Continuous-discontinuous numerical method for solid fracturing simulation
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Solution Overview
Problem
Current numerical approaches for solid fracturing simulation, such as the combined finite-discrete element method (FDEM), face challenges like artificial compliance problems, mutual overlap of finite elements, and computational inefficiencies due to the need for frequent updating of element topology.
Innovation Solution
A two-dimensional continuous-discontinuous combined numerical method is introduced, which discretizes a solid into finite elements and establishes a mapping linked list relationship between master-slave nodes. This method avoids premature activation of cohesive elements, ensuring continuous deformation until crack initiation, and updates the node relationships dynamically to manage crack propagation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If cohesive elements are activated from the beginning of the simulation, then crack initiation and propagation can be simulated, but artificial compliance problem occurs and neighboring finite elements overlap
Solution Approach 1:
The patent pre-embeds cohesive elements between adjacent finite elements before the simulation starts, but does not activate them immediately. Instead, it establishes a mapping linked list relationship between master-slave nodes that enables delayed activation only when crack initiation criteria are met, thus avoiding artificial compliance while preparing the crack simulation capability in advance
Solution Approach 2:
The patent dynamically activates cohesive elements only when the local stress of finite elements satisfies the strength criterion for crack initiation. The mapping linked list relationship between master-slave nodes is updated dynamically to reflect the crack propagation state, allowing the model to transition from a fully continuous state to a discontinuous state with activated cohesive elements at the appropriate moment
2Measurement precision
If adaptive insertion of cohesive elements is performed during simulation, then crack initiation can be captured accurately, but computation overhead increases and code parallelization becomes difficult
Solution Approach 1:
The patent pre-establishes the mapping linked list relationship between master-slave nodes and pre-embeds cohesive elements before the simulation runs. This preliminary setup eliminates the need for dynamic node splitting and topology updating during the simulation, significantly reducing computation overhead and simplifying code parallelization while maintaining accurate crack initiation detection
Solution Approach 2:
The patent extracts the topology updating operation from the simulation process by using a pre-established mapping linked list relationship. Instead of dynamically adjusting connections during simulation, the method uses the pre-defined mapping to activate cohesive elements and update node relationships only when crack initiation occurs, separating the topology management from the mechanical simulation
Data Source
AI summary
A two-dimensional continuous-discontinuous combined numerical approach for solid fracturing simulation, which includes: discretizing two-dimensional solid into finite elements to obtain a mapping linked list relationship between master-slave nodes; determining whether a crack is initiated according to whether the local stress of the finite element satisfies a strength criterion; if a crack initiates, activating a corresponding pre-embedded cohesive element, updating the mapping linked list relationship between the master-slave nodes at the same time, the cohesive element at the crack enters a yield state, and the mechanical behavior thereof is controlled by a strain softening constitutive curve; and, according to the mapping linked list relationship between the master-slave nodes, accumulating node forces and masses of the slave nodes onto the master node, and updating the velocity and the displacement of the master-slave nodes by adopting a governing equation.