Softening Laws

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 when the crack opening displacement increases from 0 to δ_max. 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.

These laws are currently only available in OSParticulas.

Normalized Softening Law

The traction during softening is give 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, G_c, 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 V_p is particle volume, A_c is area of the initiated crack within the particle domain, and δ_max 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 G_c and possibly other parameters to define the law's functional form. The laws do not need to be provided δ_max because it can be calculated from the law shape, s, and G_c from total area under the law.

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.

Name	ID	Description
Linear	1	Linear softening law.

It is relatively easy to write code for new damage initiation laws, if needed.