arXiv subjects

Michael Zaiser

Publications and source records attributed to Michael Zaiser.

At least 19 recordsLinked to original sources

arXiv2026

Multiscale Modelling of Ferroelectrics using a Physics-Informed Neural Network Driven by Molecular Dynamics Data: Parameter Identification and Field Reconstruction

In multiscale modeling of ferroelectrics, combining atomistic simulation with continuum-scale phase-field models (PFM) remains a fundamental challenge. A key difficulty lies in faithfully capturing discrete atomic-level information within a continuum modeling framework, while accurately representing material behavior at the mesoscale. In this paper, a Physics-Informed Neural Network (PINN) driven by molecular dynamics (MD) data is used. The loss function of the network consists of a supervised term that fits the discrete spatial polarization distributions obtained from MD simulations of systems containing domain walls, and a physics-based term that incorporates the residuals of partial differential equations (PDEs) of steady-state PFM. To ensure stable and balanced training among the different loss components, adaptive gradient normalization (GradNorm) is used to dynamically adjust the task weights. By minimizing the total loss, the model not only reconstructs the polarization field along with the associated strain, stress, and energy landscape at the continuum scale, but also identifies critical physical parameters of the phase-field model, including the characteristic energy density, characteristic length factor, gradient energy anisotropy factor, and Landau polynomial coefficients. By using the PINN-predicted physical parameters in COMSOL Multiphysics to solve the corresponding PDEs within a finite element framework, we demonstrate that these parameters enable accurate reproduction of the ferroelectric domain structure and the associated material response, including stress/strain distributions and energy landscape. This framework provides an effective methodology for establishing multiscale connections between atomistic and continuum descriptions, and holds the potential to infer underlying physical properties directly from polarization distributions for a wide range of materials.

cond-mat.mtrl-sci↗

arXiv2026

Patterns of load, elastic energy and damage in network models of architected composite materials

We investigate the role of architected thin films in the interfacial failure properties of bi-layer composites. Our results show that, while graded structures can be used to prescribe failure at the interface, they do not offer significant advantages in terms of fracture toughness. Hierarchically patterned layers can localize failure at the interface and simultaneously enhance interface toughness, by enforcing a buffer region where elastic energy is dissipated in the form of diffuse damage, so that no stress concentration can drive crack growth. To analyze these mechanisms, the associated patterns of local load redistribution and the soft deformation modes, we develop a network formalism that brings together concepts of discrete differential geometry and spectral graph theory.

cond-mat.mtrl-sci↗

arXiv2026

Discrete Dislocation Dynamics Modeling of Nanotwinned Materials: Orientation Effects in a Multilayer Twinned Structure of Copper

The impact of twin boundaries (TBs) on the microstructure evolution and plastic deformation mechanisms of face-centered cubic (FCC) metals has been extensively studied since the discovery that nanotwinned materials exhibit a favorable combination of high strength and ductility. In this work, a dislocation-twin boundary interaction model for copper is incorporated into a three-dimensional discrete dislocation dynamics (DDD) framework. This approach is applied to systematically investigate the orientation effects on the deformation of nanotwinned copper, utilizing a multilayer twinned structure (MTS) with a twin thickness of 160 nm. The simulation results show that the stress-strain response of MTSs under uniaxial loading depends significant on the orientation of the loading axis. Dislocations inclined to TBs are confined to slip in single- or multi-layer twin lamellae; when the loading axis is oriented perpendicular or parallel to TBs, such whereas when loading axis inclined to TBs, the dislocations with glide plane parallel to TBs are easily activated (mainly twinning dislocations) and the TBs do not hinder the dislocations and behave in soft modes. If the hard mode dominates the deformation mechanism, microstructures with single-layer confined slip lead to significant hardening behavior, while microstructures with multilayer confined slip maintain stable plastic flow and do not lead to hardening. Finally, through the introduction of critical resolved shear stresses (CRSSs) specific to various deformation modes and the adaptation of Schmid's law, we have effectively projected the additional anisotropic characteristics induced by TBs in MTSs.

cond-mat.mtrl-sci↗

arXiv2026

A phase field model of the effects of dislocation microstructure on grain boundary motion during recrystallization

The internal energy associated with the defect microstructure of strongly deformed crystals provides an important driving force for grain boundary motion during recrystallization. Typical dislocation microstructures are strongly heterogeneous and this heterogeneity affects the motion of recrystallization boundaries. In this study, a phase field model for microstructure evolution encompassing the evolution of both dislocation densities and grain order parameters is formulated. The model is employed to generate typical dislocation microstructures exhibiting multiscale features such as incidental and geometrically necessary dislocation walls. It is then used to study the motion of recrystallization boundaries in the associated complex defect energy 'landscape'. Results are compared to experimental observations.

cond-mat.mtrl-sci↗

arXiv2025

An intermediately-homogenized peridynamics approach to failure of microstructually disordered materials

Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this is surely the case are materials with strong microstructural disorder such as random composites, random porous materials or disordered metamaterials. For this class of materials we propose an intermediately-homogenized peridynamic modelling approach where the disordered microstructure is not resolved in full spatial detail but described in terms of random order parameter fields which retain essential information about the local heterogeneity and spatial correlations of material properties.

cond-mat.mtrl-sci↗

arXiv2025

Strengthening and toughening mechanisms in heterostructured laminates revealed by a phase field-enhanced crystal plasticity simulation

Heterostructured (HS) materials exhibit excellent mechanical properties, combining high strength and significant ductility. Hetero-deformation-induced (HDI) hardening and strain de-localization are key to their strength-ductility synergy. However, existing models often fall short in addressing these aspects. In this work, a coupled framework integrating strain gradient crystal plasticity and phase field damage models is developed. The interface dominated HDI hardening in HS laminates is handled by introducing a heterogeneity coefficient into the back stress. The phase field model accounts for defect energy-driven damage and accurately represents the materials ductile damage behavior by accounting for effects of microstructure on crack initiation and propagation. Simulation results on HS laminates align well with experimental results and reflect the distribution of geometrically necessary dislocations and back stresses at interfaces between regions with dissimilar microstructure. Crack initiation and propagation are accurately described, providing valuable insights into fracture behavior. The model can predict how strength and ductility change upon variations of the HS laminate microstructure, thus providing an essential tool for microstructure optimization. This work enhances the understanding of deformation mechanisms in HS laminates and provides valuable insights for design and optimization of this class of materials.

cond-mat.mtrl-sci↗

arXiv2025

Fiber bundle model of thermally activated creep failure

An equal load sharing fiber bundle model for thermally activated breakdown is developed using transition state theory to describe the rate of elementary failures. The lifetime distribution, average, variance and their asymptotic limits for uniform fiber failure thresholds are derived and found to be in excellent agreement with simulations. The asymptotic scaling with regards to the number of fibers matches analytical approximations in the low temperature limit derived by Roux and co-workers for a model of thermal breakdown by stationary Gaussian noise. For the case of randomly distributed fiber failure strengths, the lifetime distribution is derived as a multidimensional integral with no closed form solution. Simulations with different fiber strength distributions indicate that, in the limit of large fiber numbers, the statistics of bundle lifetimes shows a similar asymptotic scaling for distributed and for uniform thresholds. Fiber breakage by thermal activation occurs in avalanches triggered by individual thermally activated failure events, and the asymptotic avalanche size distribution obtained from the simulations matches earlier theoretical results derived for quasistatic loading.

cond-mat.stat-mech↗

arXiv2025

Fracture toughness and auxeticity in disordered metamaterials

Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity and the energy absorbed before fracture. By giving different weights to these optimization targets, we demonstrate that the optimal configurations are connected along a Pareto front where high auxeticity implies comparatively low energy absorption and vice versa. We study the mechanical properties of the resulting metamaterials and characterize the different deformation modes obtained for distinct optimization targets. The simulation and optimization results are validated by comparison with the deformation behavior of additively manufactured samples. Our work provides an illustration of the potentials and limitations of multi-objective optimization in the design of disordered mechanical metamaterials

cond-mat.dis-nn↗

arXiv2025

Dislocations in the elastic fields of randomly distributed defects

In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation and compression centers. More generally speaking, the arrangement of defects in metals and alloys is always characterized by statistical disorder, and the same is true for the fluctuating fields that arise from the superposition of the stress and strain fields of many defects. In order to develop models for the dynamics of dislocations interacting with such fields, a statistical description of the dislocation energy landscape and the associated configurational forces is needed, as well as methods for coarse graining these forces over dislocation segments of varying length and shape. In this context the problem arises how to regularize the highly singular stress fields associated with dislocations and other defects. Here we formulate an approach which is based upon evaluating the interaction energies and interaction forces between singular dislocations and other defects including solutes, modelled as point-like dilatation centers, and other dislocations. We characterize the interactions in terms of the probability densities of interaction energies and interaction forces, and the corresponding spatial correlation functions. We also consider the effects of dislocation core regularization, either in terms of continuously distributed Burgers vectors or by using the formalism of gradient elasticity of Helmholtz type to formulate a regularized energy functional.

cond-mat.mtrl-sci↗

arXiv2025

Peridynamics based model of anticrack-type fracture in brittle foams

A particular failure mode of highly porous brittle materials consists in the propagation of cracks under uniaxial compressive loads. Such 'anticracks' have been observed in a range of materials, from snow and porous sandstone to brittle foams. Here we present a computational model for the formation and propagation of anticrack-type failure in porous materials within the general computational framework of bond-based peridynamics. Random porosity is represented, on a scale well above the characteristic pore size, by random bond deletion (dilution disorder). We apply our framework to experimental data on anticrack propagation in silicate foams.

cond-mat.soft↗

arXiv2024

Continuum Dislocation Dynamics as a Phase Field Theory with Conserved Order Parameters

The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models can be envisaged in terms of the evolution of order-parameter like variables that strives to minimize a free energy functional which incorporates interface energy-like terms, i.e., as a phase field theory. We show that dislocation density variables obey non-standard conservation laws. These lead, in conjunction with the externally supplied work, to evolution equations that go beyond the classical framework of Ginzburg-Landau vs Cahn-Hilliard equations. The approach is applied to the evolution of dislocation patterns in materials with B1(NaCl) lattice structure.

cond-mat.mtrl-sci↗

arXiv2024

Tuning load redistribution and damage near heterogeneous interfaces

We investigate interface failure of model materials representing architected thin films in contact with heterogeneous substrates. We find that, while systems with statistically isotropic distributions of impurities derive their fracture strength from the ability to develop rough detachment fronts, materials with hierarchical microstructures confine failure near a prescribed surface, where crack growth is arrested and crack surface correlations are suppressed. We develop a theory of network Green's functions for the systems at hand, and we find that the ability of hierarchical microstructures to control failure mode and locations comes at no performance cost in terms of peak stress and specific work of failure and derives from the quenched local anistotropy of the elastic interaction kernel.

cond-mat.mtrl-sci↗

arXiv2023

Creep failure of hierarchical materials

Creep failure of hierarchical materials is investigated by simulation of beam network models. Such models are idealizations of hierarchical fibrous materials where bundles of load-carrying fibers are held together by multi-level (hierarchical) cross-links. Failure of individual beams is assumed to be governed by stress-assisted thermal activation over local barriers, and beam stresses are computed by solving the global balance equations of linear and angular momentum across the network. Disorder is mimicked by a statistical distribution of barrier heights. Both initially intact samples and samples containing side notches of various length are considered. Samples with hierarchical cross-link patterns are simulated alongside reference samples where cross-links are placed randomly without hierarchical organization. The results demonstrate that hierarchical patterning may strongly increase creep strain and creep lifetime while reducing the lifetime variation. This is due to the fact that hierarchical patterning induces a failure mode that differs significantly from the standard scenario of failure by nucleation and growth of a critical crack. Characterization of this failure mode demonstrates good agreement between the present simulations and experimental findings on hierarchically patterned paper sheets.

cond-mat.mtrl-sci↗

arXiv2023

Multiscale modeling of dislocations: Combining peridynamics with gradient elasticity

Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends on boundary conditions on the sample scale. We present a novel approach which is based on a peridynamic dislocation model to deal with the surface boundary value problem. In this model, the singularity of the stress field at the dislocation core is regularized owing to the non-local nature of peridynamics. The effective core radius is defined by the peridynamic horizon which, for reasons of computational cost, must be chosen much larger than the lattice constant. This implies that dislocation stresses in the near-core region are seriously underestimated. By exploiting relationships between peridynamics and Mindlin-type gradient elasticity, we then show that gradient elasticity can be used to construct short-range corrections to the peridynamic stress field that yield a correct description of dislocation stresses from the atomic to the sample scale.

cond-mat.soft↗

arXiv2023

Effects of disorder on deformation and failure of brittle porous materials

The mechanical behavior of porous materials depends strongly on porosity and pore geometry, but also on morphological parameters characterizing the spatial arrangement of pores. Here we use bond-based peridynamics to study effects of disorder on the deformation and failure behavior of brittle porous solids both in the quasi-static limit and in case of dynamic loading scenarios. We show that structural disorder, which has a strong influence on stiffness, strength and toughness in the quasi-static limit, becomes less relevant under dynamic loading conditions.

cond-mat.mtrl-sci↗

arXiv2023

Failure precursors and failure mechanisms in hierarchically patterned paper sheets in tensile and creep loading

Quasi-brittle materials endowed with (statistically) self-similar hierarcical microstructures show distinct failure patterns that deviate from the standard scenario of damage accumulation followed by crack nucleation-and-growth. Here we study the failure of paper sheets with hierarchical slice patterns as well as non-hierarchical and unpatterned reference samples, considering both uncracked samples and samples containing a macroscopic crack. Failure is studied under displacement-controlled tensile loading as well as under creep conditions. Acoustic emission records and surface strain patterns are recorded alongside stress-strain and creep curves. The measurements demonstrate that hierarchical patterning efficiently mitigates against strain localization and crack propagation. In tensile loading, this results in a significantly increased residual strength of cracked samples. Under creep conditions, for a given range of lifetimes hierarchically patterned samples are found to sustain larger creep strains at higher stress levels; their creep curves show unusual behavior characterized by multiple creep rate minima due to the repeated arrest of emergent localization bands.

cond-mat.mtrl-sci↗

arXiv2022

An energetically consistent surface correction method for bond-based peridynamics

A novel surface correction method is proposed for bond based peridynamics which ensures energy consistency with a classical reference body for general affine deformations. This method is validated for simple geometries and then applied to a typical surface-dominated problem, namely the indentation of a surface in the shallow to moderate-depth regime.

cs.CE↗

arXiv2022

Predicting Creep Failure by Machine Learning -- Which Features Matter?

Spatial and temporal features are studied with respect to their predictive value for failure time prediction in subcritical failure with machine learning (ML). Data are generated from simulations of a novel, brittle random fuse model (RFM), as well as elasto-plastic finite element simulations (FEM) of a stochastic plasticity model with damage, both models considering stochastic thermally activated damage/failure processes in disordered materials. Fuse networks are generated with hierarchical and nonhierarchical architectures. Random forests - a specific ML algorithm - allow us to measure the feature importance through a feature's average error reduction. RFM simulation data are found to become more predictable with increasing system size and temperature. Increasing the load or the scatter in local materials properties has the opposite effect. Damage accumulation in these models proceeds in stochastic avalanches, and statistical signatures such as avalanche rate or magnitude have been discussed in the literature as predictors of incipient failure. However, in the present study such features proved of no measurable use to the ML models, which mostly rely on global or local strain for prediction. This suggests the strain as viable quantity to monitor in future experimental studies as it is accessible via digital image correlation.

cond-mat.mtrl-sci↗