Numerical Modelling and Mechanical Characterisation

Numerical modelling and mechanical characterisation together form a multidisciplinary toolkit for predicting and measuring how materials and structures respond to load, deformation and environmental effects. At one end of the spectrum, atomistic simulations and molecular‐dynamics models capture deformation mechanisms and phase transformations at the nanoscale, informing continuum constitutive laws. At larger scales, finite‐element analysis implements these laws to resolve stress, strain and stability in complex geometries—from micro-scratch of silicon to buckling of box girders. Probabilistic homogenisation and multi-scale frameworks link local heterogeneity to macroscopic elasticity and failure, while advanced experimental methods such as nanoindentation, micro-scratch testing and in situ imaging provide direct benchmarks for model validation. Together these approaches underpin innovation in coatings, composites, microelectromechanical systems and civil infrastructures.

Research from Nature Portfolio

Recent work has derived an exact axisymmetric elastic solution for a thin layer bonded to a rigid substrate, incorporating both bulk couple‐stress effects and surface elasticity. The Hankel‐transform solution yields fundamental kernels that reveal how surface and couple stresses jointly govern load transfer and size dependence in micro-scale contact problems, and it has been validated against benchmark cases. An alternative deformation‐coordination method for vertical-web box girders establishes a fourth-order differential equation for distortional warping under combined forces, showing agreement with plate-element and energy‐variation methods to within 5 per cent and offering a simple route to predict warping stresses. A third study optimises three energy-based analytic techniques to produce a unified distortion control equation, demonstrating peak warping normal stresses within 5.4 per cent of numerical values and highlighting the role of cross-section shape and loading configuration in distortion patterns.

Research from all publishers

A continuum-particle formulation has been introduced to simulate subsurface deformations during crystalline silicon micro-scratching. By combining a continuum–discrete transition scheme with an inelastic constitutive model for phase transformations (Si-I to Si-II to amorphous), this method reproduces experimental scratch-induced phase patterns and quantifies the relationship between process parameters and subsurface damage. In computational materials science, an open-source crystal-plasticity framework enables large-scale fatigue simulations across realistic polycrystalline ensembles. Its multilevel parallelism outperforms commercial codes for evaluating fatigue indicator parameters, linking texture, grain morphology and boundary conditions to driving forces for crack initiation. In high‐rate testing, a combined experimental–numerical approach refines Johnson–Cook constitutive parameters by accounting for initial gaps from surface roughness in Split Hopkinson pressure bar tests, yielding more accurate stress–strain curves across strain-rate regimes and improving predictive capability for dynamic metal deformation.

Numerical Modelling and Mechanical Characterisation publication trend

The graph below shows the total number of articles in numerical modelling and mechanical characterisation across all publications each year (not limited to Nature Index journals).

Technical terms

Finite element analysis: A numerical method that discretises a continuum into small elements to approximate stress and strain fields under prescribed loads and boundary conditions.

Constitutive model: A mathematical relationship defining stress as a function of strain, strain rate and temperature, e.g., the Johnson–Cook law for high-rate metal deformation.

Couple stress elasticity: A generalized continuum theory that augments classical elasticity with higher-order moments and material rotations to capture size-dependent effects in microstructured materials.

Representative volume element (RVE): The smallest material volume over which microstructural heterogeneity can be statistically averaged to yield effective macroscopic properties.

Nanoindentation: A technique that applies a controlled load via a sharp indenter to measure local hardness and elastic–plastic behaviour at nanometre scales.

Homogenisation: A theoretical framework for deriving effective continuum properties of heterogeneous materials by averaging local constitutive responses and microstructural geometry.

References

1. Elastic solution of surface loaded layer with couple and surface stress effects. Scientific Reports (2023).
2. An innovative deformation coordination method for analyzing distortion effects on box girders. Scientific Reports (2024).
3. Optimization methods for the distortion of thin-walled box girders and investigation of distortion effects. Scientific Reports (2023).
4. A continuum particle model for micro-scratch simulations of crystalline silicon. Journal of the Mechanics and Physics of Solids (2024).
5. PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys. npj Computational Materials (2021).
6. Determination of Johnson-Cook constitutive model coefficients considering initial gap between contact faces in SHPB test. Journal of Materials Research and Technology (2023).