Non Local Strain Gradient Cohesive Zone Formulation for Microvia Corner Step Debonding
Non-local strain gradient cohesive zone modeling eliminates mesh-dependent stress singularities at microvia corner steps to accurately predict reflow debonding.
Non Local Parameter
Meaning
Mathematical coefficient in non-local damage models defines the spatial radius over which microstructural interactions are averaged. The non local parameter acts as a weight that determines the influence of neighboring points on the localized damage evolution at a specific coordinate. This parameter introduces a physical length into the constitutive equations to prevent mesh sensitivity in numerical simulations of material failure.
Researchers apply this formulation to model the progressive fracturing of composite materials and metal alloys.
Spatial Integration
Integral formulations calculate an averaged strain value by applying a bell-shaped weight function over a local volume. The non local parameter determines the spatial extent of this weight function to control how far the averaging region extends from the point. Strain values outside this defined radius do not contribute to the localized damage calculations.
Regularization Effect
Numerical simulations run into severe grid dependence when material softening causes deformation to localize in a single row of elements. Integrating the non local parameter into the stress calculations distributes the damage across a wider zone to restore numerical convergence. This ensures that the energy dissipated during crack growth remains finite and independent of the element size.
The resulting force-displacement curves do not show the artificial snap-back behavior that occurs in unregularized localized damage models.
Experimental Calibration
Determining the size of this averaging zone requires comparing numerical results with measured strain fields from optical measurements. The non local parameter corresponds to the width of the fracture process zone observed in structural tests. This calibration step ensures that the model reflects the actual physical behavior of the material.