Multicomplex and multidual numbers are two generalizations of complex numbers with
multiple imaginary axes, useful for numerical computation of derivatives with machine …

Generalized continuum models for representing nonlinear material behavior including
material failure in the finite strain regime are commonly formulated based on scalar elastic …

Continuum-kinematics-inspired peridynamics (CPD) has been recently proposed as a novel
reformulation of peridynamics that is characterized by one-, two-and three-neighbor …

This paper deals with the implementation of thermomechanically coupled gradient-
enhanced elastoplasticity at finite strains. The presented algorithmic formulation heavily …

In this contribution, a small strain single crystal plasticity framework in the context of an
infeasible primal–dual interior point method (IPDIPM) is discussed with a focus on the …

For error-free computation of higher-order derivatives of a complex mathematical expression
composed of elementary functions, hyper-dual numbers (HDNs) are receiving close …

Considering application to nonlinear material models, this study proposes a novel numerical
method for computing arbitrary-order derivatives of eigenvalues and eigenvectors …

This paper presents an efficient algorithm for the approximation of the rank-one convex hull
in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences …

Multiple bifurcation (MB) is a compound stability problem of nonlinear structures, in which
the singular system stiffness matrix at the stability point coincidentally undergoes two or …

This study presents a variationally consistent formulation of the thermo-mechanically
coupled problem with non-associative viscoplasticity for glassy amorphous polymers. First …