Meshfree Simulation of Brittle Material Cracks Using Strain Regularization
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Solution Overview
Problem
Current meshfree methods face challenges in accurately simulating structural behaviors of brittle materials due to issues like spurious modes and rank instability, particularly when modeling cracks and damage mechanics, which affect the accuracy of numerical simulations.
Innovation Solution
A meshfree model is developed that uses a time-marching simulation based on damage mechanics, where particles are divided into damage zones and undamaged zones, with a morphing function applied to ensure homogeneous strain conditions across damage zones, and a stabilization scheme is used to regularize the strain fields, allowing for the simulation of crack growth over time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Galerkin-based meshfree methods are used to simulate brittle material with cracks, then the ability to handle large deformation and moving discontinuity is improved, but spurious modes and rank instability occur due to under-integration of weak forms
Solution Approach 1:
The domain is segmented into damaged and undamaged zones using a level set function, allowing separate treatment of different material states. This segmentation enables accurate tracking of crack propagation while maintaining numerical stability by applying appropriate regularization to the damaged zone particles.
Solution Approach 2:
The method changes the integration scheme parameter from standard under-integration to a stabilized nodal integration approach. By modifying the integration parameters and applying strain smoothing techniques, the method eliminates spurious modes while preserving the ability to handle large deformations and crack propagation.
2Productivity
If under-integration of weak forms is used in central difference formula, then computational efficiency is improved, but rank instability is caused due to rank deficiency
Solution Approach 1:
An intermediate strain smoothing operation is introduced between the discrete particle positions and the stress calculation. This intermediary smoothing step regularizes the strain field without requiring additional integration points, thus maintaining computational efficiency while eliminating rank instability.
Solution Approach 2:
The integration scheme parameters are changed from standard under-integration to a stabilized formulation that uses a modified weight function and strain smoothing length. This parameter change maintains computational efficiency by avoiding mesh generation while eliminating the rank deficiency problem through appropriate regularization.
3Measurement precision
If local and non-local strain fields are simultaneously presented in meshfree model, then accuracy in capturing crack behavior is improved, but complexity of the model increases
Solution Approach 1:
The model segments the domain into damaged and undamaged zones, applying local strain measures in the damaged zone and non-local strain measures in the undamaged zone. This segmented approach captures crack behavior accurately while reducing overall model complexity by using the simplest appropriate measure in each region.
Solution Approach 2:
Different strain field measures are applied to different regions: local strain is used where cracks are present (damaged zone) and non-local strain is used in the surrounding material (undamaged zone). This local quality approach optimizes accuracy in each region while minimizing the overall computational complexity of the model.
Data Source
AI summary
Meshfree model containing a number of particles to represent a structure made of brittle material is defined. At each non-initial solution cycle of a numerical simulation using the meshfree model based on damage mechanics, the following operations are performed: (a) determining one or more damage zones in the structure from simulated structural responses obtained in immediate prior solution cycle; (b) dividing the particles into a first group representing the damage zones and a second group representing the remaining of the meshfree model; (c) applying a meshfree regularization scheme by modifying each particle's strain field of the first group with a morphing function that ensures a homogeneous jump condition along respective borders of the damage zones; and (e) obtaining simulated structural behaviors of the structure using a meshfree stabilization scheme that applies to all of the particle's strain field. Each damage zone represents a crack that can grow over time.