Materialgesetze

Materialgesetze is a term used in materials science and engineering to denote the constitutive relations and empirical rules that describe how materials respond to external stimuli. These laws codify observed behavior and form the basis for predictive modeling in engineering, design, and research.

In mechanics, common material laws describe how materials react to loads. Linear elasticity relates stress and strain for small deformations; plasticity criteria, such as von Mises or Tresca, define when irreversible deformation begins. Viscoelastic and viscoplastic models capture time-dependent behavior found in polymers and metals.

For transport phenomena, laws such as Fick’s laws of diffusion and Fourier’s law of heat conduction describe how mass and heat move through materials. The flow of fluids and the response of materials to stresses can be described by Newtonian viscosity or more general constitutive equations, and Darcy’s law governs flow through porous media.

Electrical and thermo-chemical aspects are also covered by material laws. Ohm’s law applies to electrical conduction in many solids; thermoelectric effects are described by related coefficients, and temperature-dependent reaction rates often follow Arrhenius-type behavior. Chemical potential and diffusion-reaction coupling are common considerations in materials processing and operation.

Materialgesetze are used to build constitutive models for simulations and design, typically calibrated from experiments and theory. They are valid within specific ranges of stress, temperature, loading rate, and microstructure, and may incorporate anisotropy, damage, phase transformations, or time-dependent effects.

Examples by class include metals (elastic-plastic with work hardening), polymers (viscoelastic), ceramics (brittle behavior), and composites (anisotropic or heterogeneous responses).