Nonlinear analysis of spatial trusses with different strain measures and compressible solid

Abstract

This paper investigates the nonlinear behavior of spatial truss elements under finite deformations, focusing on the impact of various strain measures in compressible materials. We examine both Total Lagrangian (using engineering and Green–Lagrange strains) and Eulerian formulations (using natural, Biot, and Almansi strains). The analysis assumes a linear spatial hyperelastic material where Cauchy stress is proportional to axial natural strain via Young’s modulus. For infinitesimal strains, Young’s modulus remains consistent across different stress/strain pairs. In the finite strain regime, we derive a nonlinear secant modulus based on Young’s modulus. Internal force vectors and tangent stiffness matrices are computed using the direction cosines of the truss element in its deformed state. The paper demonstrates that for infinitesimal deformations, adjusting the modulus of elasticity when using different stress/strain pairs is unnecessary. However, for finite deformations, it is essential to adjust the modulus of elasticity. Numerical simulations validate the performance of the proposed 3D truss element against established formulations. This research offers critical insights into the nonlinear response of spatial trusses, guiding the selection of appropriate strain measures for enhanced accuracy in engineering applications. These findings contribute to more reliable and efficient structural designs, especially in scenarios involving finite deformations and compressible materials.