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 realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix, …

Nonlocal Elastodynamics and Fracture

A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane …

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 variable or law. The model, a continuum variant of Newton’s second law, uses integral rather than partial …

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 setting, and the model is developed within a state-based peridynamic formulation. At each instant of the evolution, we …

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 formulation. The resulting evolution is seen to be well posed. At each instant of the evolution, we identify a damage …

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 peridynamic formulation. The resulting evolution is shown to be well posed. At each instant of the evolution we identify …