Link Search Menu Expand Document
Theory Manual Version 3.6
 Section 5.8: Reactive Elastoplastic Damage Mechanics Up Section 5.8: Reactive Elastoplastic Damage Mechanics Subsubsection 5.8.1.1: Damage to Intact Bonds 

5.8.1 Theoretical Formulation

We first briefly sketch the structure of the elastoplastic damage theory in FEBio for a single bond family . Since each bond family in reactive plasticity yields all at once, we can easily split an elastoplastic damage theory into two parts to represent elastic and plastic damage regimes. Assume that the first yielding reaction for bond family occurs at time . Prior to this initial yielding, the damage behavior described in Section 5.6↑ applies, and the material composition is generally a mixture of intact ( ) and broken ( ) bonds satisfying the reaction . The corresponding bond mass fractions satisfy and , where is the elastic damage in bond family . At , the remaining intact bonds all yield, following the reaction in eq.(5.7.2-6). The family mass balance is then given as , since after yielding. The mass fraction of broken bonds is equal to the elastic damage variable as defined in classical damage mechanics.
For time , yielded bonds may continue to yield, but they may also sustain damage according to the reaction , which reduces their mass fraction . Damage to yielded bonds may occur based on a function of state (often described as a plastic strain, though it is not an observable kinematic variable), which is distinct from the measure of elastic damage. Therefore, we denote the plastic damage measure as and its cumulative distribution function by , under the assumption that all bond families share the same functional forms for and . For each bond family , only the remaining undamaged fraction of yielded bonds may break and reform as the next yielded generation.
The modern understanding is that plastic strain is ill-defined and not a suitable state variable. It must be recognized that, just as is a constitutively-prescribed function of state and does not carry the meaning of a plastic deformation gradient, the plastic damage measure is also a function of state. This quantity is called a plastic strain for convenience only.
When plastic deformation occurs simultaneously with damage, the mass fraction of each successive yielded generation will have decreased. The following treatment now considers the superposition of multiple plastic bond families, as described in Section 5.7.2↑.
 Section 5.8: Reactive Elastoplastic Damage Mechanics Up Section 5.8: Reactive Elastoplastic Damage Mechanics Subsubsection 5.8.1.1: Damage to Intact Bonds 

Table of contents