Difference between revisions of "Softening Laws"
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<math>A(\delta,s) = \int_0^{\delta}f(\delta,s)d\delta</math> | <math>A(\delta,s) = \int_0^{\delta}f(\delta,s)d\delta</math> | ||
Each softening law requires G<sub>c</sub> and possibly other parameters to define the law's functional form. The laws do not need to be provided δ<sub>max</sub> because it can be calculated from the law shape, s, and G<sub>c</sub> from total area under the law. | Each softening law requires G<sub>c</sub> and possibly other parameters to define the law's functional form. The laws do not need to be provided δ<sub>max</sub> because it can be calculated from the law shape, s, and G<sub>c</sub> from total area under the law. Furthermore, δ<sub>max</sub> depends on mesh size while G<sub>c</sub> is a material property for damage. | ||
== Define a Damage Initiation Laws == | == Define a Damage Initiation Laws == | ||
Revision as of 17:40, 13 January 2016
Introduction
Softening laws are used in softening materials to determine crack tractions as a function of effective crack opening displacements. Each law defines a normalized function that decays from 1 to 0 as damage develops up to the point of failure. The area under the law (times an associated stress) gives the fracture toughness associated with that law. These laws also control the evolution of one damage parameter. Various softening materials will need two or more softening laws to model all possible types of damage.
Softening laws are currently only available in OSParticulas.
Normalized Softening Law
The traction during softening is given by σf(δ) where f(δ) is the normalized softening law and σ is some scaling stress provided by the softening material. The toughness associated with the law, Gc, is determined by the area under the law times a scaling factor to account for mesh size and the scaling stress σ:
[math]\displaystyle{ {G}_c = {V_p \sigma\over A_c} \int_0^{\delta_{max}}f(\delta)d\delta }[/math]
where Vp is particle volume, Ac is area of the initiated crack within the particle domain, and δmax is the critical crack opening displacement for failure (of for when the traction drops to zero). To define a scaling law, we define a scaling factor
[math]\displaystyle{ s = {A_c \over V_p \sigma} }[/math]
The softening material calculates s whenever softening law response is needed. All the softening law needs to evaulate is the normalized function value, f(δ,s), and the area under that law up to δ:
[math]\displaystyle{ A(\delta,s) = \int_0^{\delta}f(\delta,s)d\delta }[/math]
Each softening law requires Gc and possibly other parameters to define the law's functional form. The laws do not need to be provided δmax because it can be calculated from the law shape, s, and Gc from total area under the law. Furthermore, δmax depends on mesh size while Gc is a material property for damage.
Define a Damage Initiation Laws
You create a softening law using an "Softening" material property within a Material command block. You pick the law by name or ID. After picking the law, all its properties are set using property commands with the same material definition. Refer to each softening law type to learn about its softening function and about its reqjuired properties.
Softening Laws
This table lists the available softening laws. Click each one for more details and information on their properties. Note that when setting softening law properties, the softening material will preface each parameter with a code to determine which law properties are being set. For example to set mode I and mode II softening law properties in an isotropic softening material, the properties are entered as I-Gc and II-Gc where I- or II- preface the Gc softening law property.
| Name | ID | Description |
|---|---|---|
| Linear | 1 | Linear softening law. |
It is relatively easy to write code for new damage initiation laws, if needed.