Mathematical Modeling

Modeling and Simulation of Vascular Tumors Embedded in Evolving Capillary Networks
In this work, we present a coupled 3D–1D model of solid tumor growth within a dynamically changing vascular network to facilitate …
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Complex Fracture Nucleation and Evolution With Nonlocal Elastodynamics
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage …
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Dynamic Brittle Fracture from Nonlocal Double-Well Potentials: A State-Based Model
We introduce a regularized model for free fracture propagation based on nonlocal potentials. We work within the small deformation …
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Dynamic Damage Propagation with Memory: A State-Based Model
A model for dynamic damage propagation is developed using nonlocal potentials. The model is posed using a state-based peridynamic …
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Free Damage Propagation With Memory
We introduce a simple model for free damage propagation based on non-local potentials. The model is developed using a state based …
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