Saturday, April 12, 2025

Finite element analysis of plastic deformation using WELSIM

 Plastic deformation refers to the process in which a structure experiences external stress beyond its yield limit, transitioning from elastic deformation to plastic deformation. This process is also referred to as elastoplastic deformation. Plastic deformation is commonly seen in industrial applications, such as the formation of various sheet metal and die casting of automobile bodies. In a professional engineering context, engineers aim to avoid plastic deformation in structures to prevent material failure. As a result, plastic analysis is very common in structural finite element analysis.

The general-purpose engineering simulation software WELSIM already supports plastic analysis. This article gives an overview of the plastic analysis features in the current version from a practical software usage perspective.

From a computational standpoint, plastic deformation is a nonlinear process in a material’s constitutive relationship. Therefore, the software must have the capabilities to solve nonlinear problems. WELSIM uses FrontISTR as its implicit solver and OpenRadioss as its explicit solver. Users can also use other solvers such as CalculiX and Elmer, which will be covered in future articles. This article focuses on the FrontISTR and OpenRadioss solvers.

Most of the complexity in plastic deformation lies in the material behavior. Therefore, considerable effort is required for the material data input and editing. With the diversity of plastic models, the front-end interface also needs to be robust. WELSIM provides a user-friendly material editor and a fully consistent, free standalone material software called MatEditor. Currently, 25 plastic-related and 12 creep-related material properties are supported. Each property has its own parameters and editing method.

Using multilinear hardening as an example, the figure below demonstrates how to define an elastoplastic material. Basic parameters are entered:

  • Density: 7.8e-7 kg/mm³
  • Young’s modulus: 206.9 GPa
  • Poisson’s ratio: 0.29

Plastic stress-strain relationship data:

  • Strain: {0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5}
  • Stress: {450, 608, 679, 732, 752, 766, 780} MPa

Static elastoplastic analysis

For static nonlinear finite element analysis, the computation is essentially implicit. Nonlinear material deformation is solved using the Newton iterative method. In the project settings, you can retain the default “Static Structural Analysis” type.

Because plastic deformation is a nonlinear process, multiple sub-steps can be set in the analysis. In this example, 25 sub-steps are used.

The other analysis settings are almost identical to those in elastic analysis.

After setting boundary conditions and running the simulation, you will obtain common results like stress and displacement. For simple models, the stress results can also reflect the plasticity.

WELSIM uses FrontISTR as the default solver for static structural analysis. Supported default plastic models include:

  • Bilinear
  • Multilinear
  • Swift
  • Ramberg-Osgood
  • Kinematic Hardening

Transient elastoplastic analysis

For WELSIM’s transient structural analysis, it is recommended to use explicit method with OpenRadioss as the solver. OpenRadioss is an excellent open source solver for structural dynamics, known for reliable results, and it supports a wide variety of plastic models.

In the project settings, set the analysis type to “Transient” and enable “Explicit” analysis.

In transient analysis, it’s often necessary to set the physical time for each load step and time step. As shown in the figure:

  • Total time: 0.07s
  • Time step: 0.0001s

After defining boundary conditions and running the computation, results can be obtained.

Supported plastic models for explicit transient analysis are given below:

  1. LAW2 (PLAS_JOHNS) — Density + Isotropic Elasticity + Johnson-Cook
  2. PLAS_ZERIL — Density + Isotropic Elasticity + Zerilli-Armstrong
  3. LAW22 (DAMA) — Density + Isotropic Elasticity + Johnson-Cook + General Damage
  4. LAW27 (PLAS_BRIT) — Density + Isotropic Elasticity + Johnson-Cook + Orthotropic Brittle Failure
  5. LAW28 (HONEYCOMB) — Density + Honeycomb
  6. LAW32 (HILL) — Hill
  7. LAW36 (PLAS_TAB) — Density + Isotropic Elasticity + Rate-Dependent Multilinear Hardening
  8. LAW44 (COWPER) — Cowper-Symonds
  9. LAW93 (ORTH_HILL) — Orthotropic Hill
  10. LAW48 (ZHAO) — Zhao
  11. LAW49 (STEINB) — Steinberg-Guinan
  12. LAW52 (GURSON) — Gurson
  13. LAW57 (BARLET3) — Barlet3
  14. LAW78 — Yoshida-Uemori
  15. LAW79 (JOHN_HOLM) — Johnson-Holmquist
  16. LAW84 — Swift-Voce
  17. LAW103 (HENSEL-SPITTEL) — Hensel-Spittel
  18. LAW110 (VEGTER) — Vegter

Note: WELSIM does not include OpenRadioss in its installation package. Users need to download OpenRadioss separately and configure its directory in WELSIM’s preferences before using it for the first time.

Conclusion

This article introduces how to use WELSIM to perform finite element analysis (FEA) on structures with plastic materials. With its excellent material editing module and powerful solvers like OpenRadioss and FrontISTR, users can carry out plastic structural analysis and obtain results quickly.

WelSim and author are not directly related to the OpenRadioss, FrontISTR, Elmer, or CalculiX development team. The reference to OpenRadioss FrontISTR, Elmer, or CalculiX is only used here for technical blog and software usage references.

Friday, April 11, 2025

使用WELSIM进行有限元塑性变形分析

塑性变形是指结构在一定外力作用下,材料受力超过屈服极限,由纯弹性应变转变为塑性应变的过程,整个过程也称之为弹塑性变形。工业中塑性变型随处可见,如各种钣金件的冷加工,汽车车身的压铸成型。同时在很多工况下,工程师们要求结构避免发生塑性变形,以避免材料失效。因此塑性分析是结构有限元分析中经常遇到的分析类型。

通用工程仿真软件WELSIM已经提供了对塑性分析的支持。本文从实际软件操作角度,对当前版本的塑性分析功能做一个简要描述。

塑性变形从数学角度描述,是一种材料本构关系的非线性过程,因此需要软件需要有较强的求解非线性问题的能力。WELSIM的隐式求解器采用FrontISTR,显式求解器采用OpenRadioss。用户也可以使用其他求解器如CalculiX, Elmer等,这会在以后的文章中介绍。本文就以调用FrontISTR和OpenRadioss的求解功能为主。

由于塑性变形的主要复杂度集中在材料部分,因此对于材料的输入和编辑有较多的工作。同时塑性模型种类多,对前端界面提出了较高的要求。WELSIM提供了友好的材料编辑方式,同时也提供了完全一致的且免费的独立材料软件MatEditor。目前,已经支持了25个塑性相关的材料属性,12个蠕变相关的材料属性。每一个属性都有独立的参数和编辑方式。

以多线性硬化为例,下图演示了如何定义一个塑性应变材料。输入最基本的结构分析材料参数,密度7.8e-7 kg/mm3,杨氏模量206.9 Gpa,泊松比0.29。塑性应力应变关系数据分别为应变{0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5},应力{450, 608, 679, 732, 752, 766, 780} MPa。

静态塑性变形分析

对于静态的非线性有限元分析,本质上是一种隐式计算方式。材料的非线性变形通过牛顿迭代法求解得到。在项目的属性中,可以保持默认的静态结构分析类型。

由于塑性变形是一个非线性过程,在分析中可以设置多个子步数。本例设置25个子步。

其他的分析设置和弹性分析几乎一致。

经过设置边界条件,并计算后,可以得到结构分析中的常见结果,如应力,位移等。对于简单模型,应力结果也可以体现出塑性变形曲线。

WelSim的静态结构计算使用FrontISTR作为默认的求解器。因此支持的默认塑性分析有:Bilinear, Multilinear, Swift, Ramberg-Osgood, 和Kinematic塑性硬化。

瞬态塑性变形计算

对于WELSIM的瞬态结构分析,推荐使用显式计算方式,可以直接调用OpenRadioss进行计算,OpenRadioss是一款优秀的瞬态动力学有限元软件,计算结果稳定可靠,支持类型众多的塑性模型。

在项目的属性中,设置分析类型为瞬态,同时打开显式属性。

在瞬态分析中,往往需要设置每个载荷步的时间,以及计算的时间步长。如下图所示,定义物理时间为0.07s,计算步长为0.0001s。

定义好边界条件,执行计算后,即可得到计算结果。

显示动力学的计算使用OpenRadioss作为求解器,能够支持更多的塑性模型。包括:

1. LAW2 (PLAS_JOHNS) – Density + Isotropic Elasticity + Johnson-Cook

2. PLAS_ZERIL -- Density + Isotropic Elasticity + Zerilli-Armstrong

3. LAW22(DAMA) — Density + Isotropic Elasticity + Johnson-Cook + General Damage

4. LAW27(PLAS_BRIT) — Density + Isotropic Elasticity + Johnson-Cook + Orthotropic Brittle Failure

5. LAW28(HONEYCOMB) — Density + HoneyComb

6. LAW32(HILL) — Hill

7. LAW36(PLAS_TAB) — Density + Isotropic Elasticity + Rate-Dependent Multilinear Hardening

8. LAW44(COWPER) — Cowper-Symonds

9. LAW93(ORTH_HILL) — Orthotropic Hill

10. LAW48(ZHAO) — Zhao

11. LAW49(STEINB) — Steinberg-Guinan

12. LAW52(GURSON) — Gurson

13. LAW57(BARLET3) — Barlet3

14. LAW78 — Yoshida-Uemori

15. LAW79(JOHN_HOLM) — Johnson-Holmquist

16. LAW84 — Swift-Voce

17. LAW103 (HENSEL-SPITTEL) — Hensel-Spittel

18. LAW110 (VEGTER) — Vegter

WELSIM安装包不含有OpenRadioss,因此用户在第一次显式动力学计算时,需要自行下载OpenRadioss,并在WelSim的首选项中配置好OpenRadioss的目录。

总结

本文介绍了如何使用WELSIM进行塑性结构有限元分析。由于优异的材料编辑模块,和OpenRadioss、FrontISTR等求解器强大的求解功能。用户可以对含有塑性材料的结构进行有限元分析,并快速得到结果。

WelSim与作者和OpenRadioss,FrontISTR,Elmer, CalculiX开发机构没有直接关系。这里引用OpenRadioss,FrontISTR,Elmer, CalculiX仅用作技术博客文章与软件使用的参考。