Deformation Analysis Device Rigidity Reduction Fracture Simulation
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Solution Overview
Problem
Conventional deformation analysis methods struggle to accurately predict the behavior after a fracture occurs, especially when dealing with complex deformations, as they often rely on eliminating elements which can lead to inaccurate stress distribution and crack progression.
Innovation Solution
A deformation analysis device and method that calculates state variables for materials, determines fractures using a fracture limit stress curve, and reduces the rigidity of fractured elements without elimination, using the expression σ = (1-D)σ′, where σ is the stress with rigidity decrease, D is the damage variable, and σ′ is the stress without rigidity decrease, and eliminates elements when D exceeds a threshold.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If elements are eliminated after fracture occurs, then the simulation can proceed without fractured elements, but the stress distribution becomes inaccurate and crack progression is overestimated
Solution Approach 1:
The patent changes the parameter representation of fractured elements from binary (present/absent) to continuous (rigidity reduction factor). Instead of eliminating elements, the rigidity parameter is reduced by a factor α (0 < α < 1), allowing the element to remain in the model with diminished mechanical properties. This accurately represents the progressive nature of crack propagation while maintaining stress distribution continuity.
Solution Approach 2:
The patent inverts the conventional approach by not removing fractured elements but rather keeping them with reduced rigidity. This inversion allows the model to maintain element continuity and stress paths while still representing the degraded mechanical state of fractured regions, thereby improving both fracture behavior prediction and stress distribution accuracy.
2Measurement precision
If the size of eliminated element is small, then stress applied to surroundings is small and crack progresses gradually, but when the size is large, stress applied to elements therearound is large and crack progression is overestimated
Solution Approach 1:
The patent introduces a rigidity reduction factor α as a continuous parameter that can be adjusted based on element size and fracture severity. This parameter allows small elements to have gradual rigidity reduction (small α) and large elements to have more significant reduction (larger α), accurately representing different crack progression scenarios without requiring complex element management or removal logic.
3Ease of manufacture
If conventional method is used for complex deformation, then the method is easy to implement, but it is not able to find appropriate forming condition for collisions causing complicated deformation
Solution Approach 1:
The patent extends the applicability to complex deformations by using stress parameters (σ1, σ2, σ3) instead of strain parameters and applying the rigidity reduction concept in the stress space. This allows the method to handle complex deformation paths and collision scenarios while maintaining the simplicity of the implementation through the same fundamental rigidity reduction mechanism.
Data Source
AI summary
The deformation analysis device includes: a storage unit (12) which stores analysis data of a material; a state variable calculating unit (152) which calculates stresses and other state variables of respective elements of the material at each point in time of deformation of the material, based on the analysis data; a fracture determining unit (153) which, based on the calculated state variables, determines whether or not a fracture has occurred in each of the elements of the material, based on a fracture limit stress curve which is found in advance for the material; and a stress correcting unit (154) which, regarding an element in which it is determined that the fracture has occurred, out of the elements of the material, reduces σ by the following expression σ=(1−D)σ′ where σ is a stress with a rigidity decrease taken into consideration, D is a damage variable (note that 0≤D≤1) in continuum damage mechanics, and σ′ is a stress with the rigidity decrease not taken into consideration, to thereby decrease rigidity of the relevant element, without eliminating the element, and updates the analysis data.