Solid Mechanics

Solid mechanics is the study of how continuous bodies—ranging from crystals and alloys to composites and biological tissues—respond to applied forces, temperature changes and evolving internal structure. At the macroscopic scale it encompasses elasticity, plasticity, fracture and vibration; at the microscopic it addresses dislocations, phase transformations and size-dependent phenomena. Central to the field is the continuum approximation, in which materials are treated as continuous media endowed with stress and strain fields that satisfy balance laws and constitutive relations. These laws link tensorial measures of deformation to internal forces, from linear elasticity through large-deformation and viscoelastic models. Advances in multi-scale simulation and experimentation have forged connections between atomistic processes and continuum behaviour, informing the design of materials with tailored strength, ductility or functional properties. Applications span aerospace structures, electronic devices, civil infrastructure and biomedicine, reflecting the global importance of predicting reliability, optimising performance and mitigating failure.

Research from Nature Portfolio

Recent work has shown that misfit dislocation networks at crystalline interfaces can be programmed via reduced-order anisotropic elasticity models. By combining interface-synthesis constraints with optimisation algorithms, one can prescribe dislocation patterns that enhance interfacial cohesion, control defect diffusion and improve composite performance—all without full atomistic simulation. Another study has derived an exact solution for an axisymmetric, surface-loaded thin layer bonded to a rigid substrate, incorporating both couple stresses in the bulk and surface elasticity at the interface. Using Hankel transforms, the general elastic field is obtained and fundamental kernels are established for micro- and nano-scale contact problems. More recently, constitutive advance has been achieved by modifying classical flow-stress models—Fields-Backofen and Zerilli-Armstrong—for hot deformation of titanium-based superalloys. These improved expressions capture temperature- and strain-rate dependencies with high fidelity, enabling predictive processing maps for alloy design.

Research from all publishers

Analytical developments have produced closed-form stress fields for an edge dislocation near a slanted traction-free surface, revealing how the Burgers vector orientation influences image forces and guides dislocation–surface interaction. In parallel, two-dimensional discrete dislocation plasticity simulations have illuminated the strain-rate dependence of the Bauschinger effect in industrial alloys, showing that dislocation nucleation and thermally activated escape dominate forward and reverse loading responses. Finally, a concurrent coupling methodology embeds planar discrete dislocation domains within crystal-plasticity finite-element models. This hybrid scheme retains local size effects and multiplicative hardening while efficiently simulating large polycrystalline regions, bridging microstructural fidelity and macroscopic realism.

Solid Mechanics publication trend

The graph below shows the total number of articles in solid mechanics across all publications each year (not limited to Nature Index journals).

Technical terms

Continuum approximation: Treating a material as a continuous medium, described by smooth stress and strain fields, despite its discrete atomic structure.

Dislocation: A line defect in a crystal lattice whose motion under stress mediates plastic deformation.

Misfit dislocation network: Array of dislocations at an interface accommodating lattice mismatch and governing interfacial mechanics.

Cauchy stress tensor: Second-order tensor that relates internal forces to oriented areas in a deformed body under equilibrium.

Couple stress: Higher-order stress measure accounting for size effects and material rotations in microstructured solids.

Discrete dislocation plasticity (DDP): Computational method that explicitly tracks individual dislocations to model mesoscale plastic flow.

Crystal-plasticity finite-element method (CPFE): Continuum framework incorporating slip laws on crystallographic systems into finite-element simulations of polycrystalline deformation.

References

1. Computational design of patterned interfaces using reduced order models. Scientific Reports (2014).
2. Elastic solution of surface loaded layer with couple and surface stress effects. Scientific Reports (2023).
3. Modified Fields-Backofen and Zerilli-Armstrong constitutive models to predict the hot deformation behavior in titanium-based alloys. Scientific Reports (2024).
4. Analytic formulation of elastic field around edge dislocation adjacent to slanted free surface. Royal Society Open Science (2022).
5. The effect of strain rate asymmetry on the Bauschinger effect: A discrete dislocation plasticity analysis. Journal of Materials Research and Technology (2022).
6. A method of coupling discrete dislocation plasticity to the crystal plasticity finite element method. Modelling and Simulation in Materials Science and Engineering (2016).