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Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
Large Displacement Finite Element Analysis Theory Manual
Material Laws
A large variety of materials is used in the structural components and must be modeled in stress analysis problems. For any kind of these materials a range of constitutive laws is available to describe by a mathematical approach the behavior of the material.
Viscous Materials
General case of viscous materials represents a time-dependent inelastic behavior.
Generalized Maxwell-Kelvin Model for Viscoelastic Materials (LAW40)
This law may only be applied to solid elements.

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新機能
Radioss 2025の新機能を確認できます。
概要
Radioss^®は、衝突と衝撃ソリューションのための優れた陽解法有限要素ソルバーです。
Tutorials
Discover Radioss functionality with interactive tutorials.
ユーザーガイド
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
リファレンスガイド
本マニュアルは、Radiossで使用することのできるすべての入力キーワードとオプションを詳細なリストで提供しています。
例題集
このマニュアルは一般的な問題のタイプに関して、Radiossを用いて解かれた例題を示します。
検証問題
このマニュアルでは、解析済みの検証モデルを紹介します。
よくある質問
このセクションでは、Radiossに関するよくある質問へのクィックレスポンスを提供しています。
Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
- Large Displacement Finite Element Analysis Theory Manual
  - Introduction
    Nonlinear finite element analyses confront users with many choices. An understanding of the fundamental concepts of nonlinear finite element analysis is necessary if you do not want to use the finite element program as a black box. The purpose of this manual is to describe the numerical methods included in Radioss.
  - Basic Equations
  - Finite Element Formulation
  - Dynamic Analysis
  - Element Library
    Radioss element library contains elements for one, two or three dimensional problems.
  - Kinematic Constraints
    Kinematic constraints are boundary conditions that are placed on nodal velocities. They are mutually exclusive for each degree of freedom (DOF), and there can only be one constraint per DOF.
  - Linear Stability
    The stability of solution concerns the evolution of a process subjected to small perturbations. A process is considered to be stable if small perturbations of initial data result in small changes in the solution. The theory of stability can be applied to a variety of computational problems.
  - Interfaces
    Interfaces solve the contact and impact conditions between two parts of a model.
  - Material Laws
    A large variety of materials is used in the structural components and must be modeled in stress analysis problems. For any kind of these materials a range of constitutive laws is available to describe by a mathematical approach the behavior of the material.
    - Isotropic Elastic Material
    - Composite and Anisotropic Materials
    - Elastic-plasticity of Isotropic Materials
    - Viscous Materials
      General case of viscous materials represents a time-dependent inelastic behavior.
      - Boltzmann Viscoelastic Model (LAW34)
        This law valid for solid elements can be used for viscoelastic materials like polymers, elastomers, glass and fluids.
      - Generalized Kelvin-Voigt Model (LAW35)
        This law uses a generalized viscoelastic Kelvin-Voigt model whereas the viscosity is based on the Navier equations.
      - Tabulated Strain Rate Dependent Law for Viscoelastic Materials (LAW38)
        The law incorporated in Radioss can only be used with solid elements.
      - Generalized Maxwell-Kelvin Model for Viscoelastic Materials (LAW40)
        This law may only be applied to solid elements.
      - Visco-elasto Materials for Foams (LAW33)
        This material law can be used to model low density closed cell polyurethane foams, impactors, impact limiters. It can only be used with solid elements.
      - Hyper Visco-elastic Law for Foams (LAW62)
    - Hydrodynamic Analysis Materials
    - Void Materials (LAW0)
      This material can be used to define elements to act as a void, or empty space.
    - Shape Memory Superelastic Material (LAW71)
      This material can be used to define elements to act as a void, or empty space.
    - Failure Models
  - Monitored Volume
    An airbag is defined as a monitored volume. A monitored volume is defined as having one or more 3 or 4 node shell property sets.
  - Static
    Explicit scheme is generally used for time integration in Radioss, in which velocities and displacements are obtained by direct integration of nodal accelerations.
  - Radioss Parallelization
    The performance criterion in the computation was always an essential point in the architectural conception of Radioss. At first, the program has been largely optimized for the vectored super-calculators like CRAY. Then, a first parallel version SMP made possible the exploration of shared memory on processors.
- ALE, CFD and SPH Theory Manual
- Appendix A: Basic Relations of Elasticity
User Subroutines
This manual describes the interface between Altair Radioss and user subroutines.

Generalized Maxwell-Kelvin Model for Viscoelastic Materials (LAW40)

This law may only be applied to solid elements.

Bulk behavior is assumed to be linear:

図 1.

\frac{d p}{d t} = K {\dot{ε}}_{k k}

Shear behavior is computed using a shear factor as:

図 2.

G (t) = G_{\infty} + \sum_{1}^{5} G_{i} e^{- β_{i} t}

$β_{i}$ are time decays, $β_{i} = \frac{G_{i}}{η_{i}} = \frac{1}{τ_{i}}$ with $τ_{i}$ being relaxation time.