By removing the surface forces, we
return to the original problem ofD. Remove the applied surface forces:a body with an inclusion, as shown
in Figure 11.3: Matrix with Inclu-
sion (p. 344).The change from step C to step D is that a body force (or surface force on the hole in the matrix where
the inclusion is inserted), equal and opposite to the surface forces in step B, is applied.
The body (or surface) force is the material force. Essentially, the presence of an inclusion creates a
variation in the strain energy density in the matrix material, leading to the material force acting on the
inclusion and being allowed to move through the material.
The material force method essentially determines a vectorial force-like quantity conjugate to the eigen-
strain. As a general description, the material force approach is defined for elasticity as described in
Understanding the Material Force Approach (p. 371). [ 18 ]
For a crack in a linear or nonlinear elastic material, the tangential component of the material force
vector to the crack surface represents the energy-release rate. Also, the crack propagation direction and
inhomogeneity, flaws, and mismatched mesh can be characterized by the material force vectors. In
plasticity, the tangential component of the material force vector to the crack surface represents the
crack-driving force. [ 19 ]
Material force calculations do not account for surface loads on crack faces.
For more information, see Material Force Calculation (p. 371).
11.1.3. Crack Growth Simulation
Fracture/crack growth is a phenomenon in which two surfaces are separat ed from each other, or mater-
ial is progressively damaged under external loading. The following methods are available for simulating
such failure:
11.1.3.1. VCCT-Based Interface Element Method
11.1.3.2. Cohesive Zone Method
11.1.3.3. Gurson’s Model Method11.1.3.1. VCCT-Based Interface Element Method
This method uses interface elements (INTERnnn) with VCCT to simulate the fracture by separating the
interface elements between two materials with one or more user-specified fracture criteria. This approach
applies to homogeneous material fracture as well as interfacial fracture in biomaterial systems. It is most
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