Research Programs

At LaCàN, we develop novel computational methods and tools to solve problems of industrial interest, providing credible and real-time numerical solutions. Assimilating data into the model, we control accuracy and reliability of the outcomes. We are also interested in understanding fundamental mechanical functions of cells and cell aggregates such as motility, shape control and force generation to quantify and control biological processes at the tissue and organ level. We combine theoretical modelling, computer simulations and experiments to understand complex behaviours related to natural and engineered materials, such as the movement of tectonic plates, electroactive materials and fracture of materials.

We aim at developing theories and simulations, which will allow us to predict and rationally  manipulate living matter.

We aim at developing theories and simulations, which will allow us to predict and rationally  manipulate living matter.

We combine theory, computer simulations and experiments to understand and exploit the insight in the design of materials and geophysics

Computational methods and tools

Mathematical and computational modeling relies on methods and tools providing numerical solutions to complex simulation problems. These techniques range from the pre-processing (CAD interface, automatic meshing, data acquisition,…) to verification and validation via a posteriori error assessment and adaptivity, and include a diverse population of solvers. Our goal is to design and implement efficient methodologies to obtain high-fidelity solutions with certified accuracy, adapted to each particular problem under analysis. We develop these innovative methodologies both in academic codes  (with flexibility to intrusively test new ideas) and professional or commercial codes , certified by our industrial partners, with a large variety of models and methods, extensively tested and computationally optimized. In the latter case we aim at using non-intrusive implementations. In the framework of seeking real-time responses to multiparametric problems, we are particularly concerned with the efficiency of the numerical methodologies and the credibility of the solutions provided. Thus, from a methodological viewpoint, the current ongoing research includes:
•  High-fidelity simulations: high-order approximations (in particular HDG formulations) with exact geometrical descriptions (NEFEM),
•  Reduced order models (viz. PGD) for generalized parametric solutions,
•  Data assimilation and data-driven models,
•  Uncertainty quantification and model updating for reliable simulations with goal-oriented error
assessment and adaptivity,
•  Automatic generation of high-order meshes.

Credible high-fidelity data-driven models

Automatic and adaptative meshing with error assessment

CFD with industrial codes for engineering applications


Cell and tissue mechanobiology

Mechanics plays a prominent role in fundamental biological processes at the level of individual cells and of groups of cells forming tissues. Examples include cell division, the development of embryos, the ability of adult tissues to resist stress and self-repair, or cell migration during cancer invasion. In recent years, a wealth of quantitative experiments have demonstrated a tight interaction between mechanics and biological regulation. These observations also suggest that despite the daunting molecular and structural complexity of cells and tissues, there are simple underlying principles that govern their behaviour. Our goal is to use theoretical modelling and computer simulations to identify such principles. Besides recapitulating specific observations in developing embryos or in-vitro controlled systems, we aim at developing theories and simulations, which will allow us to predict and rationally manipulate living matter. We cover the following research Lines:
• Understanding the dynamics of bilayer membranes and their interaction with membrane proteins.
• Modeling epithelial mechanics.
• Developing mathematical models and finite element methods for coupled systems of interfacial/bulkpartial differential equations.
• Developing numerical tools for inferring the forces that drive morphogenesis.
• Modeling cell migration and wound healing processes.
• Describing the smaller scales of biological tissues.
• Bridging the scale gap between the organ or organoid level and the subcellular level.

Mechanics of soft and living interfaces

Cell and tissue mechanics in embryogenesis

Multi-scale and multi-physics modelling in mechanobiology


Natural and engineered material and structures

Many materials and structures of scientific and technological relevance exhibit complex behaviour. Complexity may be caused by a number of factors: poorly understood basic principles, multiphysics coupling of different effects (mechanical, electrical, thermal, chemical, flow, …), non-linearity (including material failure and fracture). This applies equally to both natural and engineered materials and structures, at very different length scales. Our goal is to combine theoretical modeling, computer simulations and possibly laboratory experiments to gain understanding on this complex behaviour, and to exploit this insight in the design and manufacture of new materials, metamaterials and structures. Among others, we work on the following  research Lines:

  • Modeling flexolectricity (i.e. the coupling between electric polarization and strain gradients).
  • Mathematical models and efficient finite element methods for coupled systems of high-order partial differential equations.
  • Accurate models for electromechanical characterization of nanomaterials.
  • Modeling large-scale plate tectonics.
  • Coupling plate tectonics to heat and fluid transport, petrology and geochemistry.
  •  Efficient models for the medium- and high-frequency range in building vibroacoustics.
  • Continuous-discontinuous models of material degradation and fracture.

Mechanics of electroactive materials

Computational Geosciences

Computational Geosciences

Sergio Zlotnik

Computational acoustics and damage mechanics