Blog on Grassl Group

CFRP-confined concrete cylinder — hardening past the unconfined peak

Tue, 26 May 2026 09:00:00 +0100

Plain concrete under uniaxial compression softens — microcracks open, stiffness drops, and the load–displacement curve descends. Wrap the same cylinder in a CFRP sheet and the macroscopic curve no longer softens: load capacity keeps growing well past the unconfined peak, often two- or three-fold. Yet if you cut a tested FRP-wrapped specimen open, the concrete inside is damaged.

The two stories are not contradictory. They come from the competition between two mechanisms. Both can be reproduced in OOFEM with CDPM2 (con2dpm) by changing only the boundary: add an array of circumferential truss hoops around the cylinder and the softening curve becomes a hardening one.

Discrete aggregates in a 2D lattice transport mesh

Tue, 19 May 2026 09:00:00 +0100

The first two posts in this series (verification against the 1D analytical and lumped vs consistent capacity under van Genuchten) held the medium homogeneous and varied just one numerical knob at a time. Concrete is not homogeneous — at the meso-scale it is a cement paste matrix with stiff, almost impermeable aggregates packed inside. This third post puts those aggregates in explicitly and watches the wetting front go around them.

The mesh

A random aggregate packing is generated by the aggregate tool from a prescribed grading curve and target volume fraction, then handed to the generator mesh tool through the converter’s #@inclusionfile directive. The mesher places lattice nodes outside the aggregate boundaries and adds anchor pairs at the disk-boundary intersections so the Voronoi tessellation respects the inclusion outlines. Any lattice element that crosses into a disk is tagged as aggregate material; everything else stays matrix.

Why lumped capacity matters in unsaturated lattice transport

Mon, 18 May 2026 09:00:00 +0100

The previous post showed the transport lattice reproducing the 1D diffusion analytical for a linear constant-capacity problem. Real porous media are rarely that easy to model: in concrete, soil, and almost any partially-saturated material the capacity c(p) = dθ/dp is a sharp peak near the air-entry value, and the relative permeability k_r(p) varies by orders of magnitude with saturation. This is the Richards-equation regime, and it’s where the choice between a consistent and a lumped capacity matrix is important.

Transport on a Voronoi lattice — verification against the 1D diffusion analytical

Sun, 17 May 2026 09:00:00 +0100

Most lattice posts on this site have been about fracture — structural frame elements that lie along the edges of the Delaunay triangulation of a random point set, carrying axial, shear, and bending action and breaking under load. Their cross-sections are the Voronoi cell faces perpendicular to each element (polygon edges in 2D, polyhedron faces in 3D).

The transport lattice is the geometric dual of that. Its conduit elements lie along the Voronoi cell edges (between Voronoi vertices), not the Delaunay edges, and their cross-sections are the Delaunay edges (triangle edges in 2D, tetrahedron faces in 3D) that each Voronoi edge perpendicularly bisects. Mechanical and transport problems share the same underlying Voronoi–Delaunay mesh, but each lives on a different part of the duality: structural on the Delaunay edges, transport on the Voronoi edges.

Crack-band vs nonlocal damage in dynamic crack branching

Sat, 09 May 2026 09:00:00 +0100

Strain-softening damage models need a regularisation, otherwise the dissipated energy and localisation width depend on the mesh. The crack-band approach and the nonlocal averaging of equivalent strain are two common fixes — but they don’t fix the same things. This post is about what each one actually does, and where the difference shows up under dynamic loading.

Two models, one specimen

I ran two analyses of a 254×254 mm Homalite-100 cruciform plate with a 50 mm central crack under biaxial impulsive loading. The geometry and loading are inspired by one of the dynamic-photoelastic experiments of Hawong et al., doi.org/10.1007/BF02319466.

How a random e0 field affects the crack in a 2D tensile lattice

Fri, 08 May 2026 09:00:00 +0100

Previously I showed that a periodic mesh removes the boundary artefact in 2D direct-tension lattice models — the crack stops locking onto the loaded face and instead reflects the heterogeneity of the random node distribution. In this post, the natural follow-up: what happens when we make the material heterogeneous too, by sampling the elastic strain threshold e0 from a spatial random field?

The random field

The parameter e0 is what controls when an individual lattice element starts to damage. In the previous case, it has been a single constant. Here the per-element value is sampled from a 2D random field generated by my own genran code, which uses the spectral representation of Shinozuka & Deodatis to produce fields with a prescribed autocorrelation and a prescribed distribution. genran supports Gaussian, Weibull, and grafted Weibull–Gaussian marginals; the iterative refinement of Shields, Deodatis & Bocchini (2011) recovers the prescribed autocorrelation when the distribution is non-Gaussian.

Boundary-independent fracture in 2D direct tensile lattice models

Thu, 07 May 2026 09:00:00 +0100

Lattice models are popular for modelling fracture. Direct uniaxial tension is one of the simplest test most people start. But it is also a difficult one to get right, because boundaries attract cracks. This post shows what the problem is with a standard lattice, and how the issue can be removed.

The artefact

A 100×100 mm specimen, lattice of Voronoi cells generated from a random point distribution, pulled in tension between two rigid platens (idealised by linking DOFs at the end to a control point). The load–displacement response and the lattice-strain magnitude are shown side by side, frame-by-frame.

Four single element tests of CDPM2

Mon, 04 May 2026 09:00:00 +0100

Sometimes people contact me who are implementing our concrete constitutive model CDPM2 in OOFEM in their own finite element codes. Usually they ask for help with implementation and calibration. To help them to get started to check their implementation I built a small verification set in OOFEM, published it as a Docker image. If their implementation reproduces all four curves (tension, compression, simple shear and pure shear), then this is a good start.

Rate dependence of corrosion-induced surface cracking in concrete: Lattice modelling and experiments

Wed, 15 Apr 2026 09:00:00 +0100

Accepted in Frontiers in Materials, April 2026. Preprint on SSRN. Lattice modelling and matched experiments examining the rate dependence of surface cracking driven by reinforcement corrosion.

3D frame element for large rotations based on the rigid-body-spring concept for analysing the failure of structures

Sun, 01 Mar 2026 09:00:00 +0100

A 3D frame finite element built on rigid-body-spring kinematics, evaluated on benchmark problems involving large rotations and progressive structural failure.

RAAC panels can suddenly collapse before any warning of corrosion-induced surface cracking

Mon, 15 Sep 2025 09:00:00 +0100

Thick-walled cylinder modelling in RAAC: The steel cross-section can be severly reduced by corrosion before any surface crack appears.