How would one virtually simulate this by turning these functions into programming code? How does the math get translated into computer code into a simulation of the ideas discussed here to produce realistic breaks in virtual materials to simulate realistic depiction of these phenomena? If someone knowledgeable in both the math and ideas discussed here as well as programming languages, could you please inform me. REALLY curious!
Generally you model the problem with something like the Finite Element Method (FEM) and then use a solver for the resulting system (with something like PCG). For the coding part, you'll see implementations in Matlab, Octave, Julia or C/C++ (for GPUs, CUDA is frequently used).
To realize relationships of damage mechanics, you should study constitutive behavior of materials and then implementation of these behavior in codes. For example this book is good to understand constitutive behavior including damage: Engineering Damage Mechanics Authors: Jean Lemaitre , Rodrigue Desmorat And you can find some books about computational plasticity for implementation of these relationships. Before these two topics you should know FEM. Studying all these matters maybe take a semester of a graduate student.
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How would one virtually simulate this by turning these functions into programming code? How does the math get translated into computer code into a simulation of the ideas discussed here to produce realistic breaks in virtual materials to simulate realistic depiction of these phenomena? If someone knowledgeable in both the math and ideas discussed here as well as programming languages, could you please inform me. REALLY curious!
Generally you model the problem with something like the Finite Element Method (FEM) and then use a solver for the resulting system (with something like PCG). For the coding part, you'll see implementations in Matlab, Octave, Julia or C/C++ (for GPUs, CUDA is frequently used).
To realize relationships of damage mechanics, you should study constitutive behavior of materials and then implementation of these behavior in codes. For example this book is good to understand constitutive behavior including damage:
Engineering Damage Mechanics
Authors: Jean Lemaitre , Rodrigue Desmorat
And you can find some books about computational plasticity for implementation of these relationships. Before these two topics you should know FEM.
Studying all these matters maybe take a semester of a graduate student.