reactive plasticity¶

Module: solid

Category: material

Type string: "reactive plasticity"

Parameters¶

Name	Description	Default	Units
`density`	density	1	[M/L^3]
`isochoric`	isochoric	true	[]
`rtol`	rtol	0.0001	[]
`secant_tangent`	secant_tangent	true	[]
`elastic`			[]
`yield_criterion`			[]
`flow_curve`			[]

Description¶

The material type of a reactive elasto-plastic solid with kinematic hardening is reactive plasticity.

The elastic property defines the constitutive relation of the intact (unconstrained) elastic material and associated material properties for unconstrained materials.

The yield_criterion property defines the yield criterion \(\Phi\). The flow_curve property defines the relation between bond mass fractions \(w_{\beta}\) and apparent yield stresses \(\Upsilon_{\beta}\) for the bond family \(\beta\).The default value in FEBio is isochoric=1.

Example 1: Idealized elastic-perfectly plastic response of steel (mm-N-s units)

<material id="1" type="reactive plasticity">
  <elastic type="neo-Hookean">
    <density>8.05e-9</density>
    <E>200e3</E>
    <v>0.30</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC paper">
    <Y0>450</Y0>
  </flow_curve>
</material>

Example 2: Annealed mild steel (mm-N-s units)

<material id="1" type="reactive plasticity">
  <isochoric>1</isochoric>
  <elastic type="neo-Hookean">
    <density>7.85e-9</density>
    <E>205e3</E>
    <v>0.29</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC paper">
    <nf>15</nf>
    <Y0>220</Y0>
    <Ymax>490</Ymax>
    <w0>0.973</w0>
    <we>0</we>
    <r>1</r>
  </flow_curve>
</material>

Example 3: Annealed copper (mm-N-s units)

<material id="1" type="reactive plasticity">
  <isochoric>1</isochoric>
  <elastic type="neo-Hookean">
    <density>7.764e-9</density>
    <E>120e3</E>
    <v>0.34</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC paper">
    <nf>15</nf>
    <Y0>60</Y0>
    <Ymax>288</Ymax>
    <w0>0.988</w0>
    <we>0</we>
    <r>1</r>
  </flow_curve>
</material>

Example 4: Unaged maraging steel (mm-N-s units)

<material id="1" type="reactive plasticity">
  <isochoric>1</isochoric>
  <elastic type="neo-Hookean">
    <density>8.00e-9</density>
    <E>165e3</E>
    <v>0.33</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC paper">
    <nf>22</nf>
    <Y0>398</Y0>
    <Ymax>1010</Ymax>
    <w0>0</w0>
    <we>0</we>
    <r>0.9</r>
  </flow_curve>
</material>

Example 5: Annealed aluminum 1100 (mm-N-s units)

<material id="1" type="reactive plasticity">
  <isochoric>1</isochoric>
  <elastic type="neo-Hookean">
    <density>2.71e-9</density>
    <E>68e3</E>
    <v>0.33</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC paper">
    <nf>18</nf>
    <Y0>63</Y0>
    <Ymax>112</Ymax>
    <w0>0.994</w0>
    <we>0</we>
    <r>0.6</r>
  </flow_curve>
</material>

Example 6: Mild steel (mm-N-s units)

<material id="1" type="reactive plasticity">
  <isochoric>1</isochoric>
  <elastic type="natural neo-Hookean">
    <density>2.71e-9</density>
    <E>206e3</E>
    <v>0.30</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC math">
    <nf>15</nf>
    <emin>0.0008403</emin>
    <emax>1.3</emax>
    <plastic_response>545.46*(0.011024+eps)^0.2589</plastic_response>
  </flow_curve>
</material>

Example 7: Steel (in-lbf-s units)

<material id="1" name="Steel" type="reactive plasticity">
  <density>1</density>
  <isochoric>1</isochoric>
  <elastic type="natural neo-Hookean">
    <E>29911000</E>
    <v>0.3</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC user">
  <plastic_response type="point">
    <interpolate>SMOOTH</interpolate>
    <points>
      <point> 0.002, 59822 </point>
      <point> 0.002841, 64450 </point>
      <point> 0.00469, 68500 </point>
      <point> 0.00953, 72000 </point>
      <point> 0.0193, 75000 </point>
    </points>
    </plastic_response>
  </flow_curve>
</material>

Example 8: elastic-perfectly plastic response, using PFC math flow curve

<material id="1" name="Elastoplastic Math" type="reactive plasticity">
  <density>1</density>
  <isochoric>1</isochoric>
  <elastic type="neo-Hookean">
    <E>200000</E>
    <v>0.3</v>
  </elastic>
  <yield_criterion type="DC von Mises stress"/>
  <flow_curve type="PFC math">
    <nf>1</nf>
    <e0>0.001</e0>
    <emax>1</emax>
    <plastic_response type="math">200</plastic_response>
  </flow_curve>
</material>