Figure 1.

Deformation of micromorphic beams: Schematics of a beam with a deformed microstructure. The beam is a composition of elongated-particles that represent the beam granular microstructure. Two independent elastic domains are defined such that Ω(x, y, z) is the macroscopic domain, and Ω_m(x′, y′, z′) is the microscopic domain of an elongated particle. Elongated particles are modeled as micro-beams exhibiting macroscopic displacements, $u_x\left(x,z\right)$ and $u_z\left(x\right)$, and micro-displacements, $u_x^{\mathrm{\prime }}(x\mathrm{\prime },x,z\mathrm{\prime },z)$ and $u_z^{\mathrm{\prime }}(x\mathrm{\prime },x,z\mathrm{\prime },z)$. The micro-beam (i.e., elongated-particle) deforms such that its cross section rotates with an angle, $\kappa (x\mathrm{\prime },x)$.