First-order computational homogenization of arterial media with solid-embedded fibers: Homogenized and micromechanical responses

Arterial response emerges from interactions among collagen, elastin, smooth muscle cells, and ground matrix, but macroscopic models resolve these mechanisms only indirectly. We propose a first-order computational homogenization framework based on a solid-embedded-fiber representative volume element (RVE) coupled to a macroscopic finite element problem. Four configurations combine two fiber-tracing strategies with linear boundary displacement or periodic microscale constraints. All four produce comparable homogenized responses and reveal phase-specific behavior unavailable from effective curves alone. Collagen dominates homogenized stress, while local fields show heterogeneous and asymmetric load transfer between fibers and matrix. Periodic constraints slightly reduce peak stresses, broaden local stress and strain distributions, and increase solution times. Recruitment-window parameters most strongly influence nonlinear stiffening, followed by collagen stiffness and volume fraction. Similar homogenized responses can hide local-field differences caused by fiber topology and boundary conditions. The nested FE² framework links each macroscopic point to an embedded-fiber RVE during equilibrium. This coupling supports complex problems and constituent viscoelasticity, damage, fiber failure, or rupture because the local deformation path need not be known beforehand. Microscale boundary conditions must be selected in advance to produce a representative RVE response. Constituent-specific data remain necessary for validation.