invariant value corresponding to the maximum deformation observed in the experiment. To determine this, find the maximum elongation ratio \u03bbmax\u200b in the experimental data and calculate the corresponding I1\u200b. Note that the formula for I1\u200b varies slightly depending on the type of experiment. The initial value of Jm\u200b is set to 1.2\u00d7(I1_max\u200b\u22123).<\/p>\n\n The empirical parameters for materials of different hardness are as follows:<\/p>\n\n The Ogden hyperelastic model is one of the most powerful and flexible hyperelastic models available today. It is constructed directly based on the principal stretches \u03bbi\u200b. The strain energy density function of the Ogden model adopts a series superposition form expanded by order n, where n represents the model order.<\/p>\n \n The Ogden model has relatively more parameters, and higher-order versions require combined fitting of multiple sets of test data, such as uniaxial, pure shear, and equibiaxial, to prevent non-physical solutions and overfitting. Parameters must satisfy thermodynamic stability constraints, and reasonable bounds must be set during fitting. For example, set \u03bc1\u200b>\u2223\u03bc2\u200b\u2223>\u2223\u03bc3\u200b\u2223, 1<\u03b11\u200b<10, \u221210<\u03b12\u200b<10, \u221215<\u03b13\u200b<15.<\/p>\n \n Initial values for curve fitting are often set as follows: \u03b11\u200b=2, \u03b12\u200b=2, \u03b13\u200b=6, \u03bc1\u200b=0.6\u03bc0\u200b, \u03bc2\u200b=0.1\u03bc0\u200b, \u03bc3\u200b=0.05\u03bc0\u200b, where the initial shear modulus \u03bc0\u200b=E\/3. Young\u2019s modulus E is obtained from the slope of the test data at low strains.<\/p>\n\n The empirical data fitted by common Ogden hyperelastic models is as follows:<\/p>\n\n![\"welsim_qt_theme_dark\"](\"\\assets\\blog\\20260320\\welsim_qt_theme_dark.png\")
\n<\/p>\n\nImplementation methods<\/h2>\n
![\"welsim_qt_theme_options\"](\"\\assets\\blog\\20260320\\welsim_qt_theme_options.png\")
\n<\/p>\n\nSetting QStyle in C++\/Python Source\u00a0Code<\/h3>\n
Setting QStyleSheet via\u00a0QSS<\/h3>\n
Light Theme vs. Dark\u00a0Theme<\/h2>\n
![\"welsim_qt_chart_light_dark\"](\"\\assets\\blog\\20260320\\welsim_qt_chart_light_dark.png\")
\n<\/p>\n\nDark Theme<\/h3>\n
Light Theme<\/h3>\n
Icons<\/h2>\n
\n
![\"welsim_icons_light_dark\"](\"\\assets\\blog\\20260320\\welsim_icons_light_dark.png\"){kind=icon}
\n<\/p>\n\n\nbool isDark() {\u00a0\n\u00a0 return qApp->styleHints()->colorScheme() == Qt::ColorScheme::Dark;\u00a0\n}\n<\/code><\/p>\n\nvoid updateIcon() {\u00a0\n\u00a0QString path = isDark()\u00a0? \":\/icons\/icon_dark.svg\"\u00a0: \":\/icons\/icon_light.svg\";\u00a0\n\u00a0ui->button->setIcon(QIcon(path));\u00a0\n}\n<\/code><\/pre><\/div><\/div>\n\nOpenGL Rendering Widgets<\/h2>\n
\n
\n<\/p>\n\nvoid myWelSimChartPlot::syncVtkThemeWithQtDark(QWidget* qtWidget)\n{\n\u00a0 vtkRenderWindow* renderWindow = this->renderWindow();\n\u00a0 vtkRendererCollection* renderers = renderWindow\u00a0? renderWindow->GetRenderers()\u00a0: nullptr;\n\u00a0 vtkRenderer* renderer = renderers\u00a0? renderers->GetFirstRenderer()\u00a0: nullptr;\n\u00a0 if (!qtWidget ||\u00a0!renderer ||\u00a0!renderWindow) return;\n const QPalette palette = qtWidget->palette();\n\u00a0 const QColor bgColor = palette.color(QPalette::Base);\n\u00a0 const QColor fgColor = palette.color(QPalette::WindowText);\n renderer->SetBackground(qColorToVtk(bgColor));\n vtkColor4ub color;\n\u00a0 color.Set(bgColor.red(), bgColor.green(), bgColor.blue(), bgColor.alpha());\n\u00a0 this->chart()->GetBackgroundBrush()->SetColor(color);\n int axisIDs[4] = { vtkAxis::BOTTOM, vtkAxis::TOP, vtkAxis::LEFT, vtkAxis::RIGHT };\n\u00a0 for (unsigned int axisIndex = 0; axisIndex < 4; ++axisIndex)\n\u00a0 {\n\u00a0 int axisID = axisIDs[axisIndex];\n\u00a0 vtkAxis* axis = this->chart()->GetAxis(axisID);\n\u00a0 if (!axis) { assert(0); continue; }\n axis->GetTitleProperties()->SetColor(qColorToVtk(fgColor));\n\u00a0 axis->GetLabelProperties()->SetColor(qColorToVtk(fgColor));\n\u00a0 axis->GetGridPen()->SetColorF(qColorToVtk(borderColor));\n\u00a0 axis->GetPen()->SetColorF(qColorToVtk(fgColor));\n\u00a0 }\n\u00a0 renderWindow->Render();\n}\n<\/code><\/pre><\/div><\/div>\n\n![\"welsim_qt_3dview_dark\"](\"\\assets\\blog\\20260320\\welsim_qt_3dview_dark.png\")
\n<\/p>\n![\"welsim_qt_3dview_light\"](\"\\assets\\blog\\20260320\\welsim_qt_3dview_light.png\")
\n<\/p>\n\nConclusion<\/h2>\n
\n![\"welsim_curvefitter_demo_ogden3\"](\"\\assets\\blog\\20260201\\welsim_curvefitter_demo_ogden3.png\")
\n<\/p>\n\n1. neo-Hookean<\/h2>\n
![\"welsim_mateditor_eqn_neo_hookean\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_neo_hookean.png\")
\n<\/p>\n\n![\"welsim_mateditor_curvefit_neohookean\"](\"\\assets\\blog\\20260201\\welsim_mateditor_curvefit_neohookean.png\")
\n<\/p>\n\n\n \n
\n Material Type<\/strong><\/td>\n Shear Modulus \u03bc (MPa)<\/strong><\/td>\n <\/tr>\n \n Extra-soft Rubber<\/td>\n 0.3 ~ 0.5<\/td>\n <\/tr>\n \n Medium-hardness Rubber<\/td>\n 1.0 ~ 1.5<\/td>\n <\/tr>\n \n Hard Rubber<\/td>\n 3.0 ~ 5.0<\/td>\n <\/tr>\n \n Biological Soft Tissue<\/td>\n 0.01 ~ 0.1<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 2. Mooney-Rivlin<\/h2>\n
![\"welsim_mateditor_eqn_mooney_rivlin9\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_mooney_rivlin9.png\")
\n<\/p>\n\n![\"welsim_mateditor_curvefit_mr9\"](\"\\assets\\blog\\20260201\\welsim_mateditor_curvefit_mr9.png\")
\n<\/p>\n\n\n \n
\n Order Classification<\/strong><\/td>\n Parameter Symbol<\/strong><\/td>\n Typical Value Range (MPa)<\/strong><\/td>\n <\/tr>\n \n 1st-order (Linear)<\/td>\n C10\u200b,C01<\/td>\n \u200b0.1 ~ 2.0<\/td>\n <\/tr>\n \n 2nd-order (Transition)<\/td>\n C20\u200b,C11\u200b,C02<\/td>\n \u200b-0.2 ~ 0.2<\/td>\n <\/tr>\n \n 3rd-order (Stiffening)<\/td>\n C30\u200b,C21\u200b,C12\u200b,C03<\/td>\n \u200b-0.05 ~ 0.1<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 3. Yeoh<\/h2>\n
![\"welsim_mateditor_eqn_yeoh\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_yeoh.png\")
\n<\/p>\n\n![\"welsim_mateditor_curvefit_yeoh3\"](\"\\assets\\blog\\20260201\\welsim_mateditor_curvefit_yeoh3.png\")
\n<\/p>\n\n\n \n
\n Material Type\/Hardness<\/strong><\/td>\n C10\u200b (MPa)<\/strong><\/td>\n C20\u200b (MPa)<\/strong><\/td>\n C30\u200b (MPa)<\/strong><\/td>\n Description<\/strong><\/td>\n <\/tr>\n \n Ultra-soft Silicone\/Gel<\/td>\n 0.01 ~ 0.1<\/td>\n \u20130.001 ~ -0.01<\/td>\n 0.0001 ~ 0.01<\/td>\n Very low initial modulus, stiffening occurs late.<\/td>\n <\/tr>\n \n Natural Rubber (40A-50A)<\/td>\n 0.2 ~ 0.5<\/td>\n \u20130.02 ~ -0.1<\/td>\n 0.01 ~ 0.05<\/td>\n Good ductility, obvious plateau in the mid-curve.<\/td>\n <\/tr>\n \n Industrial-grade Rubber (60A-70A)<\/td>\n 0.6 ~ 1.2<\/td>\n \u20130.1 ~ -0.5<\/td>\n 0.1 ~ 0.5<\/td>\n Medium stiffness, commonly used for tire sidewalls or seals.<\/td>\n <\/tr>\n \n High-hardness Elastomer (80A+)<\/td>\n 1.5 ~ 5.0<\/td>\n \u20130.5 ~ -2.0<\/td>\n 0.5 ~ 2.0<\/td>\n Stiffening occurs very early, curve is steep.<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 4. Polynomial<\/h2>\n
![\"welsim_mateditor_eqn_polynominal\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_polynominal.png\")
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\n Parameter Category<\/strong><\/td>\n Parameter Item<\/strong><\/td>\n Typical Range (MPa)<\/strong><\/td>\n Physical Behavior Description<\/strong><\/td>\n <\/tr>\n \n Base Modulus<\/td>\n C10<\/td>\n \u200b0.1 ~ 0.6<\/td>\n Dominates small-to-medium deformation stiffness, usually positive.<\/td>\n <\/tr>\n \n Shear Correction<\/td>\n C01\u200b<\/td>\n 0.01 ~ 0.1<\/td>\n Corrects shear behavior, usually positive.<\/td>\n <\/tr>\n \n Mid-range Adjustment<\/td>\n C20<\/td>\n \u200b-0.05 ~ 0.05<\/td>\n Controls slope change in the mid-curve, often negative.<\/td>\n <\/tr>\n \n Large-deformation Stiffening<\/td>\n C30<\/td>\n \u200b0.001 ~ 0.01<\/td>\n Controls the upturn stiffening at very high strains, must be positive.<\/td>\n <\/tr>\n \n Coupling Terms<\/td>\n C11\u200b,C02<\/td>\n \u200b-0.01 ~ 0.01<\/td>\n Cross-effects between I1\u200b and I2\u200b, usually close to zero.<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 5. Arruda-Boyce<\/h2>\n
![\"welsim_mateditor_eqn_arruda_boyce\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_arruda_boyce.png\")
\n<\/p>\n\n![\"welsim_mateditor_curvefit_arruda_boyce\"](\"\\assets\\blog\\20260201\\welsim_mateditor_curvefit_arruda_boyce.png\")
\n<\/p>\n\n\n \n
\n Material<\/strong><\/td>\n \u03bc (MPa)<\/strong><\/td>\n \u03bbm<\/strong><\/td>\n <\/tr>\n \n Soft Rubber (Shore 30A - 40A)<\/td>\n 0.3 ~ 0.6<\/td>\n 5.0 ~ 8.0<\/td>\n <\/tr>\n \n Medium-hardness (Shore 50A - 60A)<\/td>\n 1.0 ~ 2.5<\/td>\n 3.0 ~ 5.0<\/td>\n <\/tr>\n \n Hard Rubber (Shore 70A - 80A)<\/td>\n 3.0 ~ 8.0<\/td>\n 1.5 ~ 2.5<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 6. Blatz-Ko<\/h2>\n
![\"welsim_mateditor_eqn_blatz_ko\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_blatz_ko.png\")
\n<\/p>\n\n\n \n
\n Material Type<\/strong><\/td>\n \u03bc Value Range (MPa)<\/strong><\/td>\n Description<\/strong><\/td>\n <\/tr>\n \n Ultra-light Polyurethane Foam<\/td>\n 0.05 ~ 0.5<\/td>\n Extremely low density, highly compressible.<\/td>\n <\/tr>\n \n Medium-density Foamed Rubber<\/td>\n 0.5 ~ 2.0<\/td>\n Common for shock pads and packaging.<\/td>\n <\/tr>\n \n High-hardness Closed-cell Foam<\/td>\n 2.0 ~ 10.0<\/td>\n Structural support foam, high stiffness.<\/td>\n <\/tr>\n \n Solid Compressible Rubber<\/td>\n 10.0+<\/td>\n Special synthetic rubbers with voids.<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 7. Gent<\/h2>\n
![\"welsim_mateditor_eqn_gent\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_gent.png\")
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\n Material Hardness\/Type<\/strong><\/td>\n Shear Modulus \u03bc (MPa)<\/strong><\/td>\n Limiting Constant Jm<\/strong><\/td>\n Description<\/strong><\/td>\n <\/tr>\n \n Ultra-soft Gel\/Soft Tissue<\/td>\n 0.01 ~ 0.15<\/td>\n 0 ~ 150<\/td>\n Extremely stretchable, stiffens very late.<\/td>\n <\/tr>\n \n Natural Rubber (40A)<\/td>\n 0.3 ~ 0.6<\/td>\n 30 ~ 80<\/td>\n Excellent ductility, high stiffening point.<\/td>\n <\/tr>\n \n Industrial Rubber (60A)<\/td>\n 1.0 ~ 2.0<\/td>\n 10 ~ 25<\/td>\n Medium stiffness, stiffens rapidly after 3\u20134x stretch.<\/td>\n <\/tr>\n \n High-hardness Elastomer (80A)<\/td>\n 3.0 ~ 7.0<\/td>\n 2 ~ 8<\/td>\n Stiffens within a very short distance, increased brittleness.<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n 8. Ogden<\/h2>\n
![\"welsim_mateditor_eqn_ogden\"](\"\\assets\\blog\\20260201\\welsim_mateditor_eqn_ogden.png\")
\n<\/p>\n\n\n
![\"welsim_mateditor_curvefit_ogden3\"](\"\\assets\\blog\\20260201\\welsim_mateditor_curvefit_ogden3.png\")
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![\"welsim_finite_element_thermal_exhaust_manifold\"](\"\\assets\\blog\\20260116\\welsim_finite_element_thermal_exhaust_manifold.png\")
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\n<\/p>\n\n![\"welsim_sph_generate_particles_mesh_denser\"](\"\\assets\\blog\\20260105\\welsim_sph_generate_particles_mesh_denser.png\")
\n<\/p>\n\n![\"mateditor_hill_orthotropic\"](\"\\assets\\blog\\20260105\\mateditor_hill_orthotropic.png\")
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