Building a Digital Twin for Material Testing: Model Reduction and Data Assimilation
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT The rapid advancement of industrial technologies, data collection, and handling methods has paved the way for the widespread adoption of digital twins (DTs) in engineering, enabling seamless integration between physical systems and their virtual counterparts.
Rubén Aylwin +5 more
wiley +1 more source
A Novel Mixed‐Hybrid, Higher‐Order Accurate Formulation for Kirchhoff–Love Shells
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT This paper presents a novel mixed‐hybrid finite element formulation for Kirchhoff–Love shells, designed to enable the use of standard C0$C^0$‐continuous higher‐order Lagrange elements. This is possible by introducing the components of the moment tensor as a primary unknown alongside the displacement vector, circumventing the need for C1$C^1 ...
Jonas Neumeyer, Thomas‐Peter Fries
wiley +1 more source
Scientific Machine Learning for Elastic and Acoustic Wave Propagation: Neural Operator and Physics-Guided Neural Network. [PDF]
Sensors (Basel)Mehtaj N, Banerjee S.
europepmc +1 more source
A Compact Algorithm for Applying Periodic Boundary Conditions in 3D RVE Modeling with Abaqus
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT Periodic boundary conditions (PBCs) are essential in multiscale modeling for computing the effective properties of heterogeneous materials via representative volume elements (RVEs). While several automated solutions have been developed for implementing PBCs in finite element software, many rely on structured node classification and predefined ...
Reza Sadeghpour, Martin Kraska
wiley +1 more source
Gradient-Driven Physics Informed Neural Networks for Conduction Heat Transfer and Incompressible Laminar Flow. [PDF]
J Comput Nonlinear DynLu T +5 more
europepmc +1 more source
On the Performance and Convergence of PINNs for Problems in Linear Elasticity
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT Physics‐informed neural networks (PINNs) have emerged as a promising approach for solving partial differential equations by embedding physical laws directly into the loss function. However, their performance characteristics for problems in computational mechanics remain insufficiently understood.
Dipraj Kadlag +3 more
wiley +1 more source
Computational analysis of a spatiotemporal model of cancer-immune-chemotherapy dynamics with nonlinear diffusive interactions using spectral technique. [PDF]
Sci RepShi H +5 more
europepmc +1 more source
Two Scale FE‐FFT‐Based Modeling of Cancellous Bone
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT Osteoporosis is characterized by a loss of volume percentage of cortical bone, which reduces the loading capacity of this organ and increases its likelihood for fractures. The disease has the highest prevalence of any bone disease worldwide, with a particularly high incidence among the elderly.
Mischa Blaszczyk +3 more
wiley +1 more source
Time fractional modeling of MHD natural convection flow between parallel plates via caputo-fabrizio integral. [PDF]
Sci RepMasood K.
europepmc +1 more source
On MAP Estimates and Source Conditions for Drift Identification in SDEs
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT We consider the inverse problem of identifying the drift in an stochastic differential equation (SDE) from n$n$ observations of its solution at M+1$M+1$ distinct time points. We derive a corresponding maximum a posteriori (MAP) estimate, we prove differentiability properties as well as a so‐called tangential cone condition for the forward ...
Daniel Tenbrinck +3 more
wiley +1 more source