Онлайн-руководства Проверка программного обеспечения

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2023-09-28

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Нелинейность материала

Если аддон Нелинейная работа материала активирован (требуется дополнительная лицензия) в разделе Модель - основные данные, в списке моделей материала будут доступны и другие опции для выбора, кроме 'Изотропной | Linear Elastic' and 'Orthotropic | Linear Elastic' material models.

Модели материалов для надстройки ' нелинейного анализа поведения материалов '

If you use nonlinear material models in RFEM, an iterative calculation is always performed. В зависимости от модели материала определяется различное соотношение между напряжениями и деформациями.

Жёсткость конечных элементов многократно корректируется до тех пор, пока не будет соблюдено требуемое соотношение напряжения и деформации. The adjustment is always carried out for an entire surface or solid element. Therefore, we recommend always using the Constant on mesh elements smoothing type when evaluating stresses.

Сглаживание результатов

Some material models in RFEM are indicated by 'Plastic', others by 'Nonlinear Elastic'.

If a structural component with a nonlinear elastic material is released again, the strain goes back on the same path. When completely unloaded, there is no strain left.

Диаграмма напряжение-деформация, нелинейно-упругая

When unloading a structural component with a Plastic material model, the strain remains after it has been completely unloaded.

Диаграмма напряжение-деформация, пластическая

Background information about nonlinear material models can be found in the technical article describing the Yield laws in isotropic nonlinear elastic material model.

The internal forces and moments in plates with nonlinear material result from the numerical integration of the stresses over the thickness d of the plate. To define the integration method for the thickness, select the Specify integration method option in the 'Edit Thickness' dialog box. The following integration methods are available:

Квадратура Гаусса-Лобатто
Правило Симпсона
Трапециевидное правило

Определить метод интегрирования для толщины поверхности

Furthermore, you can specify the 'Number of integration points' from 3 to 99 by the plate thickness.

Инфо

A theoretical explanation of the individual integration methods can be found in the Multilayer Surfaces online manual.

Isotropic Plastic (Members)

When selecting the Isotropic | Plastic (Members) entry in the 'Material model' drop-down list, the tab for entering nonlinear material parameters is enabled.

Активация нелинейной модели материала

Определение нелинейных параметров материала

In this tab, you define the stress-strain diagram. Для лицензирования программы затем доступны следующие возможности:

Basic
Билинейный
Рабочая диаграмма

If Basic is selected, RFEM uses a bilinear material model. Values from the material database are used for the modulus of elasticity E and the yield strength f_y For numerical reasons, the branch of the graph is not exactly horizontal, but has a small E_p slope.

If you want to change the values for yield strength and modulus of elasticity, activate the "User-defined material" check box in the 'Main' tab.

Активировать пользовательский материал

For a bilinear definition, you can also enter a value for E_p.

More complex relations between stress and strain can be defined by means of the "Stress-strain diagram". When selecting this option, the 'Stress-Strain Diagram' tab is displayed.

Ввод пользовательской диаграммы напряжение-деформация

Define a point for the stress-strain relation in each table row. You can select how the diagram continues after the last definition point in the 'Diagram end' list below the diagram:

Распределение после последней точки определения

In the case of 'Tearing', stress after the last definition point jumps back to zero. 'Yielding' means that stress remains constant when strain increases. 'Continuous' means that the graph continues with the slope of the last section.

Инфо

In this material model, the stress-strain diagram refers to the longitudinal stress σ_x. Different yield strengths for tension and compression cannot be considered by this material model.

Isotropic Plastic (Surfaces/Solids)

When selecting the "Isotropic | Plastic (Surfaces/Solids)" entry in the 'Material model' drop-down list, the tab for entering nonlinear material parameters is enabled.

Выберите модель пластического материала

Wählen Sie zunächst die 'Spannungsversagenshypothese' aus. Zur Auswahl stehen diese Hypothesen:

First, select the 'Stress failure hypothesis'. The following hypotheses are available for selection:

von Mises (von Mises yield criterion)

Tresca (Tresca yield criterion)

Друкер-Прагер

Моор-Кулон

Определение гипотезы разрушения при напряжении

When selecting "von Mises", the following stress is used in the stress-strain diagram:

Поверхности:

$σ_{v} = \sqrt{σ_{x}^{2} + σ_{y}^{2} - σ_{x} σ_{y} + 3 (τ_{x y}^{2})}$

Эквивалентное напряжение из основных напряжений по фон Мизесу

Объемы:

$σ_{v, Mises} = \sqrt{σ_{x}^{2} + σ_{y}^{2} + σ_{z}^{2} - σ_{x} σ_{y} - σ_{x} σ_{z} - σ_{y} σ_{z} + 3 (τ_{x y}^{2} + τ_{x z}^{2} + τ_{y z}^{2})}$

Эквивалентное напряжение σ_{v, Мизес} от основных напряжений

$σ_{v, Mises} = \sqrt{\frac{1}{2} [(σ_{1} - σ_{2})^{2} + (σ_{1} - σ_{3})^{2} + (σ_{2} - σ_{3})^{2}]}$

Эквивалентное напряжение σ_{v, Мизес} от главных напряжений

According to the "Tresca" hypothesis, the following stress is used:

Поверхности:

$σ_{v} = \sqrt{(^{σ_{x} - σ_{y}) 2} + 4 {τ_{x y}}^{2}}$

Эквивалентное напряжение по Треске

Объемы:

$σ_{v, Tresca} = max (|σ_{1} - σ_{2}); |σ_{2} - σ_{3}); |σ_{3} - σ_{1}))|||$

Эквивалентное напряжение σ_{v, Tresca}

According to the "Drucker-Prager" hypothesis, the following stress is used for surfaces and solids:

$σ_{v} = \frac{m - 1}{2} (σ_{1} + σ_{2} + σ_{3}) + \frac{m + 1}{2} \sqrt{\frac{1}{2} [(^{σ_{1} - σ_{2}) 2} + (^{σ_{2} - σ_{3}) 2} + (^{σ_{3} - σ_{1}) 2})]}$

$m = \frac{σ_{c}}{σ_{t}}$

σ_c Предельное напряжение при сжатии

σ_t Предельное напряжение при растяжении

Критерий текучести по Друкеру-Прагеру

According to the "Mohr-Coulomb" hypothesis, the following stress is used for surfaces and solids:

$σ_{v} = \frac{m + 1}{2} m a x \{|σ_{1} - σ_{2}) + K (σ_{1} + σ_{2}), |σ_{2} - σ_{3}) + K (σ_{2} + σ_{3}), |σ_{3} - σ_{1}) + K (σ_{3} + σ_{1})|||)\}$

$K = \frac{m - 1}{m + 1}$

$m = \frac{σ_{c}}{σ_{t}}$

Мор - Кулон

Isotropic Nonlinear Elastic (Members)

The functionality largely corresponds to that of the isotropic plastic (members) material model. The difference is that no plastic strain remains after the unloading.

Isotropic Nonlinear Elastic (Surfaces/Solids)

The functionality largely corresponds to that of the isotropic plastic (surfaces/solids) material model. The difference is that no plastic strain remains after the unloading.

Isotropic Damage (Surfaces/Solids)

In contrast to other material models, the stress-strain diagram for this material model is not antimetric to the origin. Thus, the behavior of steel fiber-reinforced concrete can be displayed with this material model, for example. Find detailed information about modeling steel fiber-reinforced concrete in the technical article about Determining the material properties of steel-fiber-reinforced concrete.

Модель материала «Изотропная | Ущерб »

In this material model, the isotropic stiffness is reduced with a scalar damage parameter. This damage parameter is determined from the stress curve defined in the Diagram. This does not take the direction of the principal stresses into account; rather, the damage occurs in the direction of the equivalent strain, which also covers the third direction perpendicular to the plane. The tension and compression area of the stress tensor is treated separately. Different damage parameters apply in each case.

The "Reference element size" controls how the strain in the crack area is scaled to the length of the element. With the default value zero, no scaling is performed. Thus, the material behavior of the steel fiber concrete is modeled realistically.

Find more information about the theoretical background of the 'Isotropic Damage' material model in the technical article describing the [https://www.dlubal.com/en/support-and-learning/support/knowledge-base/001461 Nonlinear Material Model Damage.

Orthotropic Plastic (Surfaces) / Orthotropic Plastic (Solids)

The material model according to "Tsai-Wu" unifies plastic with orthotropic properties. This allows for special modeling of materials with anisotropic characteristics, such as fiber-reinforced plastics or timber.

Когда материал достигает пластификации, считается, что напряжения остаются неизменными. Перераспределение затем осуществляется в соответствии с жесткостями, доступными в отдельных направлениях.

BILD

BILD

The elastic area corresponds to the Orthotropic material model. The following yielding condition according to Tsai-Wu applies to the plastic zone:

Surfaces (2D):

FORMEL

Solids (3D):

FORMEL

Все прочности требуется задать в качестве положительных значений.

You can think of the stress criterion as an elliptical surface in a six-dimensional stress space. Если один из трех компонентов напряжения применяется в качестве постоянного значения, то поверхность можно спроецировать в трехмерное пространство напряжений.

If the value for f_y(σ) according to the Tsai-Wu equation, plane stress condition, is smaller than 1, the stresses are in the elastic zone. The plastic zone is reached as soon as f_y(σ) = 1. Values higher than 1 are not allowed. The model behavior is ideal-plastic, which means there is no stiffening.

Родительское сечение

Нелинейность

σ_c	Предельное напряжение при сжатии
σ_t	Предельное напряжение при растяжении