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LUSAS Concrete Material Model

The new LUSAS concrete material model enables the nonlinear stress/strain behaviour of concrete structures to be modelled to failure. Cyclic loading can also be taken into account. It is developed in collaboration with Cardiff University, and is seen by many in the field to be one of, if not the leading concrete material model available today.

  • It has been developed within a thermodynamically consistent framework and lets you model both plain, reinforced and post-tensioned concrete structures.
  • It simulates multiple non-orthogonal cracking with exponential softening that can be linked to either a fracture energy parameter or to a fixed limiting strain parameter. The fracture energy approach is appropriate for localised fractures (e.g. mass concrete) and the limiting strain approach is appropriate for distributed fracture (e.g. reinforced concrete).
  • It simulates crack closure in both shear (due to aggregate interlock) and compression. This enables the response of a structure subjected to load reversal to be modelled. The model can also simulate diffuse cracking degradation associated with crushing by reduction of the first fracture stress.
  • It simulates nonlinear behaviour in compression and incorporates a triaxial failure surface and nonlinear friction hardening and softening. The biaxial and triaxial failure surfaces both match experimentally determined envelopes accurately.
  • It requires a relatively small number of material parameters, where each can be directly related to a physical characteristic. In the absence of test data specific to a project, many parameters can be defined using the CEB FIB Model Code 1990.
  • Quadratic convergence ensures that the number of iterations are minimized, resulting in substantially reduced problem solving time when compared to previous and other concrete models.

Reinforced concrete beam stress results plot showing development of crack planes


Numerical modeling of concrete has a history that spans more than three decades, during which time considerable advances have been made in both the underlying theories of the constitutive models as well as in the practical capabilities of finite element codes for concrete analysis. The development of the new LUSAS concrete model has extended the analytical capabilities for modelling concrete cracking and crushing to a new level and can model a complete range of concrete characteristic behaviour in a consistent and robust manner. It is seen by many in the field to be one of, if not the leading concrete material model available today.

Planes of Damage

The LUSAS concrete model simulates directional cracking, crack closure and shear contact (or aggregate interlock) behaviour in an integrated manner, while accounting for the type of damage and triaxial frictional response that characterises the behaviour of concrete in compression. In order to achieve all of these these aims within a thermodynamically consistent framework the model calculates directional damage planes that at some point in a loading process become fixed in direction. However, a problem in deriving a model that predicts directional damage is how to simulate complete loss of strength in one direction whilst maintaining strength in other directions. This and other difficulties are well known to those involved with concrete material model development and some long-standing concrete material models provide solutions to some of the problems, however unlike the LUSAS concrete model they do not address the problem of how to correctly simulate the shear behaviour of formed macro cracks or fully three-dimensional behaviour.

In the LUSAS concrete material model embedded damage-contact planes have been integrated with a plasticity component by using a thermodynamically consistent plastic-damage framework. The essential elements of the model are:

  • A local stress – strain relationship, which here is a damage-contact model
  • A function from which local strains can be computed such that the local and global constitutive relationships are both satisfied. This is termed the total-local function.
  • A triaxial plasticity component for simulating frictional behaviour and strength increase with triaxial confinement
  • A thermodynamically consistent global stress-strain relationship
  • The model has been developed with an implicit stress recovery – consistent tangent matrix algorithm.


FIB (Fédération Internationale du Béton) Bulletin 45 "Practitioners guide to finite element modelling of reinforced concrete structures" states: "The state of the art in nonlinear finite element analysis of reinforced concrete has progressed to the point where such procedures are close to being practical everyday tools for design office engineers. No longer solely within the domain of researchers, they are finding use in various applications; many relating to our aging infrastructure. Nonlinear computer analysis procedures can be used to provide reliable assessments of the strength and integrity of damaged or deteriorated structures, or of structures built to previous codes, standards or practices deemed to be deficient today. They can serve as valuable tools in assessing the expected behaviour from retrofitted structures, or in investigating and rationally selecting amongst various repair alternatives"

Use of the LUSAS nonlinear concrete material model can help make a significant contribution to the assessment of ageing structures and to the design and long-term management of structural assets.

Validation testing

Over the course of the development of the LUSAS concrete material model and also after its inclusion into LUSAS a number of validation and quality assurance testcases were used to verify its usage against both experimental and theoretical results. Three representative examples of some of the tests undertaken are shown here:

  • Notch test by Barr and Brokenshire
  • Reinforced concrete beam by Bresler and Scordelis
  • Single edge notched beam, by Arrea and Ingraffea


Notch test by Barr and Brokenshire

This torsion fracture test twists a notched specimen causing a crack to gradually form. The Crack Mouth Opening Displacement (CMOD) is measured on the surface at the notch mouth, normal to the notch. Experimental and LUSAS calculated results from a research version (red) are shown on the graph with good correlation being seen for this unreinforced test piece.

Test specimen after failure and load versus CMOD normal  graph LUSAS notched test model and results plot for final load increment

Reinforced concrete beam by Bresler and Scordelis

In this 2D analysis the beam is simply supported and is loaded with a central point load. It has two layers of longitudinal reinforcement but no shear reinforcement. Only half the beam is modelled due to symmetry. The results from the new LUSAS concrete material model (model 94 shown in red) are a closer fit to the experimental data than the previously used concrete model (model 84).

Modelling of half-beam Load verses displacement graph

Single edge notched beam, by Arrea and Ingraffea

This single edge notched beam test by Arrea and Ingraffea has been used by a number of researchers to assess their concrete models (e.g. Rots and de Borst, Rots, Tano et al.) and has been used to show crack path sensitivity to the orientation of element local coordinate systems. This analysis was controlled via an arc-length method and the main load was applied in a patch on the upper edge, as illustrated. Good correlation is seen for this unreinforced test piece.

Modelling and results showing crack planes and crushed zones for an intermediate load step

Load verses crack mouth sliding displacement (CMSD) graph

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