This paper reviews the development of the space–time conservation element and solution
element (CESE) method and summarizes its applications in various research areas. The …

This open access book introduces the fundamentals of the space–time conservation
element and solution element (CESE) method, which is a novel numerical approach for …

Compressional waves in saturated porous media are relevant to many fields from oil
exploration to diagnostic of human cancellous bone and can be used to interpret physical …

This article reports an improved Taylor approximation of the Arruda-Boyce model. Aided by
recurrence relationships for the inverse Langevin function, this new expansion can be used …

Macroscopic mechanical properties of polymers are determined by their microscopic
molecular chain distribution. Due to randomness of these molecular chains, probability …

This paper reports the construction of viscoelasticity models for simulation of wave
propagation in soft tissues. Aided by the Carson transform, Fung's model and Iatridis's model …

Hyperelastic models have been widely used to model polymers and soft tissues. However,
most hyperelastic models are phenomenological material models. Based on statistical …

This paper reports a theoretical and numerical framework to model nonlinear waves in
elastic-plastic solids. Formulated in the Eulerian frame, the governing equations employed …

In this dissertation, a new theoretical and numerical approach to model linear and nonlinear
stress waves in complex solids has been developed. The model equations are derived …

This dissertation reports a novel approach to achieve high-fidelity solutions of conservation
laws by designing a software framework that focuses on hybrid parallel computing. The …