Although the phase field method has been widely used in the field of fracture, various
models exist, such as the second-order and fourth-order phase field model in the field of …

This paper presents a general thermodynamically consistent non-isothermal phase field
framework to model effects of damage, fracture and fatigue evolutions in elasto-plastic …

Earthquake fault zones are more complex, both geometrically and rheologically, than an
idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear …

This work applies concepts of artificial neural networks to identify the parameters of a
mathematical model based on phase fields for damage and fracture. Damage mechanics is …

In this work, we present a nonlocal phase field model for damage in brittle materials. We
define a non-conservative order parameter for representing the damage. The Helmholtz free …

Materials accumulate energy around voids and defects under external loading, causing the
formation of microcracks. With increasing or repeated loads, those microcracks eventually …

Failure in brittle materials led by the evolution of micro-to macro-cracks under repetitive or
increasing loads is often catastrophic with no significant plasticity to advert the onset of …

This work applies concepts of artificial neural networks to identify the parameters of a
mathematical model based on phase fields for damage and fracture. Damage mechanics is …

An adaptive fourth-order phase-field model is proposed using consistent element-free
Galerkin method (EFG). Convenient construction of high-order interpolation functions in EFG …

We present the application of simultaneous diagonalization and minimum energy (SDME)
high-order finite element modal bases for simulation of transient non-linear elastodynamic …