arXiv subjects

C. Hesch

Publications and source records attributed to C. Hesch.

2 recordsLinked to original sources

arXiv2026

Space--time formulation of geometrically exact beams

We formulate the dynamics of a straight-reference geometrically exact Cosserat beam as a directed world sheet in non-relativistic space--time. The centerline history is embedded in \(\mathbb R^4\), while absolute time remains prescribed and is not an additional mechanical degree of freedom. Spatial force and moment resultants and temporal linear and intrinsic angular momenta are combined into common space--time fluxes, so that spatial Neumann data and temporal inflow and outflow are represented by one co-normal boundary operator. A mixed configuration--momentum system is discretized by continuous tensor-product finite elements and stabilized by a future-directed Petrov--Galerkin perturbation. The resulting time-aligned \(Q_2/Q_2\) method requires one scalar stabilization parameter and retains the interior momentum trace as the free terminal outflow. The numerical study verifies the terminal flux treatment by an exact rigid-motion state, establishes monotone convergence for a smooth manufactured shear--bending solution, quantifies the pre-response--accuracy trade-off under delayed loading, and verifies covariance under constant superposed spatial rotations. The stabilization is not a proof of strict domain-of-dependence causality; it biases the global space-time approximation in the future direction and reduces the measured pre-activation response. A conservative extension to non-aligned simplex facets is also analyzed. Although this extension is consistent and locally conservative, continuous equal-order \(P_2/P_2\) simplex spaces exhibit strongly mesh- and orientation-dependent inverse amplification and do not show mesh-uniform stability. The aligned \(Q_2/Q_2\) discretization is therefore recommended as the practical realization of the formulation.

cs.CE↗

arXiv2026

Monolithic solution and null-space condensation of internal variables in finite viscoelasticity

Finite-strain viscoelasticity is commonly discussed from a constitutive perspective, whereas the nonlinear solution architecture induced by time and space discretization is studied less systematically. In this work, we consider a representative viscoelastic model with a strain-like internal variable and focus on the fully discrete coupled problem in the deformation and the internal state. Starting from the underlying energy-dissipation structure, we derive the discrete weak forms and obtain a monolithic Newton system with a naturally non-symmetric block tangent. The increment of the internal variable is eliminated consistently at the level of the linearized system by a Schur complement, and the same reduction is shown to admit a geometric interpretation in terms of a null-space basis of the tangent space of the internal constraint manifold. This yields a genuinely monolithic counterpart to classical nested Gauss-point condensation, in which local constitutive equations are solved separately before the global equilibrium step. Numerical results for two- and three-dimensional Cook's membrane benchmarks show that the proposed strategy retains essentially the same outer Newton behavior as the classical approach while substantially reducing computational cost by avoiding repeated local Newton solves, it also remains convergent for load increments for which the nested scheme fails. Moreover, the numerical study suggests that suitably chosen approximation spaces for the internal variable can yield additional savings in computational effort without significant loss of accuracy. Although presented for finite viscoelasticity, the construction extends naturally to broader classes of thermodynamically consistent internal-variable models.

cs.CE↗